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2004-12-18 | Fluctuations of the Magnetization in Thin Films due to Conduction Electrons | A detailed analysis of damping and noise due to a {\it sd}-interaction in a
thin ferromagnetic film sandwiched between two large normal metal layers is
carried out. The magnetization is shown to obey in general a non-local equation
of motion which differs from the the Gilbert equation and is extended to the
non-adiabatic regime. To lowest order in the exchange interaction and in the
limit where the Gilbert equation applies, we show that the damping term is
enhanced due to interfacial effects but it also shows oscillations as a
function of the film thickness. The noise calculation is however carried out to
all orders in the exchange coupling constant. The ellipticity of the precession
of the magnetization is taken into account. The damping is shown to have a
Gilbert form only in the adiabatic limit while the relaxation time becomes
strongly dependent on the geometry of the thin film. It is also shown that the
induced noise characteristic of sd-exchange is inherently colored in character
and depends on the symmetry of the Hamiltonian of the magnetization in the
film. We show that the sd-noise can be represented in terms of an external
stochastic field which is white only in the adiabatic regime. The temperature
is also renormalized by the spin accumulation in the system. For large
intra-atomic exchange interactions, the Gilbert-Brown equation is no longer
valid. | 0412510v1 |
2018-04-02 | Anisotropic Gilbert damping in perovskite La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ thin film | The viscous Gilbert damping parameter governing magnetization dynamics is of
primary importance for various spintronics applications. Although, the damping
constant is believed to be anisotropic by theories. It is commonly treated as a
scalar due to lack of experimental evidence. Here, we present an elaborate
angle dependent broadband ferromagnetic resonance study of high quality
epitaxial La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ films. Extrinsic effects are suppressed
and we show convincing evidence of anisotropic damping with twofold symmetry at
room temperature. The observed anisotropic relaxation is attributed to the
magnetization orientation dependence of the band structure. In addition, we
demonstrated that such anisotropy can be tailored by manipulating the stain.
This work provides new insights to understand the mechanism of magnetization
relaxation. | 1804.00554v1 |
2009-04-21 | Tensor damping in metallic magnetic multilayers | The mechanism of spin-pumping, described by Tserkovnyak et al., is formally
analyzed in the general case of a magnetic multilayer consisting of two or more
metallic ferromagnetic (FM) films separated by normal metal (NM) layers. It is
shown that the spin-pumping-induced dynamic coupling between FM layers modifies
the linearized Gilbert equations in a way that replaces the scalar Gilbert
damping constant with a nonlocal matrix of Cartesian damping tensors. The
latter are shown to be methodically calculable from a matrix algebra solution
of the Valet-Fert transport equations. As an example, explicit analytical
results are obtained for a 5-layer (spin-valve) of form NM/FM/NM'/FM/NM.
Comparisons with earlier well known results of Tserkovnyak et al. for the
related 3-layer FM/NM/FM indicate that the latter inadvertently hid the tensor
character of the damping, and instead singled out the diagonal element of the
local damping tensor along the axis normal to the plane of the two
magnetization vectors. For spin-valve devices of technological interest, the
influence of the tensor components of the damping on thermal noise or
spin-torque critical currents are strongly weighted by the relative magnitude
of the elements of the nonlocal, anisotropic stiffness-field tensor-matrix, and
for in-plane magnetized spin-valves are generally more sensitive to the
in-plane element of the damping tensor. | 0904.3150v2 |
2023-12-20 | An effective field theory of damped ferromagnetic systems | Using the in-in formalism, we generalize the recently constructed
magnetoelastic EFT arXiv:2112.13873 [hep-th] to describe the damping dynamics
of ferromagnetic systems at long wavelengths. We find that the standard Gilbert
damping term naturally arises as the simplest leading-order symmetry-consistent
non-conservative contribution within the in-in framework. The EFT is easily
generalized to scenarios with anisotropy and inhomogeneity. In particular, we
find the classic Landau-Lifshitz damping term emerges when isotropy is broken
by a constant external background field. This provides a first principle
explanation for distinguishing the two types of damping dynamics that were
originally constructed phenomenologically. Furthermore, the EFT framework could
also incorporate intrinsic anisotropy of the material in a straightforward way
using the spurion method. For systems with inhomogeneity such as nontrivial
spin textures, we find that the leading order derivative correction yields the
generalized Gilbert damping equations that were found in condensed matter
literature. This shows that the EFT approach enables us to derive the form of
higher-derivative-order corrections in a systematic way. Lastly, using the
phonon-magnon coupling deduced in the magnetoelastic EFT, we are able to make a
prediction for the generic form of the phononic contribution to the damping
equation. | 2312.13093v1 |
2019-09-06 | The interplay of large two-magnon ferromagnetic resonance linewidths and low Gilbert damping in Heusler thin films | We report on broadband ferromagnetic resonance linewidth measurements
performed on epitaxial Heusler thin films. A large and anisotropic two-magnon
scattering linewidth broadening is observed for measurements with the
magnetization lying in the film plane, while linewidth measurements with the
magnetization saturated perpendicular to the sample plane reveal low Gilbert
damping constants of $(1.5\pm0.1)\times 10^{-3}$, $(1.8\pm0.2)\times 10^{-3}$,
and $<8\times 10^{-4}$ for Co$_2$MnSi/MgO, Co$_2$MnAl/MgO, and Co$_2$FeAl/MgO,
respectively. The in-plane measurements are fit to a model combining Gilbert
and two-magnon scattering contributions to the linewidth, revealing a
characteristic disorder lengthscale of 10-100 nm. | 1909.02738v2 |
2018-02-15 | Damping's effect on the magnetodynamics of spin Hall nano-oscillators | We study the impact of spin wave damping ($\alpha$) on the auto-oscillation
properties of nano-constriction based spin Hall nano-oscillators (SHNOs). The
SHNOs are based on a 5 nm Pt layer interfaced to a 5 nm
Py$_{100-x-y}$Pt$_{x}$Ag$_{y}$ magnetic layer, where the Pt and Ag contents are
co-varied to keep the saturation magnetization constant (within 10 %), while
$\alpha$ varies close to a factor of three. We systematically investigate the
influence of the Gilbert damping on the magnetodynamics of these SHNOs by means
of electrical microwave measurements. Under the condition of a constant field,
the threshold current scales with the damping in the magnetic layer. The
threshold current as a function of field shows a parabolic-like behavior, which
we attribute to the evolution of the spatial profile of the auto-oscillation
mode. The signal linewidth is smaller for the high-damping materials in low
magnetic fields, although the lowest observed linewidth was measured for the
alloy with least damping. | 1802.05548v1 |
2015-09-06 | Study of spin dynamics and damping on the magnetic nanowire arrays with various nanowire widths | We investigate the spin dynamics including Gilbert damping in the
ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of
ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic
resonance (VNA-FMR) and analyzed the results with the micromagnetic
simulations. We find excellent agreement between the experimental VNA-FMR
spectra and micromagnetic simulations result for various applied magnetic
fields. We find that the demagnetization factor for longitudinal conditions, Nz
(Ny) increases (decreases) as decreasing the nanowire width in the
micromagnetic simulations. For the transverse magnetic field, Nz (Ny) increases
(decreases) as increasing the nanowire width. We also find that the Gilbert
damping constant increases from 0.018 to 0.051 as the increasing nanowire width
for the transverse case, while it is almost constant as 0.021 for the
longitudinal case. | 1509.01807v1 |
2005-03-24 | Fast magnetization switching of Stoner particles: A nonlinear dynamics picture | The magnetization reversal of Stoner particles is investigated from the point
of view of nonlinear dynamics within the Landau-Lifshitz-Gilbert formulation.
The following results are obtained. 1) We clarify that the so-called
Stoner-Wohlfarth (SW) limit becomes exact when damping constant is infinitely
large. Under the limit, the magnetization moves along the steepest energy
descent path. The minimal switching field is the one at which there is only one
stable fixed point in the system. 2) For a given magnetic anisotropy, there is
a critical value for the damping constant, above which the minimal switching
field is the same as that of the SW-limit. 3) We illustrate how fixed points
and their basins change under a field along different directions. This change
explains well why a non-parallel field gives a smaller minimal switching field
and a short switching time. 4) The field of a ballistic magnetization reversal
should be along certain direction window in the presence of energy dissipation.
The width of the window depends on both of the damping constant and the
magnetic anisotropy. The upper and lower bounds of the direction window
increase with the damping constant. The window width oscillates with the
damping constant for a given magnetic anisotropy. It is zero for both zero and
infinite damping. Thus, the perpendicular field configuration widely employed
in the current experiments is not the best one since the damping constant in a
real system is far from zero. | 0503594v1 |
2018-08-20 | Gilbert damping of [Co/Pd]n/Py multilayer thin films | Understanding the Gilbert damping in exchange-coupled multilayer materials is
particularly important to develop future fast switching spintronics devices.
Here, we report an experimental investigation of temperature-dependent Gilbert
damping in [Co/Pd]n/Py multilayer films of varying the number of Co/Pd
repetitions by ferromagnetic resonance. The results demonstrate that three
independent contributions to the Gilbert damping are identified, namely the
intrinsic Gilbert damping, the inhomogeneous linewidth broadening and the
two-magnon scattering contribution. Of particular interest, the two-magnon
scattering intensity increases as the enlargement of number repetitions of
Co/Pd due to the larger pinning effect at the interface between Py and the
Co/Pd layers. The Gilbert damping increases monotonically as the temperature
decreases from 300K to 50K. Our findings open the door to comprehend the
physical origin of the Gilbert damping in ultrathin exchange-coupled multilayer
films. | 1808.06515v2 |
2023-05-17 | Material Parameters for Faster Ballistic Switching of an In-plane Magnetized Nanomagnet | High-speed magnetization switching of a nanomagnet is necessary for faster
information processing. The ballistic switching by a pulsed magnetic filed is a
promising candidate for the high-speed switching. It is known that the
switching speed of the ballistic switching can be increased by increasing the
magnitude of the pulsed magnetic field. However it is difficult to generate a
strong and short magnetic field pulse in a small device. Here we explore
another direction to achieve the high-speed ballistic switching by designing
material parameters such as anisotropy constant, saturation magnetization, and
the Gilbert damping constant. We perform the macrospin simulations for the
ballistic switching of in-plane magnetized nano magnets with varying material
parameters. The results are analyzed based on the switching dynamics on the
energy density contour. We show that the pulse width required for the ballistic
switching can be reduced by increasing the magnetic anisotropy constant or by
decreasing the saturation magnetization. We also show that there exists an
optimal value of the Gilbert damping constant that minimizes the pulse width
required for the ballistic switching. | 2305.10111v1 |
2015-11-16 | Determination of intrinsic damping of perpendicularly magnetized ultrathin films from time resolved precessional magnetization measurements | Magnetization dynamics are strongly influenced by damping. An effective
damping constant {\alpha}eff is often determined experimentally from the
spectral linewidth of the free induction decay of the magnetization after the
system is excited to its non-equilibrium state. Such an {\alpha}eff, however,
reflects both intrinsic damping as well as inhomogeneous broadening. In this
paper we compare measurements of the magnetization dynamics in ultrathin
non-epitaxial films having perpendicular magnetic anisotropy using two
different techniques, time-resolved magneto optical Kerr effect (TRMOKE) and
hybrid optical-electrical ferromagnetic resonance (OFMR). By using an external
magnetic field that is applied at very small angles to the film plane in the
TRMOKE studies, we develop an explicit closed-form analytical expression for
the TRMOKE spectral linewidth and show how this can be used to reliably extract
the intrinsic Gilbert damping constant. The damping constant determined in this
way is in excellent agreement with that determined from the OFMR method on the
same samples. Our studies indicate that the asymptotic high-field approach that
is often used in the TRMOKE method to distinguish the intrinsic damping from
the effective damping may result in significant error, because such high
external magnetic fields are required to make this approach valid that they are
out of reach. The error becomes larger the lower is the intrinsic damping
constant, and thus may account for the anomalously high damping constants that
are often reported in TRMOKE studies. In conventional ferromagnetic resonance
(FMR) studies, inhomogeneous contributions can be readily distinguished from
intrinsic damping contributions from the magnetic field dependence of the FMR
linewidth. Using the analogous approach, we show how reliable values of the
intrinsic damping can be extracted from TRMOKE. | 1511.04802v1 |
2016-03-25 | Large spin pumping effect in antisymmetric precession of Ni$_{79}$Fe$_{21}$/Ru/Ni$_{79}$Fe$_{21}$ | In magnetic trilayer structures, a contribution to the Gilbert damping of
ferromagnetic resonance arises from spin currents pumped from one layer to
another. This contribution has been demonstrated for layers with weakly
coupled, separated resonances, where magnetization dynamics are excited
predominantly in one layer and the other layer acts as a spin sink. Here we
show that trilayer structures in which magnetizations are excited
simultaneously, antisymmetrically, show a spin-pumping effect roughly twice as
large. The antisymmetric (optical) mode of antiferromagnetically coupled
Ni$_{79}$Fe$_{21}$(8nm)/Ru/Ni$_{79}$Fe$_{21}$(8nm) trilayers shows a Gilbert
damping constant greater than that of the symmetric (acoustic) mode by an
amount as large as the intrinsic damping of Py ($\Delta
\alpha\simeq\textrm{0.006}$). The effect is shown equally in field-normal and
field-parallel to film plane geometries over 3-25 GHz. The results confirm a
prediction of the spin pumping model and have implications for the use of
synthetic antiferromagnets (SAF)-structures in GHz devices. | 1603.07977v1 |
2015-11-13 | Magnified Damping under Rashba Spin Orbit Coupling | The spin orbit coupling spin torque consists of the field-like [REF: S.G. Tan
et al., arXiv:0705.3502, (2007).] and the damping-like terms [REF: H.
