Using first-principles methods based on density-functional theory we investigate the spin relaxation in W(001) ultrathin films. Within the framework of the Elliott-Yafet theory we calculate the spin mixing of the Bloch states and we explicitly consider spin-flip scattering off self-adatoms. We find an oscillatory behavior of the spin-mixing parameter and relaxation rate as a function of the film thickness, which we trace back tosurface-state properties. We also analyze the Rashba effect experienced by the surface states and discuss its influence on the spin relaxation. Finally we calculate the anisotropy of the spin-relaxation rate with respect to the polarization direction of the excited spin population relative to the crystallographic axes of thefilm. We find that the spin-relaxation rate can increase by as much as 47% when the spin polarization is directed out of plane, compared to the case when it is in plane. Our calculations are based on the multiple-scattering formalism of the Korringa-Kohn-Rostoker Green-function method.
We extend our recent result for the spin-relaxation time due to acoustic electron-phonon scattering in degenerate bands with spin mixing [New J. Phys. 18, 023012 (2015)] to include interactions with optical phonons, and present a numerical evaluation of the spin-relaxation time for intraband hole-phonon scattering in the heavy-hole (HH) bands of bulk GaAs. Comparing our computed spin-relaxation times to the conventional Elliott-Yafet result quantitatively demonstrates that the latter underestimates the spin-relaxation time because it does not correctly describe how electron-phonon interactions…
We analyze spin-dependent carrier dynamics due to incoherent electron-phonon scattering, which is commonly referred to as Elliott-Yafet (EY) spin-relaxation mechanism. For this mechanism one usually distinguishes two contributions: (1) from the electrostatic interaction together with spin-mixing in the wave functions, which is often called the Elliott contribution, and (2) the phonon-modulated spin-orbit interaction, which is often called the Yafet or Overhauser contribution. By computing the reduced electronic density matrix, we improve Yafet's original calculation, which is not valid for pro…
In contrast to the long-known fact that spin-flip hot spots, i.e., special \vc{k}-points on the Fermi surface showing a high spin-mixing parameter, do not occur in the bulk of monovalent (noble and alkali) metals, we found them on the surface Brillouin-zone boundary of ultrathin films of these metals. Density-functional calculations within the Korringa-Kohn-Rostoker Green function method for ultrathin (001) oriented Cu, Ag, and Au films of 10-layer thickness show that the region around the hot spots can have a substantial contribution, e.g.\ 52\% in Au(001), to the integrated spin-mixing param…
Temperature dependent electron spin resonance (ESR) measurements are reported on stage 1 potassium doped graphite, a model system of biased graphene. The ESR linewidth is nearly isotropic and although the g-factor has a sizeable anisotropy, its majority is shown to arise due to macroscopic magnetization. Albeit the homogeneous ESR linewidth shows an unusual, non-linear temperature dependence, it appears to be proportional to the resistivity which is a quadratic function of the temperature. These observations suggests the validity of the Elliott-Yafet relaxation mechanism in KC8 and allows to p…
We present a first-principles approach for computing the phonon-limited $T_1$ spin relaxation time due to the Elliot-Yafet mechanism. Our scheme combines fully-relativistic spin-flip electron-phonon interactions with an approach to compute the effective spin of band electrons in materials with inversion symmetry. We apply our method to silicon and diamond, for which we compute the temperature dependence of the spin relaxation times and analyze the contributions to spin relaxation from different phonons and valley processes. The computed spin relaxation times in silicon are in excellent agreeme…
Aiming to understand the main spin relaxation mechanism in graphene, we investigate the spin relaxation with random Rashba field induced by both adatoms and substrate, by means of the kinetic spin Bloch equation approach. The charged adatoms on one hand enhance the Rashba spin-orbit coupling locally and on the other hand serve as Coulomb potential scatterers. Both effects contribute to spin relaxation limited by the D'yakonov-Perel' mechanism. In addition, the random Rashba field also causes spin relaxation by spin-flip scattering, manifesting itself as an Elliott-Yafet--like mechanism. Both m…
The Elliott-Yafet mechanism is arguably the most promising candidate to explain the ultrafast demagnetization dynamics in ferromagnetic transition metals on timescales on the order of 100 femtoseconds. So far, only electron-phonon scattering has been analyzed as the scattering process needed to account for the demagnetization due to the Elliott-Yafet mechanism. We show for the first time that the electron-electron scattering contribution to the Elliott-Yafet mechanism has the potential to explain time-resolved magneto-optical Kerr effect measurements on thin magnetic cobalt and nickel films, w…
The spin relaxation induced by the Elliott-Yafet mechanism and the extrinsic spin Hall conductivity due to the skew-scattering are investigated in 5d transition-metal ultrathin films with self-adatom impurities as scatterers. The values of the Elliott-Yafet parameter and of the spin-flip relaxation rate reveal a correlation with each other that is in agreement with the Elliott approximation. At 10-layer thickness, the spin-flip relaxation time in 5d transition-metal films is quantitatively reported about few hundred nanoseconds at atomic percent which is one and two orders of magnitude shorter…
Hole spin relaxation in $p$-type (111) GaAs quantum wells is investigated in the case with only the lowest hole subband, which is heavy-hole like in (111) GaAs/AlAs and light-hole like in (111) GaAs/InP quantum wells, being relevant. The subband Löwdin perturbation method is applied to obtain the effective Hamiltonian including the Dresselhaus and Rashba spin-orbit couplings. Under a proper gate voltage, the total in-plane effective magnetic field in (111) GaAs/AlAs quantum wells can be strongly suppressed in the whole momentum space, while the one in (111) GaAs/InP quantum wells can be suppre…