Kurebayashi et al., Nature Nanotechnology 9, 211 (2014).] that have been widely
studied for applications in magnetic memory. We focus, in this article, not on
the spin orbit effect producing the above spin torques, but on its magnifying
the damping constant of all field like spin torques. As first order precession
leads to second order damping, the Rashba constant is naturally co-opted,
producing a magnified field-like damping effect. The Landau-Liftshitz-Gilbert
equations are written separately for the local magnetization and the itinerant
spin, allowing the progression of magnetization to be self-consistently locked
to the spin. | 1511.04227v1 |
2022-05-13 | Precession dynamics of a small magnet with non-Markovian damping: Theoretical proposal for an experiment to determine the correlation time | Recent advances in experimental techniques have made it possible to
manipulate and measure the magnetization dynamics on the femtosecond time scale
which is the same order as the correlation time of the bath degrees of freedom.
In the equations of motion of magnetization, the correlation of the bath is
represented by the non-Markovian damping. For development of the science and
technologies based on the ultrafast magnetization dynamics it is important to
understand how the magnetization dynamics depend on the correlation time. It is
also important to determine the correlation time experimentally. Here we study
the precession dynamics of a small magnet with the non-Markovian damping.
Extending the theoretical analysis of Miyazaki and Seki [J. Chem. Phys. 108,
7052 (1998)] we obtain analytical expressions of the precession angular
velocity and the effective damping constant for any values of the correlation
time under assumption of small Gilbert damping constant. We also propose a
possible experiment for determination of the correlation time. | 2205.06399v1 |
2002-07-19 | Gilbert Damping in Magnetic Multilayers | We study the enhancement of the ferromagnetic relaxation rate in thin films
due to the adjacent normal metal layers. Using linear response theory, we
derive the dissipative torque produced by the s-d exchange interaction at the
ferromagnet-normal metal interface. For a slow precession, the enhancement of
Gilbert damping constant is proportional to the square of the s-d exchange
constant times the zero-frequency limit of the frequency derivative of the
local dynamic spin susceptibility of the normal metal at the interface.
Electron-electron interactions increase the relaxation rate by the Stoner
factor squared. We attribute the large anisotropic enhancements of the
relaxation rate observed recently in multilayers containing palladium to this
mechanism. For free electrons, the present theory compares favorably with
recent spin-pumping result of Tserkovnyak et al. [Phys. Rev. Lett.
\textbf{88},117601 (2002)]. | 0207471v1 |
2018-10-17 | Perpendicularly magnetized YIG films with small Gilbert damping constant and anomalous spin transport properties | The Y3Fe5O12 (YIG) films with perpendicular magnetic anisotropy (PMA) have
recently attracted a great deal of attention for spintronics applications.
Here, we report the induced PMA in the ultrathin YIG films grown on
(Gd2.6Ca0.4)(Ga4.1Mg0.25Zr0.65)O12 (SGGG) substrates by epitaxial strain
without preprocessing. Reciprocal space mapping shows that the films are
lattice-matched to the substrates without strain relaxation. Through
ferromagnetic resonance and polarized neutron reflectometry measurements, we
find that these YIG films have ultra-low Gilbert damping constant with a
magnetic dead layer as thin as about 0.3 nm at the YIG/SGGG interfaces.
Moreover, the transport behavior of the Pt/YIG/SGGG films reveals an
enhancement of spin mixing conductance and a large non-monotonic magnetic field
dependence of anomalous Hall effect as compared with the Pt/YIG/Gd3Ga5O12 (GGG)
films. The non-monotonic anomalous Hall signal is extracted in the temperature
range from 150 to 350 K, which has been ascribed to the possible non-collinear
magnetic order at the Pt/YIG interface induced by uniaxial strain. | 1810.07384v2 |
2017-06-14 | Temperature-dependent Gilbert damping of Co2FeAl thin films with different degree of atomic order | Half-metallicity and low magnetic damping are perpetually sought for in
spintronics materials and full Heusler alloys in this respect provide
outstanding properties. However, it is challenging to obtain the well-ordered
half-metallic phase in as-deposited full Heusler alloys thin films and theory
has struggled to establish a fundamentals understanding of the temperature
dependent Gilbert damping in these systems. Here we present a study of the
temperature dependent Gilbert damping of differently ordered as-deposited
Co2FeAl full Heusler alloy thin films. The sum of inter- and intraband electron
scattering in conjunction with the finite electron lifetime in Bloch states
govern the Gilbert damping for the well-ordered phase in contrast to the
damping of partially-ordered and disordered phases which is governed by
interband electronic scattering alone. These results, especially the ultralow
room temperature intrinsic damping observed for the well-ordered phase provide
new fundamental insights to the physical origin of the Gilbert damping in full
Heusler alloy thin films. | 1706.04670v2 |
2023-11-27 | Gilbert damping in two-dimensional metallic anti-ferromagnets | A finite spin life-time of conduction electrons may dominate Gilbert damping
of two-dimensional metallic anti-ferromagnets or anti-ferromagnet/metal
heterostructures. We investigate the Gilbert damping tensor for a typical
low-energy model of a metallic anti-ferromagnet system with honeycomb magnetic
lattice and Rashba spin-orbit coupling for conduction electrons. We distinguish
three regimes of spin relaxation: exchange-dominated relaxation for weak
spin-orbit coupling strength, Elliot-Yafet relaxation for moderate spin-orbit
coupling, and Dyakonov-Perel relaxation for strong spin-orbit coupling. We
show, however, that the latter regime takes place only for the in-plane Gilbert
damping component. We also show that anisotropy of Gilbert damping persists for
any finite spin-orbit interaction strength provided we consider no spatial
variation of the N\'eel vector. Isotropic Gilbert damping is restored only if
the electron spin-orbit length is larger than the magnon wavelength. Our theory
applies to MnPS3 monolayer on Pt or to similar systems. | 2311.16268v2 |
2018-07-31 | Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences | Relaxation effects are of primary importance in the description of magnetic
excitations, leading to a myriad of methods addressing the phenomenological
damping parameters. In this work, we consider several well-established forms of
calculating the intrinsic Gilbert damping within a unified theoretical
framework, mapping out their connections and the approximations required to
derive each formula. This scheme enables a direct comparison of the different
methods on the same footing and a consistent evaluation of their range of
validity. Most methods lead to very similar results for the bulk ferromagnets
Fe, Co and Ni, due to the low spin-orbit interaction strength and the absence
of the spin pumping mechanism. The effects of inhomogeneities, temperature and
other sources of finite electronic lifetime are often accounted for by an
empirical broadening of the electronic energy levels. We show that the
contribution to the damping introduced by this broadening is additive, and so
can be extracted by comparing the results of the calculations performed with
and without spin-orbit interaction. Starting from simulated ferromagnetic
resonance spectra based on the underlying electronic structure, we
unambiguously demonstrate that the damping parameter obtained within the
constant broadening approximation diverges for three-dimensional bulk magnets
in the clean limit, while it remains finite for monolayers. Our work puts into
perspective the several methods available to describe and compute the Gilbert
damping, building a solid foundation for future investigations of magnetic
relaxation effects in any kind of material. | 1807.11808v3 |
2003-10-13 | Domain wall mobility in nanowires: transverse versus vortex walls | The motion of domain walls in ferromagnetic, cylindrical nanowires is
investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a
classical spin model in which energy contributions from exchange, crystalline
anisotropy, dipole-dipole interaction, and a driving magnetic field are
considered. Depending on the diameter, either transverse domain walls or vortex
walls are found. The transverse domain wall is observed for diameters smaller
than the exchange length of the given material. Here, the system behaves
effectively one-dimensional and the domain wall mobility agrees with a result
derived for a one-dimensional wall by Slonczewski. For low damping the domain
wall mobility decreases with decreasing damping constant. With increasing
diameter, a crossover to a vortex wall sets in which enhances the domain wall
mobility drastically. For a vortex wall the domain wall mobility is described
by the Walker-formula, with a domain wall width depending on the diameter of
the wire. The main difference is the dependence on damping: for a vortex wall
the domain wall mobility can be drastically increased for small values of the
damping constant up to a factor of $1/\alpha^2$. | 0310277v1 |
2017-09-21 | Low Gilbert Damping Constant in Perpendicularly Magnetized W/CoFeB/MgO Films with High Thermal Stability | Perpendicular magnetic materials with low damping constant and high thermal
stability have great potential for realizing high-density, non-volatile, and
low-power consumption spintronic devices, which can sustain operation
reliability for high processing temperatures. In this work, we study the
Gilbert damping constant ({\alpha}) of perpendicularly magnetized W/CoFeB/MgO
films with a high perpendicular magnetic anisotropy (PMA) and superb thermal
stability. The {\alpha} of these PMA films annealed at different temperatures
is determined via an all-optical Time-Resolved Magneto-Optical Kerr Effect
method. We find that {\alpha} of these W/CoFeB/MgO PMA films decreases with
increasing annealing temperature, reaches a minimum of {\alpha} = 0.016 at an
annealing temperature of 350 {\deg}C, and then increases to 0.024 after
post-annealing at 400 {\deg}C. The minimum {\alpha} observed at 350 {\deg}C is
rationalized by two competing effects as the annealing temperature becomes
higher: the enhanced crystallization of CoFeB and dead-layer growth occurring
at the two interfaces of the CoFeB layer. We further demonstrate that {\alpha}
of the 400 {\deg}C-annealed W/CoFeB/MgO film is comparable to that of a
reference Ta/CoFeB/MgO PMA film annealed at 300 {\deg}C, justifying the
enhanced thermal stability of the W-seeded CoFeB films. | 1709.07483v1 |
2008-07-31 | Scattering Theory of Gilbert Damping | The magnetization dynamics of a single domain ferromagnet in contact with a
thermal bath is studied by scattering theory. We recover the
Landau-Liftshitz-Gilbert equation and express the effective fields and Gilbert
damping tensor in terms of the scattering matrix. Dissipation of magnetic
energy equals energy current pumped out of the system by the time-dependent
magnetization, with separable spin-relaxation induced bulk and spin-pumping
generated interface contributions. In linear response, our scattering theory
for the Gilbert damping tensor is equivalent with the Kubo formalism. | 0807.5009v1 |
2006-11-22 | Magnetization damping in a local-density approximation | The linear response of itinerant transition metal ferromagnets to transverse
magnetic fields is studied in a self-consistent adiabatic local-density
approximation. The susceptibility is calculated from a microscopic Hamiltonian,
including spin-conserving impurities, impurity induced spin-orbit interaction
and magnetic impurities using the Keldysh formalism. The Gilbert damping
constant in the Landau-Lifshitz-Gilbert equation is identified, parametrized by
an effective transverse spin dephasing rate, and is found to be inversely
proportional to the exchange splitting. Our result justify the phenomenological
treatment of transverse spin dephasing in the study of current-induced
magnetization dynamics in weak, itinerant ferromagnets by Tserkovnyak
\textit{et al.}. We show that neglect of gradient corrections in the
quasiclassical transport equations leads to incorrect results when the exchange
potential becomes of the order of the Fermi energy. | 0611588v1 |
2020-08-14 | Large enhancement of spin pumping due to the surface bound states in normal metal/superconductor structures | We show that the spin pumping from ferromagnetic insulator into the adjacent
metallic spin sink can be strongly stimulated by the superconducting
correlations.
The key physical mechanism responsible for this effect is the presence of
quasiparticle surface states at the ferromagnetic insulator/superconductor
interface. We consider the minimal model when these states appear because of
the suppressed pairing constant within the interfacial normal layer. For thin
normal layers we obtain a strongly peaked temperature dependence of the Gilbert
damping coefficient which has been recently observed in such systems. For
thicker normal layers the Gilbert damping monotonically increases down to the
temperatures much smaller than the critical one. The suggested model paves the
way to controlling the temperature dependence of the spin pumping by
fabricating hybrid normal metal/superconductor spin sinks. | 2008.06253v1 |
2024-01-18 | Real-space nonlocal Gilbert damping from exchange torque correlation applied to bulk ferromagnets and their surfaces | In this work we present an ab initio scheme based on linear response theory
of exchange torque correlation, implemented into the real-space
Korringa-Kohn-Rostoker (RS-KKR) framework to calculate diagonal elements of the
atomic-site-dependent intrinsic Gilbert damping tensor. The method is first
applied to bcc iron and fcc cobalt bulk systems. Beside reproducing earlier
results from the literature for those bulk magnets, the effect of the lattice
compression is also studied for Fe bulk, and significant changes for the
Gilbert damping are found. Furthermore, (001)-oriented surfaces of Fe and Co
are also investigated. It is found that the on-site Gilbert damping increases
in the surface atomic layer and decreases in the subsurface layer, and
approaches the bulk value moving further inside the magnets. Realistic atomic
relaxation of the surface layers enhances the identified effects. The
first-neighbor damping parameters are extremely sensitive to the surface
relaxation. Despite their inhomogeneity caused by the surface, the transverse
Gilbert damping tensor components remain largely insensitive to the
magnetization direction. | 2401.09938v2 |
2007-06-12 | Gilbert and Landau-Lifshitz damping in the presense of spin-torque | A recent article by Stiles et al. (cond-mat/0702020) argued in favor of the
Landau-Lifshitz damping term in the micromagnetic equations of motion over that
of the more commonly accepted Gilbert damping form. Much of their argument
revolved around spin-torque driven domain wall motion in narrow magnetic wires,
since the presence of spin-torques can more acutely draw a distinction between
the two forms of damping. In this article, the author uses simple arguments and
examples to offer an alternative point of view favoring Gilbert. | 0706.1736v1 |
2008-04-04 | Inhomogeneous Gilbert damping from impurities and electron-electron interactions | We present a unified theory of magnetic damping in itinerant electron
ferromagnets at order $q^2$ including electron-electron interactions and
disorder scattering. We show that the Gilbert damping coefficient can be
expressed in terms of the spin conductivity, leading to a Matthiessen-type
formula in which disorder and interaction contributions are additive. In a weak
ferromagnet regime, electron-electron interactions lead to a strong enhancement
of the Gilbert damping. | 0804.0820v2 |
2015-03-04 | Critical current destabilizing perpendicular magnetization by the spin Hall effect | The critical current needed to destabilize the magnetization of a
perpendicular ferromagnet via the spin Hall effect is studied. Both the
dampinglike and fieldlike torques associated with the spin current generated by
the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to
model the system. In the absence of the fieldlike torque, the critical current
is independent of the damping constant and is much larger than that of
conventional spin torque switching of collinear magnetic systems, as in
magnetic tunnel junctions. With the fieldlike torque included, we find that the
critical current scales with the damping constant as $\alpha^{0}$ (i.e.,
damping independent),$\alpha$, and $\alpha^{1/2}$ depending on the sign of the
fieldlike torque and other parameters such as the external field. Numerical and
analytical results show that the critical current can be significantly reduced
when the fieldlike torque possesses the appropriate sign, i.e. when the
effective field associated with the fieldlike torque is pointing opposite to
the spin direction of the incoming electrons. These results provide a pathway
to reducing the current needed to switch magnetization using the spin Hall
effect. | 1503.01478v2 |
2015-10-23 | Laser-induced THz magnetization precession for a tetragonal Heusler-like nearly compensated ferrimagnet | Laser-induced magnetization precessional dynamics was investigated in
epitaxial films of Mn$_3$Ge, which is a tetragonal Heusler-like nearly
compensated ferrimagnet. The ferromagnetic resonance (FMR) mode was observed,
the precession frequency for which exceeded 0.5 THz and originated from the
large magnetic anisotropy field of approximately 200 kOe for this ferrimagnet.
The effective damping constant was approximately 0.03. The corresponding
effective Landau-Lifshitz constant of approximately 60 Mrad/s and is comparable
to those of the similar Mn-Ga materials. The physical mechanisms for the
Gilbert damping and for the laser-induced excitation of the FMR mode were also
discussed in terms of the spin-orbit-induced damping and the laser-induced
ultrafast modulation of the magnetic anisotropy, respectively. | 1510.06793v1 |
2017-04-11 | CoFeAlB alloy with low damping and low magnetization for spin transfer torque switching | We investigate the effect of Al doping on the magnetic properties of the
alloy CoFeB. Comparative measurements of the saturation magnetization, the
Gilbert damping parameter $\alpha$ and the exchange constant as a function of
the annealing temperature for CoFeB and CoFeAlB thin films are presented. Our
results reveal a strong reduction of the magnetization for CoFeAlB in
comparison to CoFeB. If the prepared CoFeAlB films are amorphous, the damping
parameter $\alpha$ is unaffected by the Al doping in comparison to the CoFeB
alloy. In contrast, in the case of a crystalline CoFeAlB film, $\alpha$ is
found to be reduced. Furthermore, the x-ray characterization and the evolution
of the exchange constant with the annealing temperature indicate a similar
crystallization process in both alloys. The data proves the suitability of
CoFeAlB for spin torque switching properties where a reduction of the switching
current in comparison with CoFeB is expected. | 1704.03326v1 |
2021-01-07 | Mechanisms behind large Gilbert damping anisotropies | A method with which to calculate the Gilbert damping parameter from a
real-space electronic structure method is reported here. The anisotropy of the
Gilbert damping with respect to the magnetic moment direction and local
chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$
alloys from first principles electronic structure in a real space formulation.
The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is
demonstrated to be significant. Depending on details of the simulations, it
reaches a maximum-minimum damping ratio as high as 200%. Several microscopic
origins of the strongly enhanced Gilbert damping anisotropy have been examined,
where in particular interface/surface effects stand out, as do local
distortions of the crystal structure. Although theory does not reproduce the
experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203
(2019)], it nevertheless identifies microscopic mechanisms that can lead to
huge damping anisotropies. | 2101.02794v2 |
2018-08-13 | Gilbert damping phenomenology for two-sublattice magnets | We present a systematic phenomenological description of Gilbert damping in
two-sublattice magnets. Our theory covers the full range of materials from
ferro- via ferri- to antiferromagnets. Following a Rayleigh dissipation
functional approach within a Lagrangian classical field formulation, the theory
captures intra- as well as cross-sublattice terms in the Gilbert damping,
parameterized by a 2$\times$2 matrix. When spin-pumping into an adjacent
conductor causes dissipation, we obtain the corresponding Gilbert damping
matrix in terms of the interfacial spin-mixing conductances. Our model
reproduces the experimentally observed enhancement of the ferromagnetic
resonance linewidth in a ferrimagnet close to its compensation temperature
without requiring an increased Gilbert parameter. It also predicts new
contributions to damping in an antiferromagnet and suggests the resonance
linewidths as a direct probe of the sublattice asymmetry, which may stem from
boundary or bulk. | 1808.04385v2 |
2021-07-02 | Anomalous Gilbert Damping and Duffing Features of the SFS {\boldmath $\varphi_0$} Josephson Junction | We demonstrate unusual features of phase dynamics, IV-characteristics and
magnetization dynamics of the $\varphi_0$ Josephson junction at small values of
spin-orbit interaction, ratio of Josephson to magnetic energy and Gilbert
damping. In particular, an anomalous shift of the ferromagnetic resonance
frequency with an increase of Gilbert damping is found. The ferromagnetic
resonance curves show the Duffing oscillator behaviour, reflecting the
nonlinear nature of Landau-Lifshitz-Gilbert (LLG) equation. Based on the
numerical analysis of each term in LLG equation we obtained an approximated
equation demonstrated both damping effect and Duffing oscillator features. The
resulting Duffing equation incorporates the Gilbert damping in a special way
across the dissipative term and the restoring force. A resonance method for the
determination of spin-orbit interaction in noncentrosymmetric materials which
play the role of barrier in $\varphi_0$ junctions is proposed. | 2107.00982v3 |
2023-03-07 | Electrically tunable Gilbert damping in van der Waals heterostructures of two-dimensional ferromagnetic metals and ferroelectrics | Tuning the Gilbert damping of ferromagnetic (FM) metals via a nonvolatile way
is of importance to exploit and design next-generation novel spintronic
devices. Through systematical first-principles calculations, we study the
magnetic properties of the van der Waals heterostructure of two-dimensional FM
metal CrTe2 and ferroelectric (FE) In2Te3 monolayers. The ferromagnetism of
CrTe2 is maintained in CrTe2/In2Te3 and its magnetic easy axis can be switched
from in-plane to out-of-plane by reversing the FE polarization of In2Te3.
Excitingly, we find that the Gilbert damping of CrTe2 is tunable when the FE
polarization of In2Te3 is reversed from upward to downward. By analyzing the
k-dependent contributions to the Gilbert damping, we unravel that such
tunability results from the changed intersections between the bands of CrTe2
and Fermi level on the reversal of the FE polarizations of In2Te3 in
CrTe2/In2Te3. Our work provides an appealing way to electrically tailor Gilbert
dampings of two-dimensional FM metals by contacting them with ferroelectrics. | 2303.03852v1 |
2014-05-19 | Comparison of micromagnetic parameters of ferromagnetic semiconductors (Ga,Mn)(As,P) and (Ga,Mn)As | We report on the determination of micromagnetic parameters of epilayers of
the ferromagnetic semiconductor (Ga,Mn)As, which has easy axis in the sample
plane, and (Ga,Mn)(As,P) which has easy axis perpendicular to the sample plane.
We use an optical analog of ferromagnetic resonance where the
laser-pulse-induced precession of magnetization is measured directly in the
time domain. By the analysis of a single set of pump-and-probe magneto-optical
data we determined the magnetic anisotropy fields, the spin stiffness and the
Gilbert damping constant in these two materials. We show that incorporation of
10% of phosphorus in (Ga,Mn)As with 6% of manganese leads not only to the
expected sign change of the perpendicular to plane anisotropy field but also to
an increase of the Gilbert damping and to a reduction of the spin stiffness.
The observed changes in the micromagnetic parameters upon incorporating P in
(Ga,Mn)As are consistent with the reduced hole density, conductivity, and Curie
temperature of the (Ga,Mn)(As,P) material. We report that the magnetization
precession damping is stronger for the n = 1 spin wave resonance mode than for
the n = 0 uniform magnetization precession mode. | 1405.4677v1 |
2015-03-24 | Spin dynamics and frequency dependence of magnetic damping study in soft ferromagnetic FeTaC film with a stripe domain structure | Perpendicular magnetic anisotropy (PMA) and low magnetic damping are the key
factors for the free layer magnetization switching by spin transfer torque
technique in magnetic tunnel junction devices. The magnetization precessional
dynamics in soft ferromagnetic FeTaC thin film with a stripe domain structure
was explored in broad band frequency range by employing micro-strip
ferromagnetic resonance technique. The polar angular variation of resonance
field and linewidth at different frequencies have been analyzed numerically
using Landau-Lifshitz-Gilbert equation by taking into account the total free
energy density of the film. The numerically estimated parameters Land\'{e}
$g$-factor, PMA constant, and effective magnetization are found to be 2.1,
2$\times10^{5}$ erg/cm$^{3}$ and 7145 Oe, respectively. The frequency
dependence of Gilbert damping parameter ($\alpha$) is evaluated by considering
both intrinsic and extrinsic effects into the total linewidth analysis. The
value of $\alpha$ is found to be 0.006 at 10 GHz and it increases with
decreasing precessional frequency. | 1503.07043v5 |
2015-08-28 | The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space | We prove that in dimensions three and higher the Landau-Lifshitz- Gilbert
equation with small initial data in the critical Besov space is globally
wellposed in a uniform way with respect to the Gilbert damping parameter. Then
we show that the global solution converges to that of the Schrodinger maps in
the natural space as the Gilbert damping term vanishes. The proof is based on
some studies on the derivative Ginzburg-Landau equations. | 1508.07118v3 |
2006-06-05 | Phenomenological theory of current driven exchange switching in ferromagnetic nanojunctions | Phenomenological approach is developed in the theory of spin-valve type
ferromagnetic junctions to describe exchange switching by current flowing
perpendicular to interfaces. Forward and backward current switching effects are
described and they may be principally different in nature. Mobile electron
spins are considered as being free in all the contacting ferromagnetic layers.
Joint action of the following two current effects is investigated: the
nonequilibrium longitudinal spin-injection effective field and the transverse
spin-transfer surface torque. Dispersion relation for fluctuations is derived
and solved for a junction model having spatially localized spin transfer
torque: depth of the torque penetration into the free layer is assumed much
smaller than the total free layer thickness. Some critical value of the well
known Gilbert damping constant is established for the first time. Spin transfer
torque dominates in the instability threshold determination for small enough
damping constants, while the spin-injection effective field dominates for high
damping. Fine interplay between spin transfer torque and spin injection is
necessary to provide a hysteretic behavior of the resistance versus current
dependence. The state diagram building up shows the possibility of
non-stationary (time dependent) nonlinear states arising due to instability
development. Calculations lead to the instability rise time values of the order
of 0.1 ns. Spin wave resonance frequency spectrum softening occurs under the
current growing to the instability threshold. Magnetization fluctuations above
the threshold rise oscillating with time for low damping, but rise
aperiodically and much more rapid for high damping. | 0606102v2 |
2005-01-27 | Current-induced macrospin vs spin-wave excitations in spin valves | The mode dependence of current-induced magnetic excitations in spin valves is
studied theoretically. The torque exerted on the magnetization by transverse
spin currents as well as the Gilbert damping constant are found to depend
strongly on the wave length of the excitation (spin wave). Analytic expressions
are presented for the critical currents that excite a selected spin wave. The
onset of macrospin (zero wavelength) vs finite wavelength instabilities depends
on the device parameters and the current direction, in agreement with recent
experimental findings. | 0501672v3 |
2011-04-15 | Lagrangian approach and dissipative magnetic systems | A Lagrangian is introduced which includes the coupling between magnetic
moments $\mathbf{m}$ and the degrees of freedom $\boldsymbol{\sigma}$ of a
reservoir. In case the system-reservoir coupling breaks the time reversal
symmetry the magnetic moments perform a damped precession around an effective
field which is self-organized by the mutual interaction of the moments. The
resulting evolution equation has the form of the Landau-Lifshitz-Gilbert
equation. In case the bath variables are constant vector fields the moments
$\mathbf{m}$ fulfill the reversible Landau-Lifshitz equation. Applying
Noether's theorem we find conserved quantities under rotation in space and
within the configuration space of the moments. | 1104.3002v1 |
2011-07-04 | Minimization of the Switching Time of a Synthetic Free Layer in Thermally Assisted Spin Torque Switching | We theoretically studied the thermally assisted spin torque switching of a
synthetic free layer and showed that the switching time is minimized if the
condition H_J=|H_s|/(2 alpha) is satisfied, where H_J, H_s and alpha are the
coupling field of two ferromagnetic layers, the amplitude of the spin torque,
and the Gilbert damping constant. We also showed that the coupling field of the
synthetic free layer can be determined from the resonance frequencies of the
spin-torque diode effect. | 1107.0753v2 |
2013-03-12 | Thermally excited spin waves in a nano-structure: thermal gradient vs. constant temperature | Using micromagnetic simulations, we have investigated spin dynamics in a
nanostructure in the presence of thermal fluctuations. In particular, we have
studied the effects of a uniform temperature and of a uniform thermal gradient.
In both cases, the stochastic field leads to an increase of the precession
angle of the magnetization, and to a mild decreas of the linewidth of the
resonance peaks. Our results indicate that the Gilbert damping parameter plays
the role of control parameter for the amplification of spin waves. | 1303.2895v1 |
2015-07-24 | Boosting Domain Wall Propagation by Notches | We report a counter-intuitive finding that notches in an otherwise
homogeneous magnetic nanowire can boost current-induced domain wall (DW)
propagation. DW motion in notch-modulated wires can be classified into three
phases: 1) A DW is pinned around a notch when the current density is below the
depinning current density. 2) DW propagation velocity is boosted by notches
above the depinning current density and when non-adiabatic spin-transfer torque
strength $\beta$ is smaller than the Gilbert damping constant $\alpha$. The
boost can be manyfold. 3) DW propagation velocity is hindered when $\beta >
\alpha$. The results are explained by using the Thiele equation. | 1507.06748v1 |
2020-01-17 | Fermi Level Controlled Ultrafast Demagnetization Mechanism in Half-Metallic Heusler Alloy | The electronic band structure-controlled ultrafast demagnetization mechanism
in Co2FexMn1-xSi Heusler alloy is underpinned by systematic variation of
composition. We find the spin-flip scattering rate controlled by spin density
of states at Fermi level is responsible for non-monotonic variation of
ultrafast demagnetization time ({\tau}M) with x with a maximum at x = 0.4.
Furthermore, Gilbert damping constant exhibits an inverse relationship with
{\tau}M due to the dominance of inter-band scattering mechanism. This
establishes a unified mechanism of ultrafast spin dynamics based on Fermi level
position. | 2001.06217v1 |
2019-06-25 | Conductivity-Like Gilbert Damping due to Intraband Scattering in Epitaxial Iron | Confirming the origin of Gilbert damping by experiment has remained a
challenge for many decades, even for simple ferromagnetic metals. In this
Letter, we experimentally identify Gilbert damping that increases with
decreasing electronic scattering in epitaxial thin films of pure Fe. This
observation of conductivity-like damping, which cannot be accounted for by
classical eddy current loss, is in excellent quantitative agreement with
theoretical predictions of Gilbert damping due to intraband scattering. Our
results resolve the longstanding question about a fundamental damping mechanism
and offer hints for engineering low-loss magnetic metals for cryogenic
spintronics and quantum devices. | 1906.10326v2 |
2008-08-28 | Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula | We report on a study of Gilbert damping due to particle-hole pair excitations
in conducting ferromagnets. We focus on a toy two-band model and on a four-band
spherical model which provides an approximate description of ferromagnetic
(Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex
corrections to the long-wavelength spin-spin response function can be summed to
all orders. An important objective of this study is to assess the reliability
of practical approximate expressions which can be combined with electronic
structure calculations to estimate Gilbert damping in more complex systems. | 0808.3923v1 |
2010-01-26 | Effect of spin-conserving scattering on Gilbert damping in ferromagnetic semiconductors | The Gilbert damping in ferromagnetic semiconductors is theoretically
investigated based on the $s$-$d$ model. In contrast to the situation in
metals, all the spin-conserving scattering in ferromagnetic semiconductors
supplies an additional spin relaxation channel due to the momentum dependent
effective magnetic field of the spin-orbit coupling, thereby modifies the
Gilbert damping. In the presence of a pure spin current, we predict a new
contribution due to the interplay of the anisotropic spin-orbit coupling and a
pure spin current. | 1001.4576v1 |
2020-10-15 | Spin injection characteristics of Py/graphene/Pt by gigahertz and terahertz magnetization dynamics driven by femtosecond laser pulse | Spin transport characteristics of graphene has been extensively studied so
far. The spin transport along c-axis is however reported by rather limited
number of papers. We have studied spin transport characteristics through
graphene along c-axis with permalloy(Py)/graphene(Gr)/Pt by gigahertz (GHz) and
terahertz (THz) magnetization dynamics driven by femtosecond laser pulses. The
relatively simple sample structure does not require electrodes on the sample.
The graphene layer was prepared by chemical vapor deposition and transferred on
Pt film. The quality of graphene layer was characterized by Raman microscopy.
Time resolved magneto-optical Kerr effect is used to characterize gigahertz
magnetization dynamics. Magnetization precession is clearly observed both for
Pt/Py and Pt/Gr/Py. The Gilbert damping constant of Pt/Py was 0.015, indicates
spin pumping effect from Py to Pt. The Gilbert damping constant of Pt/Gr/Py is
found to be 0.011, indicates spin injection is blocked by graphene layer. We
have also performed the measurement of THz emission for Pt/Py and Pt/Gr/Py.
While the THz emission is clearly observed for Pt/Py, a strong reduction of THz
emission is observed for Pt/Gr/Py. With these two different experiments, and
highly anisotropic resistivity of graphite, we conclude that the vertical spin
transport is strongly suppressed by the graphene layer. | 2010.07694v1 |
2015-02-05 | Nonlinear analysis of magnetization dynamics excited by spin Hall effect | We investigate the possibility of exciting self-oscillation in a
perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear
analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation
state, the energy supplied by the spin torque during a precession on a constant
energy curve should equal the dissipation due to damping. Also, the current to
balance the spin torque and the damping torque in the self-oscillation state
should be larger than the critical current to destabilize the initial state. We
find that the second condition in the spin Hall system is not satisfied by
deriving analytical solutions of the energy supplied by the spin transfer
effect and the dissipation due to the damping from the nonlinear LLG equation.
This indicates that the self-oscillation of a perpendicular ferromagnet cannot
be excited solely by the spin Hall torque. | 1502.01420v2 |
2008-12-17 | Origin of intrinsic Gilbert damping | The damping of magnetization, represented by the rate at which it relaxes to
equilibrium, is successfully modeled as a phenomenological extension in the
Landau-Lifschitz-Gilbert equation. This is the damping torque term known as
Gilbert damping and its direction is given by the vector product of the
magnetization and its time derivative. Here we derive the Gilbert term from
first principles by a non-relativistic expansion of the Dirac equation. We find
that the Gilbert term arises when one calculates the time evolution of the spin
observable in the presence of the full spin-orbital coupling terms, while
recognizing the relationship between the curl of the electric field and the
time varying magnetic induction. | 0812.3184v2 |
2019-07-01 | Magnon decay theory of Gilbert damping in metallic antiferromagnets | Gilbert damping is a key property governing magnetization dynamics in ordered
magnets. We present a theoretical study of intrinsic Gilbert damping induced by
magnon decay in antiferromagnetic metals through $s$-$d$ exchange interaction.
Our theory delineates the qualitative features of damping in metallic
antiferromagnets owing to their bipartite nature, in addition to providing
analytic expressions for the damping parameters. Magnon-induced intraband
electron scattering is found to predominantly cause magnetization damping,
whereas the N\'eel field is found to be damped via disorder. Depending on the
conduction electron band structure, we predict that magnon-induced interband
electron scattering around band crossings may be exploited to engineer a strong
N\'eel field damping. | 1907.01045v1 |
2022-11-24 | Influence of non-local damping on magnon properties of ferromagnets | We study the influence of non-local damping on magnon properties of Fe, Co,
Ni and Fe$_{1-x}$Co$_{x}$ ($x=30\%,50\%$) alloys. The Gilbert damping parameter
is typically considered as a local scalar both in experiment and in theoretical
modelling. However, recent works have revealed that Gilbert damping is a
non-local quantity that allows for energy dissipation between atomic sites.
With the Gilbert damping parameters calculated from a state-of-the-art
real-space electronic structure method, magnon lifetimes are evaluated from
spin dynamics and linear response, where a good agreement is found between
these two methods. It is found that non-local damping affects the magnon
lifetimes in different ways depending on the system. Specifically, we find that
in Fe, Co, and Ni the non-local damping decreases the magnon lifetimes, while
in $\rm Fe_{70}Co_{30}$ and Fe$_{50}$Co$_{50}$ an opposite, non-local damping
effect is observed, and our data show that it is much stronger in the former. | 2211.13486v1 |
2005-07-20 | All-optical probe of precessional magnetization dynamics in exchange biased NiFe/FeMn bilayers | An internal anisotropy pulse field is launched by an 8.3 ps short laser
excitation, which triggers precessional magnetization dynamics of a
polycrystalline NiFe/FeMn exchange bias system on the picosecond timescale. Due
to the excitation the unidirectional anisotropy and, thus, the exchange
coupling across the interface between the ferromagnetic and the
antiferromagnetic layer is reduced, leading to a fast reduction of the exchange
bias field and to a dramatic increase of the zero-field susceptibility. The
fast optical unpinning is followed by a slower recovery of the interfacial
exchange coupling dominated by spin-lattice and heat flow relaxation with a
time constant of the order of 160 ps. The measured picosecond time evolution of
the exchange decoupling and restoration is interpreted as an anisotropy pulse
field giving rise to fast precessional magnetization dynamics of the
ferromagnetic layer. The strength of the internal pulse field and even the
initial magnetization deflection direction from the equilibrium orientation can
be controlled by the absorbed photons. The dependence of the effective Gilbert
damping on both small and large angle precessional motion was studied, yielding
that both cases can be modeled with reasonable accuracy within the
Landau-Lifshitz and Gilbert framework. | 0507475v1 |
2013-09-21 | Patterns formation in axially symmetric Landau-Lifshitz-Gilbert-Slonczewski equations | The Landau-Lifshitz-Gilbert-Slonczewski equation describes magnetization
dynamics in the presence of an applied field and a spin polarized current. In
the case of axial symmetry and with focus on one space dimension, we
investigate the emergence of space-time patterns in the form of wavetrains and
coherent structures, whose local wavenumber varies in space. A major part of
this study concerns existence and stability of wavetrains and of front- and
domain wall-type coherent structures whose profiles asymptote to wavetrains or
the constant up-/down-magnetizations. For certain polarization the Slonczewski
term can be removed which allows for a more complete charaterization, including
soliton-type solutions. Decisive for the solution structure is the polarization
parameter as well as size of anisotropy compared with the difference of field
intensity and current intensity normalized by the damping. | 1309.5523v4 |
2017-03-28 | Temperature dependent magnetic damping of yttrium iron garnet spheres | We investigate the temperature dependent microwave absorption spectrum of an
yttrium iron garnet sphere as a function of temperature (5 K to 300 K) and
frequency (3 GHz to 43.5 GHz). At temperatures above 100 K, the magnetic
resonance linewidth increases linearly with temperature and shows a
Gilbert-like linear frequency dependence. At lower temperatures, the
temperature dependence of the resonance linewidth at constant external magnetic
fields exhibits a characteristic peak which coincides with a non-Gilbert-like
frequency dependence. The complete temperature and frequency evolution of the
linewidth can be modeled by the phenomenology of slowly relaxing rare-earth
impurities and either the Kasuya-LeCraw mechanism or the scattering with
optical magnons. Furthermore, we extract the temperature dependence of the
saturation magnetization, the magnetic anisotropy and the g-factor. | 1703.09444v2 |
2017-12-10 | Magnetic field gradient driven dynamics of isolated skyrmions and antiskyrmions in frustrated magnets | The study of skyrmion/antiskyrmion motion in magnetic materials is very
important in particular for the spintronics applications. In this work, we
study the dynamics of isolated skyrmions and antiskyrmions in frustrated
magnets driven by magnetic field gradient, using the Landau-Lifshitz-Gilbert
simulations on the frustrated classical Heisenberg model on the triangular
lattice. A Hall-like motion induced by the gradient is revealed in bulk system,
similar to that in the well-studied chiral magnets. More interestingly, our
work suggests that the lateral confinement in nano-stripes of the frustrated
system can completely suppress the Hall motion and significantly speed up the
motion along the gradient direction. The simulated results are well explained
by the Thiele theory. It is demonstrated that the acceleration of the motion is
mainly determined by the Gilbert damping constant, which provides useful
information for finding potential materials for skyrmion-based spintronics. | 1712.03550v1 |
2010-02-26 | Correlation Effects in the Stochastic Landau-Lifshitz-Gilbert Equation | We analyze the Landau-Lifshitz-Gilbert equation when the precession motion of
the magnetic moments is additionally subjected to an uniaxial anisotropy and is
driven by a multiplicative coupled stochastic field with a finite correlation
time $\tau$. The mean value for the spin wave components offers that the
spin-wave dispersion relation and its damping is strongly influenced by the
deterministic Gilbert damping parameter $\alpha$, the strength of the
stochastic forces $D$ and its temporal range $\tau$. The spin-spin-correlation
function can be calculated in the low correlation time limit by deriving an
evolution equation for the joint probability function. The stability analysis
enables us to find the phase diagram within the $\alpha-D$ plane for different
values of $\tau$ where damped spin wave solutions are stable. Even for zero
deterministic Gilbert damping the magnons offer a finite lifetime. We detect a
parameter range where the deterministic and the stochastic damping mechanism
are able to compensate each other leading to undamped spin-waves. The onset is
characterized by a critical value of the correlation time. An enhancement of
$\tau$ leads to an increase of the oscillations of the correlation function. | 1002.4958v1 |
2014-10-02 | Investigation of the temperature-dependence of ferromagnetic resonance and spin waves in Co2FeAl0.5Si0.5 | Co2FeAl0.5Si0.5 (CFAS) is a Heusler compound that is of interest for
spintronics applications, due to its high spin polarization and relatively low
Gilbert damping constant. In this study, the behavior of ferromagnetic
resonance as a function of temperature was investigated in CFAS, yielding a
decreasing trend of damping constant as the temperature was increased from 13
to 300 K. Furthermore, we studied spin waves in CFAS using both frequency
domain and time domain techniques, obtaining group velocities and attenuation
lengths as high as 26 km/s and 23.3 um, respectively, at room temperature. | 1410.0439v1 |
2018-10-11 | Propagating spin waves in nanometer-thick yttrium iron garnet films: Dependence on wave vector, magnetic field strength and angle | We present a comprehensive investigation of propagating spin waves in
nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave
spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas
on top of continuous and patterned YIG films to characterize spin waves with
wave vectors up to 10 rad/$\mu$m. All films are grown by pulsed laser
deposition. From spin-wave transmission spectra, parameters such as the Gilbert
damping constant, spin-wave dispersion relation, group velocity, relaxation
time, and decay length are derived and their dependence on magnetic bias field
strength and angle is systematically gauged. For a 40-nm-thick YIG film, we
obtain a damping constant of $3.5 \times 10^{-4}$ and a maximum decay length of
1.2 mm. Our experiments reveal a strong variation of spin-wave parameters with
magnetic bias field and wave vector. Spin-wave properties change considerably
up to a magnetic bias field of about 30 mT and above a field angle of
$\theta_{H} = 20^{\circ}$, where $\theta_{H} = 0^{\circ}$ corresponds to the
Damon-Eshbach configuration. | 1810.04973v1 |
2019-02-26 | Enhanced Gilbert Damping in Re doped FeCo Films: A Combined Experimental and Theoretical Study | The effects of rhenium doping in the range 0 to 10 atomic percent on the
static and dynamic magnetic properties of Fe65Co35 thin films have been studied
experimentally as well as with first principles electronic structure
calculations focusing on the change of the saturation magnetization and the
Gilbert damping parameter. Both experimental and theoretical results show that
the saturation magnetization decreases with increasing Re doping level, while
at the same time Gilbert damping parameter increases. The experimental low
temperature saturation magnetic induction exhibits a 29 percent decrease, from
2.31 T to 1.64 T, in the investigated doping concentration range, which is more
than predicted by the theoretical calculations. The room temperature value of
the damping parameter obtained from ferromagnetic resonance measurements,
correcting for extrinsic contributions to the damping, is for the undoped
sample 0.0027, which is close to the theoretically calculated Gilbert damping
parameter. With 10 atomic percent Re doping, the damping parameter increases to
0.0090, which is in good agreement with the theoretical value of 0.0073. The
increase in damping parameter with Re doping is explained by the increase in
density of states at Fermi level, mostly contributed by the spin-up channel of
Re. Moreover, both experimental and theoretical values for the damping
parameter are observed to be weakly decreasing with decreasing temperature. | 1902.09896v1 |
2021-09-13 | Control of magnetization dynamics by substrate orientation in YIG thin films | Yttrium Iron Garnet (YIG) and bismuth (Bi) substituted YIG (Bi0.1Y2.9Fe5O12,
BYG) films are grown in-situ on single crystalline Gadolinium Gallium Garnet
(GGG) substrates [with (100) and (111) orientations] using pulsed laser
deposition (PLD) technique. As the orientation of the Bi-YIG film changes from
(100) to (111), the lattice constant is enhanced from 12.384 {\AA} to 12.401
{\AA} due to orientation dependent distribution of Bi3+ ions at dodecahedral
sites in the lattice cell. Atomic force microscopy (AFM) images show smooth
film surfaces with roughness 0.308 nm in Bi-YIG (111). The change in substrate
orientation leads to the modification of Gilbert damping which, in turn, gives
rise to the enhancement of ferromagnetic resonance (FMR) line width. The best
values of Gilbert damping are found to be (0.54)*10-4, for YIG (100) and
(6.27)*10-4, for Bi-YIG (111) oriented films. Angle variation measurements of
the Hr are also performed, that shows a four-fold symmetry for the resonance
field in the (100) grown film. In addition, the value of effective
magnetization (4{\pi}Meff) and extrinsic linewidth ({\Delta}H0) are observed to
be dependent on substrate orientation. Hence PLD growth can assist
single-crystalline YIG and BYG films with a perfect interface that can be used
for spintronics and related device applications. | 2109.05901v1 |
2022-09-01 | Growth parameters of Bi0.1Y2.9Fe5O12 thin films for high frequency applications | The growth and characterization of Bismuth (Bi) substituted YIG (Bi-YIG,
Bi0.1Y2.9Fe5O12) thin films are reported. Pulsed laser deposited (PLD) films
with thicknesses ranging from 20 to 150 nm were grown on Gadolinium Gallium
Garnet substrates. Two substrate orientations of (100) and (111) were
considered. The enhanced distribution of Bi3+ ions at dodecahedral site along
(111) is observed to lead to an increment in lattice constant from 12.379
angstrom in (100) to 12.415 angstrom in (111) oriented films. Atomic force
microscopy images showed decreasing roughness with increasing film thickness.
Compared to (100) grown films, (111) oriented films showed an increase in
ferromagnetic resonance linewidth and consequent increase in Gilbert damping.
The lowest Gilbert damping values are found to be (1.06) * 10E-4 for (100) and
(2.30) * 10E-4 for (111) oriented films with thickness of 150 nm. The observed
values of extrinsic linewidth, effective magnetization, and anisotropic field
are related to thickness of the films and substrate orientation. In addition,
the in-plane angular variation established four-fold symmetry for the (100)
deposited films unlike the case of (111) deposited films. This study prescribes
growth conditions for PLD grown single-crystalline Bi-YIG films towards desired
high frequency and magneto-optical device applications. | 2209.00558v1 |
2023-06-07 | Helicity-dependent optical control of the magnetization state emerging from the Landau-Lifshitz-Gilbert equation | It is well known that the Gilbert relaxation time of a magnetic moment scales
inversely with the magnitude of the externally applied field, H, and the
Gilbert damping, {\alpha}. Therefore, in ultrashort optical pulses, where H can
temporarily be extremely large, the Gilbert relaxation time can momentarily be
extremely short, reaching even picosecond timescales. Here we show that for
typical ultrashort pulses, the optical control of the magnetization emerges by
merely considering the optical magnetic field in the Landau-Lifshitz-Gilbert
(LLG) equation. Surprisingly, when circularly polarized optical pulses are
introduced to the LLG equation, an optically induced helicity-dependent torque
results. We find that the strength of the interaction is determined by
{\eta}={\alpha}{\gamma}H/f_opt, where f_opt and {\gamma} are the optical
frequency and gyromagnetic ratio. Our results illustrate the generality of the
LLG equation to the optical limit and the pivotal role of the Gilbert damping
in the general interaction between optical magnetic fields and spins in solids. | 2306.04617v2 |
2018-04-03 | Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms | The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains
as the cornerstone of contemporary magnetisation dynamics studies, wherein the
Gilbert damping parameter has been attributed to first-order relativistic
effects. To include magnetic inertial effects the LLG equation has previously
been extended with a supplemental inertia term and the arising inertial
dynamics has been related to second-order relativistic effects. Here we start
from the relativistic Dirac equation and, performing a Foldy-Wouthuysen
transformation, derive a generalised Pauli spin Hamiltonian that contains
relativistic correction terms to any higher order. Using the Heisenberg
equation of spin motion we derive general relativistic expressions for the
tensorial Gilbert damping and magnetic inertia parameters, and show that these
tensors can be expressed as series of higher-order relativistic correction
terms. We further show that, in the case of a harmonic external driving field,
these series can be summed and we provide closed analytical expressions for the
Gilbert and inertial parameters that are functions of the frequency of the
driving field. | 1804.09242v1 |
2016-08-02 | Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach | In this paper, we investigate theoretically the spin-orbit torque as well as
the Gilbert damping for a two band model of a 2D helical surface state with a
Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the
Fermi sea and Fermi surface components and obtain their contributions to the
electronic transport as well as the spin-orbit torque (SOT). Furthermore, we
obtain the expression for the Gilbert damping due to the surface state of a 3D
Topological Insulator (TI) and predicted its dependence on the direction of the
magnetization precession axis. | 1608.00984v2 |
2016-02-19 | A systematic study of magnetodynamic properties at finite temperatures in doped permalloy from first principles calculations | By means of first principles calculations, we have systematically
investigated how the magnetodynamic properties Gilbert damping, magnetization
and exchange stiffness are affected when permalloy (Py)
(Fe$_{0.19}$Ni$_{0.81}$) is doped with 4d or 5d transition metal impurities. We
find that the trends in the Gilbert damping can be understood from relatively
few basic parameters such as the density of states at the Fermi level, the
spin-orbit coupling and the impurity concentration. % The temperature
dependence of the Gilbert damping is found to be very weak which we relate to
the lack of intraband transitions in alloys. % Doping with $4d$ elements has no
major impact on the studied Gilbert damping, apart from diluting the host.
However, the $5d$ elements have a profound effect on the damping and allows it
to be tuned over a large interval while maintaining the magnetization and
exchange stiffness. % As regards spin stiffness, doping with early transition
metals results in considerable softening, whereas late transition metals have a
minor impact. % Our result agree well with earlier calculations where
available. In comparison to experiments, the computed Gilbert damping appears
slightly underestimated while the spin stiffness show good general agreement. | 1602.06201v2 |
2002-11-01 | Exploring dynamical magnetism with time-dependent density-functional theory: from spin fluctuations to Gilbert damping | We use time-dependent spin-density-functional theory to study dynamical
magnetic phenomena. First, we recall that the local-spin-density approximation
(LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic
state of iron and other itinerant ferromagnets. Next, we construct a
gradient-dependent density functional that does not suffer from this problem of
the LSDA. This functional is then used to derive, for the first time, the
phenomenological Gilbert equation of micromagnetics directly from
time-dependent density-functional theory. Limitations and extensions of Gilbert
damping are discussed on this basis, and some comparisons with phenomenological
theories and experiments are made. | 0211021v1 |
2012-04-24 | Nonlocal feedback in ferromagnetic resonance | Ferromagnetic resonance in thin films is analyzed under the influence of
spatiotemporal feedback effects. The equation of motion for the magnetization
dynamics is nonlocal in both space and time and includes isotropic, anisotropic
and dipolar energy contributions as well as the conserved Gilbert- and the
non-conserved Bloch-damping. We derive an analytical expression for the
peak-to-peak linewidth. It consists of four separate parts originated by
Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a
contribution arising from retardation. In an intermediate frequency regime the
results are comparable with the commonly used Landau-Lifshitz-Gilbert theory
combined with two-magnon processes. Retardation effects together with Gilbert
damping lead to a linewidth the frequency dependence of which becomes strongly
nonlinear. The relevance and the applicability of our approach to ferromagnetic
resonance experiments is discussed. | 1204.5342v1 |
2017-04-24 | Spin injection into silicon detected by broadband ferromagnetic resonance spectroscopy | We studied the spin injection in a NiFe(Py)/Si system using broadband
ferromagnetic resonance spectroscopy. The Gilbert damping parameter of the Py
layer on top of the Si channel was determined as a function of the Si doping
concentration and Py layer thickness. For fixed Py thickness we observed an
increase of the Gilbert damping parameter with decreasing resistivity of the Si
channel. For a fixed Si doping concentration we measured an increasing Gilbert
damping parameter for decreasing Py layer thickness. No increase of the Gilbert
damping parameter was found Py/Si samples with an insulating interlayer. We
attribute our observations to an enhanced spin injection into the
low-resistivity Si by spin pumping. | 1704.07006v1 |
2021-03-11 | Magnetoelastic Gilbert damping in magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films | We report an enhanced magnetoelastic contribution to the Gilbert damping in
highly magnetostrictive Fe$_{0.7}$Ga$_{0.3}$ thin films. This effect is
mitigated for perpendicular-to-plane fields, leading to a large anisotropy of
the Gilbert damping in all of the films (up to a factor of 10 at room
temperature). These claims are supported by broadband measurements of the
ferromagnetic resonance linewidths over a range of temperatures (5 to 400 K),
which serve to elucidate the effect of both the magnetostriction and phonon
relaxation on the magnetoelastic Gilbert damping. | 2103.07008v1 |
2022-01-27 | Effect of vertex corrections on the enhancement of Gilbert damping in spin pumping into a two-dimensional electron gas | We theoretically consider the effect of vertex correction on spin pumping
from a ferromagnetic insulator (FI) into a two-dimensional electron gas (2DEG)
in which the Rashba and Dresselhaus spin-orbit interactions coexist. The
Gilbert damping in the FI is enhanced by elastic spin-flipping or magnon
absorption. We show that the Gilbert damping due to elastic spin-flipping is
strongly enhanced by the vertex correction when the ratio of the two spin-orbit
interactions is near a special value at which the spin relaxation time diverges
while that due to magnon absorption shows only small modification. We also show
that the shift in the resonant frequency due to elastic spin-flipping is
strongly enhanced in a similar way as the Gilbert damping. | 2201.11498v3 |
2016-02-22 | Effects of Landau-Lifshitz-Gilbert damping on domain growth | Domain patterns are simulated by the Landau-Lifshitz-Gilbert (LLG) equation
with an easy-axis anisotropy. If the Gilbert damping is removed from the LLG
equation, it merely describes the precession of magnetization with a
ferromagnetic interaction. However, even without the damping, domains that look
similar to those of scalar fields are formed, and they grow with time. It is
demonstrated that the damping has no significant effects on domain growth laws
and large-scale domain structure. In contrast, small-scale domain structure is
affected by the damping. The difference in small-scale structure arises from
energy dissipation due to the damping. | 1602.06673v3 |
2023-06-22 | Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling | Understanding the origin of damping mechanisms in magnetization dynamics of
metallic ferromagnets is a fundamental problem for nonequilibrium many-body
physics of systems where quantum conduction electrons interact with localized
spins assumed to be governed by the classical Landau-Lifshitz-Gilbert (LLG)
equation. It is also of critical importance for applications, as damping
affects energy consumption and speed of spintronic and magnonic devices. Since
the 1970s, a variety of linear-response and scattering theory approaches have
been developed to produce widely used formulas for computation of
spatially-independent Gilbert scalar parameter as the magnitude of the Gilbert
damping term in the LLG equation. The largely unexploited for this purpose
Schwinger-Keldysh field theory (SKFT) offers additional possibilities, such as
to rigorously derive an extended LLG equation by integrating quantum electrons
out. Here we derive such equation whose Gilbert damping for metallic
ferromagnets is nonlocal, i.e., dependent on all localized spins at a given
time, and nonuniform, even if all localized spins are collinear and spin-orbit
coupling (SOC) is absent. This is in sharp contrast to standard lore, where
nonlocal damping is considered to emerge only if localized spins are
noncollinear; for such situations, direct comparison on the example of magnetic
domain wall shows that SKFT-derived nonlocal damping is an order of magnitude
larger than the previously considered one. Switching on SOC makes such nonlocal
damping anisotropic, in contrast to standard lore where SOC is usually
necessary to obtain nonzero Gilbert damping scalar parameter. Our analytical
formulas, with their nonlocality being more prominent in low spatial
dimensions, are fully corroborated by numerically exact quantum-classical
simulations. | 2306.13013v4 |
2014-12-12 | Spin waves in micro-structured yttrium iron garnet nanometer-thick films | We investigated the spin-wave propagation in a micro-structured yttrium iron
garnet waveguide of $40$ nm thickness. Utilizing spatially-resolved Brillouin
light scattering microscopy, an exponential decay of the spin-wave amplitude of
$(10.06 \pm 0.83)$ $\mu$m was observed. This leads to an estimated Gilbert
damping constant of $\alpha=(8.79\pm 0.73)\times 10^{-4}$, which is larger than
damping values obtained through ferromagnetic resonance measurements in
unstructured films. The theoretically calculated spatial interference of
waveguide modes was compared to the spin-wave pattern observed experimentally
by means of Brillouin light scattering spectroscopy. | 1412.4032v1 |
2017-06-05 | Consistent microscopic analysis of spin pumping effects | We present a consistent microscopic study of spin pumping effects for both
metallic and insulating ferromagnets. As for metallic case, we present a simple
quantum mechanical picture of the effect as due to the electron spin flip as a
result of a nonadiabatic (off-diagonal) spin gauge field. The effect of
interface spin-orbit interaction is briefly discussed. We also carry out
field-theoretic calculation to discuss on the equal footing the spin current
generation and torque effects such as enhanced Gilbert damping constant and
shift of precession frequency both in metallic and insulating cases. For thick
ferromagnetic metal, our study reproduces results of previous theories such as
the correspondence between the dc component of the spin current and enhancement
of the damping. For thin metal and insulator, the relation turns out to be
modified. For the insulating case, driven locally by interface $sd$ exchange
interaction due to magnetic proximity effect, physical mechanism is distinct
from the metallic case. Further study of proximity effect and interface
spin-orbit interaction would be crucial to interpret experimental results in
particular for insulators. | 1706.01185v1 |
2019-05-30 | Predicting New Iron Garnet Thin Films with Perpendicular Magnetic Anisotropy | Perpendicular magnetic anisotropy (PMA) is a necessary condition for many
spintronic applications like spin-orbit torques switching, logic and memory
devices. An important class of magnetic insulators with low Gilbert damping at
room temperature are iron garnets, which only have a few PMA types such as
terbium and samarium iron garnet. More and stable PMA garnet options are
necessary for researchers to be able to investigate new spintronic phenomena.
In this study, we predict 20 new substrate/magnetic iron garnet film pairs with
stable PMA at room temperature. The effective anisotropy energies of 10
different garnet films that are lattice-matched to 5 different commercially
available garnet substrates have been calculated using shape, magnetoelastic
and magnetocrystalline anisotropy terms. Strain type, tensile or compressive
depending on substrate choice, as well as the sign and the magnitude of the
magnetostriction constants of garnets determine if a garnet film may possess
PMA. We show the conditions in which Samarium, Gadolinium, Terbium, Holmium,
Dysprosium and Thulium garnets may possess PMA on the investigated garnet
substrate types. Guidelines for obtaining garnet films with low damping are
presented. New PMA garnet films with tunable saturation moment and field may
improve spin-orbit torque memory and compensated magnonic thin film devices. | 1905.13042v1 |
2019-07-17 | Inhomogeneous domain walls in spintronic nanowires | In case of a spin-polarized current, the magnetization dynamics in nanowires
are governed by the classical Landau-Lifschitz equation with Gilbert damping
term, augmented by a typically non-variational Slonczewski term. Taking axial
symmetry into account, we study the existence of domain wall type coherent
structure solutions, with focus on one space dimension and spin-polarization,
but our results also apply to vanishing spin-torque term. Using methods from
bifurcation theory for arbitrary constant applied fields, we prove the
existence of domain walls with non-trivial azimuthal profile, referred to as
inhomogeneous. We present an apparently new type of domain wall, referred to as
non-flat, whose approach of the axial magnetization has a certain oscillatory
character. Additionally, we present the leading order mechanism for the
parameter selection of flat and non-flat inhomogeneous domain walls for an
applied field below a threshold, which depends on anisotropy, damping, and
spin-transfer. Moreover, numerical continuation results of all these domain
wall solutions are presented. | 1907.07470v2 |
2021-11-16 | Ultrathin ferrimagnetic GdFeCo films with very low damping | Ferromagnetic materials dominate as the magnetically active element in
spintronic devices, but come with drawbacks such as large stray fields, and low
operational frequencies. Compensated ferrimagnets provide an alternative as
they combine the ultrafast magnetization dynamics of antiferromagnets with a
ferromagnet-like spin-orbit-torque (SOT) behavior. However to use ferrimagnets
in spintronic devices their advantageous properties must be retained also in
ultrathin films (t < 10 nm). In this study, ferrimagnetic Gdx(Fe87.5Co12.5)1-x
thin films in the thickness range t = 2-20 nm were grown on high resistance
Si(100) substrates and studied using broadband ferromagnetic resonance
measurements at room temperature. By tuning their stoichiometry, a nearly
compensated behavior is observed in 2 nm Gdx(Fe87.5Co12.5)1-x ultrathin films
for the first time, with an effective magnetization of Meff = 0.02 T and a low
effective Gilbert damping constant of {\alpha} = 0.0078, comparable to the
lowest values reported so far in 30 nm films. These results show great promise
for the development of ultrafast and energy efficient ferrimagnetic spintronic
devices. | 2111.08768v1 |
2021-11-30 | First and second order magnetic anisotropy and damping of europium iron garnet under high strain | Understanding and tailoring static and dynamic properties of magnetic
insulator thin films is important for spintronic device applications. Here, we
grow atomically flat epitaxial europium iron garnet (EuIG) thin films by pulsed
laser deposition on (111)-oriented garnet substrates with a range of lattice
parameters. By controlling the lattice mismatch between EuIG and the
substrates, we tune the strain in EuIG films from compressive to tensile
regime, which is characterized by X-ray diffraction. Using ferromagnetic
resonance, we find that in addition to the first-order perpendicular magnetic
anisotropy which depends linearly on the strain, there is a significant
second-order one that has a quadratic strain dependence. Inhomogeneous
linewidth of the ferromagnetic resonance increases notably with increasing
strain, while the Gilbert damping parameter remains nearly constant (~
2x10^-2). These results provide valuable insight into the spin dynamics in
ferrimagnetic insulators and useful guidance for material synthesis and
engineering of next-generation spintronics applications. | 2111.15142v1 |
2011-11-18 | Charge and Spin Transport in Magnetic Tunnel Junctions: Microscopic Theory | We study the charge and spin currents passing through a magnetic tunnel
junction (MTJ) on the basis of a tight-binding model. The currents are
evaluated perturbatively with respect to the tunnel Hamiltonian. The charge
current has the form $A[\bm M_1(t)\times\dot{\bm M}_1(t)]\cdot\bm M_2+B\dot{\bm
M}_1(t)\cdot\bm M_2$, where $\bm M_1(t)$ and $\bm M_2$ denote the directions of
the magnetization in the free layer and fixed layer, respectively. The constant
$A$ vanishes when one or both layers are insulators, {while the constant $B$
disappears when both layers are insulators or the same ferromagnets.} The first
term in the expression for charge current represents dissipation driven by the
effective electric field induced by the dynamic magnetization. In addition,
from an investigation of the spin current, we obtain the microscopic expression
for the enhanced Gilbert damping constant $\varDelta \alpha$. We show that
$\varDelta\alpha$ is proportional to the tunnel conductance and depends on the
bias voltage. | 1111.4295v2 |
2017-05-21 | Dynamical depinning of chiral domain walls | The domain wall depinning field represents the minimum magnetic field needed
to move a domain wall, typically pinned by samples' disorder or patterned
constrictions. Conventionally, such field is considered independent on the
Gilbert damping since it is assumed to be the field at which the Zeeman energy
equals the pinning energy barrier (both damping independent). Here, we analyse
numerically the domain wall depinning field as function of the Gilbert damping
in a system with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya
interaction. Contrary to expectations, we find that the depinning field depends
on the Gilbert damping and that it strongly decreases for small damping
parameters. We explain this dependence with a simple one-dimensional model and
we show that the reduction of the depinning field is related to the internal
domain wall dynamics, proportional to the Dzyaloshinskii-Moriya interaction,
and the finite size of the pinning barriers. | 1705.07489v2 |
2019-01-07 | Giant anisotropy of Gilbert damping in epitaxial CoFe films | Tailoring Gilbert damping of metallic ferromagnetic thin films is one of the
central interests in spintronics applications. Here we report a giant Gilbert
damping anisotropy in epitaxial Co$_{50}$Fe$_{50}$ thin film with a
maximum-minimum damping ratio of 400 \%, determined by broadband spin-torque as
well as inductive ferromagnetic resonance. We conclude that the origin of this
damping anisotropy is the variation of the spin orbit coupling for different
magnetization orientations in the cubic lattice, which is further corroborate
from the magnitude of the anisotropic magnetoresistance in Co$_{50}$Fe$_{50}$. | 1901.01941v1 |
2019-11-02 | Tuning Non-Gilbert-type damping in FeGa films on MgO(001) via oblique deposition | The ability to tailor the damping factor is essential for spintronic and
spin-torque applications. Here, we report an approach to manipulate the damping
factor of FeGa/MgO(001) films by oblique deposition. Owing to the defects at
the surface or interface in thin films, two-magnon scattering (TMS) acts as a
non-Gilbert damping mechanism in magnetization relaxation. In this work, the
contribution of TMS was characterized by in-plane angular dependent
ferromagnetic resonance (FMR). It is demonstrated that the intrinsic Gilbert
damping is isotropic and invariant, while the extrinsic mechanism related to
TMS is anisotropic and can be tuned by oblique deposition. Furthermore, the two
and fourfold TMS related to the uniaxial magnetic anisotropy (UMA) and
magnetocrystalline anisotropy were discussed. Our results open an avenue to
manipulate magnetization relaxation in spintronic devices. | 1911.00728v1 |
2001-10-11 | Enhanced Gilbert Damping in Thin Ferromagnetic Films | Using a scattering matrix approach, the precession of the magnetization of a
ferromagnet is shown to transfer spins into adjacent normal metal layers. This
``pumping'' of spins slows down the precession corresponding to an enhanced
Gilbert damping factor in the Landau-Lifshitz equation. The damping is
expressed in terms of the scattering matrix of the ferromagnet-normal metal
interface, which is accessible to model and first-principles calculations. Our
estimates for permalloy thin films explain the trends observed in recent
experiments. | 0110247v2 |
2002-02-11 | Radiation Induced Landau-Lifshitz-Gilbert Damping in Ferromagnets | The Landau-Lifshitz-Gilbert damping coefficient employed in the analysis of
spin wave ferromagnetic resonance is related to the electrical conductivity of
the sample. The changing magnetization (with time) radiates electromagnetic
fields. The electromagnetic energy is then absorbed by the sample and the
resulting heating effect describes magnetic dissipative damping. The
ferromagnetic resonance relaxation rate theoretically depends on the geometry
(shape and size) of the sample as well as temperature in agreement with
experiment. | 0202181v1 |
2006-01-10 | Voltage dependence of Landau-Lifshitz-Gilbert damping of a spin in a current driven tunnel junction | We present a theory of Landau-Lifshitz-Gilbert damping $\alpha$ for a
localized spin ${\vec S}$ in the junction coupled to the conduction electrons
in both leads under an applied volatege $V$. We find the voltage dependence of
the damping term reflecting the energy dependence of the density of states. We
find the effect is linear in the voltage and cotrolled by particle-hole
asymmetry of the leads. | 0601185v1 |
2015-02-06 | Microscopic theory of Gilbert damping in metallic ferromagnets | We present a microscopic theory for magnetization relaxation in metallic
ferromagnets of nanoscopic dimensions that is based on the dynamic spin
response matrix in the presence of spin-orbit coupling. Our approach allows the
calculation of the spin excitation damping rate even for perfectly crystalline
systems, where existing microscopic approaches fail. We demonstrate that the
relaxation properties are not completely determined by the transverse
susceptibility alone, and that the damping rate has a non-negligible frequency
dependence in experimentally relevant situations. Our results indicate that the
standard Landau-Lifshitz-Gilbert phenomenology is not always appropriate to
describe spin dynamics of metallic nanostructure in the presence of strong
spin-orbit coupling. | 1502.02068v1 |
2011-09-22 | Hole spin relaxation and coefficients in Landau-Lifshitz-Gilbert equation in ferromagnetic GaMnAs | We investigate the temperature dependence of the coefficients in the
Landau-Lifshitz-Gilbert equation in ferromagnetic GaMnAs by employing the Zener
model. We first calculate the hole spin relaxation time based on the
microscopic kinetic equation. We find that the hole spin relaxation time is
typically several tens femtoseconds and can present a nonmonotonic temperature
dependence due to the variation of the interband spin mixing, influenced by the
temperature related Zeeman splitting. With the hole spin relaxation time, we
are able to calculate the coefficients in the Landau-Lifshitz-Gilbert equation,
such as the Gilbert damping, nonadiabatic spin torque, spin stiffness and
vertical spin stiffness coefficients. We find that the nonadiabatic spin torque
coefficient $\beta$ is around $0.1\sim 0.3$ at low temperature, which is
consistent with the experiment [Adam {\em et al.}, Phys. Rev. B {\bf 80},
193204 (2009)]. As the temperature increases, $\beta$ monotonically increases
and can exceed one in the vicinity of the Curie temperature. In the low
temperature regime with $\beta<1$, the Gilbert damping coefficient $\alpha$
increases with temperature, showing good agreement with the experiments [Sinova
{\em et al.}, Phys. Rev. B {\bf 69}, 085209 (2004); Khazen {\em et al.}, {\em
ibid.} {\bf 78}, 195210 (2008)]. Furthermore, we predict that $\alpha$
decreases with increasing temperature once $\beta>1$ near the Curie
temperature. We also find that the spin stiffness decreases with increasing
temperature, especially near the Curie temperature due to the modification of
the finite $\beta$. Similar to the Gilbert damping, the vertical spin stiffness
coefficient is also found to be nonmonotonically dependent on the temperature. | 1109.4964v1 |
2011-04-08 | Magnetization Dissipation in Ferromagnets from Scattering Theory | The magnetization dynamics of ferromagnets are often formulated in terms of
the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation
describes the response of the magnetization in terms of effective fields,
whereas the dissipative part is parameterized by the Gilbert damping tensor. We
formulate a scattering theory for the magnetization dynamics and map this
description on the linearized LLG equation by attaching electric contacts to
the ferromagnet. The reactive part can then be expressed in terms of the static
scattering matrix. The dissipative contribution to the low-frequency
magnetization dynamics can be described as an adiabatic energy pumping process
to the electronic subsystem by the time-dependent magnetization. The Gilbert
damping tensor depends on the time derivative of the scattering matrix as a
function of the magnetization direction. By the fluctuation-dissipation
theorem, the fluctuations of the effective fields can also be formulated in
terms of the quasistatic scattering matrix. The theory is formulated for
general magnetization textures and worked out for monodomain precessions and
domain wall motions. We prove that the Gilbert damping from scattering theory
is identical to the result obtained by the Kubo formalism. | 1104.1625v1 |
2022-02-12 | Generalization of the Landau-Lifshitz-Gilbert equation by multi-body contributions to Gilbert damping for non-collinear magnets | We propose a systematic and sequential expansion of the
Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert
damping tensor on the angle between magnetic moments, which arises from
multi-body scattering processes. The tensor consists of a damping-like term and
a correction to the gyromagnetic ratio. Based on electronic structure theory,
both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral
and scalar-chiral products of magnetic moments: $\vec{e}_i\cdot\vec{e}_j$,
$(\vec{n}_{ij}\cdot\vec{e}_i)(\vec{n}_{ij}\cdot\vec{e}_j)$,
$\vec{n}_{ij}\cdot(\vec{e}_i\times\vec{e}_j)$, $(\vec{e}_i\cdot\vec{e}_j)^2$,
$\vec{e}_i\cdot(\vec{e}_j\times\vec{e}_k)$..., where some terms are subjected
to the spin-orbit field $\vec{n}_{ij}$ in first and second order. We explore
the magnitude of the different contributions using both the Alexander-Anderson
model and time-dependent density functional theory in magnetic adatoms and
dimers deposited on Au(111) surface. | 2202.06154v1 |
2022-11-23 | The fractional Landau-Lifshitz-Gilbert equation | The dynamics of a magnetic moment or spin are of high interest to
applications in technology. Dissipation in these systems is therefore of
importance for improvement of efficiency of devices, such as the ones proposed
in spintronics. A large spin in a magnetic field is widely assumed to be
described by the Landau-Lifshitz-Gilbert (LLG) equation, which includes a
phenomenological Gilbert damping. Here, we couple a large spin to a bath and
derive a generic (non-)Ohmic damping term for the low-frequency range using a
Caldeira-Leggett model. This leads to a fractional LLG equation, where the
first-order derivative Gilbert damping is replaced by a fractional derivative
of order $s \ge 0$. We show that the parameter $s$ can be determined from a
ferromagnetic resonance experiment, where the resonance frequency and linewidth
no longer scale linearly with the effective field strength. | 2211.12889v1 |
2018-05-04 | Effective damping enhancement in noncollinear spin structures | Damping mechanisms in magnetic systems determine the lifetime, diffusion and
transport properties of magnons, domain walls, magnetic vortices, and
skyrmions. Based on the phenomenological Landau-Lifshitz-Gilbert equation, here
the effective damping parameter in noncollinear magnetic systems is determined
describing the linewidth in resonance experiments or the decay parameter in
time-resolved measurements. It is shown how the effective damping can be
calculated from the elliptic polarization of magnons, arising due to the
noncollinear spin arrangement. It is concluded that the effective damping is
larger than the Gilbert damping, and it may significantly differ between
excitation modes. Numerical results for the effective damping are presented for
the localized magnons in isolated skyrmions, with parameters based on the
Pd/Fe/Ir(111) model-type system. | 1805.01815v2 |
2017-01-12 | Dynamic coupling of ferromagnets via spin Hall magnetoresistance | The synchronized magnetization dynamics in ferromagnets on a nonmagnetic
heavy metal caused by the spin Hall effect is investigated theoretically. The
direct and inverse spin Hall effects near the ferromagnetic/nonmagnetic
interface generate longitudinal and transverse electric currents. The
phenomenon is known as the spin Hall magnetoresistance effect, whose magnitude
depends on the magnetization direction in the ferromagnet due to the spin
transfer effect. When another ferromagnet is placed onto the same nonmagnet,
these currents are again converted to the spin current by the spin Hall effect
and excite the spin torque to this additional ferromagnet, resulting in the
excitation of the coupled motions of the magnetizations. The in-phase or
antiphase synchronization of the magnetization oscillations, depending on the
value of the Gilbert damping constant and the field-like torque strength, is
found in the transverse geometry by solving the Landau-Lifshitz-Gilbert
equation numerically. On the other hand, in addition to these synchronizations,
the synchronization having a phase difference of a quarter of a period is also
found in the longitudinal geometry. The analytical theory clarifying the
relation among the current, frequency, and phase difference is also developed,
where it is shown that the phase differences observed in the numerical
simulations correspond to that giving the fixed points of the energy supplied
by the coupling torque. | 1701.03201v2 |
2023-12-14 | Nonlocal damping of spin waves in a magnetic insulator induced by normal, heavy, or altermagnetic metallic overlayer: a Schwinger-Keldysh field theory approach | Understanding spin wave (SW) damping, and how to control it to the point of
being able to amplify SW-mediated signals, is one of the key requirements to
bring the envisaged magnonic technologies to fruition. Even widely used
magnetic insulators with low magnetization damping in their bulk, such as
yttrium iron garnet, exhibit 100-fold increase in SW damping due to inevitable
contact with metallic layers in magnonic circuits, as observed in very recent
experiments [I. Bertelli et al., Adv. Quantum Technol. 4, 2100094 (2021)]
mapping SW damping in spatially-resolved fashion. Here, we provide microscopic
and rigorous understanding of wavevector-dependent SW damping using extended
Landau-Lifshitz-Gilbert equation with nonlocal damping tensor, instead of
conventional local scalar Gilbert damping, as derived from Schwinger-Keldysh
nonequilibrium quantum field theory. In this picture, the origin of nonlocal
magnetization damping and thereby induced wavevector-dependent SW damping is
interaction of localized magnetic moments of magnetic insulator with conduction
electrons from the examined three different types of metallic overlayers --
normal, heavy, and altermagnetic. Due to spin-split energy-momentum dispersion
of conduction electrons in the latter two cases, the nonlocal damping is
anisotropic in spin and space, and it can be dramatically reduced by changing
the relative orientation of the two layers when compared to the usage of normal
metal overlayer. | 2312.09140v1 |
2006-04-21 | Dynamic approach for micromagnetics close to the Curie temperature | In conventional micromagnetism magnetic domain configurations are calculated
based on a continuum theory for the magnetization which is assumed to be of
constant length in time and space. Dynamics is usually described with the
Landau-Lifshitz-Gilbert (LLG) equation the stochastic variant of which includes
finite temperatures. Using simulation techniques with atomistic resolution we
show that this conventional micromagnetic approach fails for higher
temperatures since we find two effects which cannot be described in terms of
the LLG equation: i) an enhanced damping when approaching the Curie temperature
and, ii) a magnetization magnitude that is not constant in time. We show,
however, that both of these effects are naturally described by the
Landau-Lifshitz-Bloch equation which links the LLG equation with the theory of
critical phenomena and turns out to be a more realistic equation for
magnetization dynamics at elevated temperatures. | 0604508v1 |
2017-03-20 | Relativistic theory of magnetic inertia in ultrafast spin dynamics | The influence of possible magnetic inertia effects has recently drawn
attention in ultrafast magnetization dynamics and switching. Here we derive
rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on
the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen
transformation up to the order of $1/c^4$ gives the intrinsic inertia of a pure
system through the 2$^{\rm nd}$ order time-derivative of magnetization in the
dynamical equation of motion. Thus, the inertial damping $\mathcal{I}$ is a
higher order spin-orbit coupling effect, $\sim 1/c^4$, as compared to the
Gilbert damping $\Gamma$ that is of order $1/c^2$. Inertia is therefore
expected to play a role only on ultrashort timescales (sub-picoseconds). We
also show that the Gilbert damping and inertial damping are related to one
another through the imaginary and real parts of the magnetic susceptibility
tensor respectively. | 1704.01559v1 |
2020-06-30 | Negative Gilbert damping in cavity optomagnonics | Exceptional point (EP) associated with the parity-time (PT) symmetry breaking
is receiving considerable recent attention by the broad physics community. By
introducing balanced gain and loss, it has been realized in photonic, acoustic,
and electronic structures. However, the observation of magnonic EP remains
elusive. The major challenge is to experimentally generate the negative Gilbert
damping, which was thought to be highly unlikely but is demanded by the PT
symmetry. In this work, we study the magneto-optical interaction of
circularly-polarized lasers with a submicron magnet placed in an optical
cavity. We show that the off-resonant coupling between the driving laser and
cavity photon in the far-blue detuning can induce the magnetic gain (or
negative damping) exactly of the Gilbert type. A hyperbolic-tangent function
ansatz is found to well describe the time-resolved spin switching as the
intrinsic magnetization dissipation is overcome. When the optically pumped
magnet interacts with a purely lossy one, we observe a phase transition from
the imbalanced to passive PT symmetries by varying the detuning coeffcient. Our
findings provide a feasible way to manipulate the sign of the magnetic damping
parameter and to realize the EP in cavity optomagnonics. | 2006.16510v1 |
2023-05-16 | Non-Hermitian Casimir Effect of Magnons | There has been a growing interest in non-Hermitian quantum mechanics. The key
concepts of quantum mechanics are quantum fluctuations. Quantum fluctuations of
quantum fields confined in a finite-size system induce the zero-point energy
shift. This quantum phenomenon, the Casimir effect, is one of the most striking
phenomena of quantum mechanics in the sense that there are no classical analogs
and has been attracting much attention beyond the hierarchy of energy scales,
ranging from elementary particle physics to condensed matter physics, together
with photonics. However, the non-Hermitian extension of the Casimir effect and
the application to spintronics have not yet been investigated enough, although
exploring energy sources and developing energy-efficient nanodevices are its
central issues. Here we fill this gap. By developing a magnonic analog of the
Casimir effect into non-Hermitian systems, we show that this non-Hermitian
Casimir effect of magnons is enhanced as the Gilbert damping constant (i.e.,
the energy dissipation rate) increases. When the damping constant exceeds a
critical value, the non-Hermitian Casimir effect of magnons exhibits an
oscillating behavior, including a beating one, as a function of the film
thickness and is characterized by the exceptional point. Our result suggests
that energy dissipation serves as a key ingredient of Casimir engineering. | 2305.09231v1 |
2014-04-05 | Gilbert damping in noncollinear ferromagnets | The precession and damping of a collinear magnetization displaced from its
equilibrium are described by the Landau-Lifshitz-Gilbert equation. For a
noncollinear magnetization, it is not known how the damping should be
described. We use first-principles scattering theory to investigate the damping
in one-dimensional transverse domain walls (DWs) of the important ferromagnetic
alloy Ni$_{80}$Fe$_{20}$ and interpret the results in terms of phenomenological
models. The damping is found to depend not only on the magnetization texture
but also on the specific dynamic modes of Bloch and N\'eel DWs. Even in the
highly disordered Ni$_{80}$Fe$_{20}$ alloy, the damping is found to be
remarkably nonlocal. | 1404.1488v2 |
2023-08-14 | Temperature Evolution of Magnon Propagation Length in Tm$_3$Fe$_5$O$_{12}$ Thin Films: Roles of Magnetic Anisotropy and Gilbert Damping | The magnon propagation length ($\langle\xi\rangle$) of a ferro/ferrimagnet
(FM) is one of the key factors that controls the generation and propagation of
thermally-driven spin current in FM/heavy metal (HM) bilayer based
spincaloritronic devices. Theory predicts that for the FM layer,
$\langle\xi\rangle$ is inversely proportional to the Gilbert damping ($\alpha$)
and the square root of the effective magnetic anisotropy constant ($K_{\rm
eff}$). However, direct experimental evidence of this relationship is lacking.
To experimentally confirm this prediction, we employ a combination of
longitudinal spin Seebeck effect (LSSE), transverse susceptibility, and
ferromagnetic resonance experiments to investigate the temperature evolution of
$\langle\xi\rangle$ and establish its correlation with the effective magnetic
anisotropy field, $H_K^{\rm eff}$ ($\propto K_{\rm eff}$) and $\alpha$ in
Tm$_3$Fe$_5$O$_{12}$ (TmIG)/Pt bilayers. We observe concurrent drops in the
LSSE voltage and $\langle\xi\rangle$ below 200$^\circ$K in TmIG/Pt bilayers
regardless of TmIG film thickness and substrate choice and attribute it to the
noticeable increases in $H_K^{\rm eff}$ and $\alpha$ that occur within the same
temperature range. From the TmIG thickness dependence of the LSSE voltage, we
determined the temperature dependence of $\langle\xi\rangle$ and highlighted
its correlation with the temperature-dependent $H_K^{\rm eff}$ and $\alpha$ in
TmIG/Pt bilayers, which will be beneficial for the development of rare-earth
iron garnet-based efficient spincaloritronic nanodevices. | 2308.07236v3 |
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