We theoretically investigate spin-dependent carrier dynamics due to the electron-phonon interaction after ultrafast optical excitation in ferromagnetic metals. We calculate the electron-phonon matrix elements including the spin-orbit interaction in the electronic wave functions and the interaction potential. Using the matrix elements in Boltzmann scattering integrals, the momentum-resolved carrier distributions are obtained by solving their equation of motion numerically. We find that the optical excitation with realistic laser intensities alone leads to a negligible magnetization change, and …
A unique spin depolarization mechanism, induced by the presence of g-factor anisotropy and intervalley scattering, is revealed by spin transport measurements on long-distance germanium devices in a longitudinal magnetic field. The confluence of electron-phonon scattering (leading to Elliott-Yafet spin flips) and this previously unobserved physics enables the extraction of spin lifetime solely from spin-valve measurements, without spin precession, and in a regime of substantial electric-field-generated carrier heating. We find spin lifetimes in Ge up to several hundreds of ns at low temperature…
A realistic pseudopotential model is introduced to investigate the phonon-induced spin relaxation of conduction electrons in bulk silicon. We find a surprisingly subtle interference of the Elliott and Yafet processes affecting the spin relaxation over a wide temperature range, suppressing the significance of the intravalley spin-flip scattering, previously considered dominant, above roughly 120 K. The calculated spin relaxation times $T_1$ agree with the spin resonance and spin injection data, following a $T^{-3}$ temperature dependence. The valley anisotropy of $T_1$ and the spin relaxation r…
We report the first experimental demonstration of room-temperature spin transport in n-type Ge epilayers grown on a Si(001) substrate. By utilizing spin pumping under ferromagnetic resonance, which inherently endows a spin battery function for semiconductors connected with the ferromagnet, a pure spin current is generated in the n-Ge at room temperature. The pure spin current is detected by using the inverse spin Hall effect of either Pt or Pd electrode on the n-Ge. A theoretical model including a geometrical contribution allows to estimate a spin diffusion length in n-Ge at room temperature t…
In this work, a scanning inverse spin Hall effect measurement system based on a shorted coaxial resonator has been built, which provides a high throughput method to characterize spin transport properties. The spin diffusion length of Ta at room temperature is determined via automatic measurements of Py/Ta bilayer strips with different thicknesses of Ta. The results show that the spin diffusion length is about 4 nm with a conductivity of about 7.5E5 Ω-1m-1, which leads to the conclusion that the intrinsic mechanism of spin relaxation of Ta is the Elliott-Yafet interactions. The setup developed …
We comment on the conclusion by Ma et al. [Appl. Phys. Lett. {\bf 94}, 241112 (2009)] that the Elliott-Yafet mechanism is more important than the D'yakonov-Perel' mechanism at high carrier density in intrinsic bulk CdTe at room temperature. We point out that the spin relaxation is solely from the D'yakonov-Perel' mechanism. The observed peak in the density dependence of spin relaxation time is exactly what we predicted in a recent work [Phys. Rev. B {\bf 79}, 125206 (2009)].
The concept of anisotropy of spin relaxation in non-magnetic metals with respect to the spin direction of the injected electrons relative to the crystal orientation is introduced. The effect is related to an anisotropy of the Elliott-Yafet parameter, arising from a modulation of the decomposition of the spin-orbit Hamiltonian into spin-conserving and spin-flip terms as the spin quantization axis is varied. This anisotropy, reaching gigantic values for uniaxial transition-metals (e.g. 830% for hcp Hf) as density-functional calculations show, is related to extended "spin-flip hot areas" on the F…
We investigate hole spin relaxation in intrinsic and $p$-type bulk GaAs from a fully microscopic kinetic spin Bloch equation approach. In contrast to the previous study on hole spin dynamics, we explicitly include the intraband coherence and the nonpolar hole-optical-phonon interaction, both of which are demonstrated to be of great importance to the hole spin relaxation. The relative contributions of the D'yakonov-Perel' and Elliott-Yafet mechanisms on hole spin relaxation are also analyzed. In our calculation, the screening constant, playing an important role in the hole spin relaxation, is t…
In tunnel junctions between ferromagnets and heavy elements with strong spin orbit coupling the magnetoresistance is often dominated by tunneling anisotropic magnetoresistance (TAMR). This makes conventional DC spin injection techniques impractical for determining the spin relaxation time ($τ_s$). Here, we show that this obstacle for measurements of $τ_s$ can be overcome by 2nd harmonic spin-injection-magnetoresistance (SIMR). In the 2nd harmonic signal the SIMR is comparable in magnitude to TAMR, thus enabling Hanle-induced SIMR as a powerful tool to directly determine $τ_s$. Using this appro…
First-principles calculations enable accurate predictions of electronic interactions and dynamics. However, computing the electron spin dynamics remains challenging. The spin-orbit interaction causes various dynamical phenomena that couple with phonons, such as spin precession and spin-flip e-ph scattering, which are difficult to describe with current first-principles calculations. In this work, we show a rigorous framework to study phonon-induced spin relaxation and decoherence, by computing the spin-spin correlation function and its vertex corrections due to e-ph interactions. We apply this …
Stripe width variation in ultrathin magnetic films is a well known phenomenon still not well understood. We analyze this problem considering a 2D Heisenberg model with ferromagnetic exchange interactions, dipolar interactions and perpendicular anisotropy, relevant e.g. in Fe/Cu(001) films. By extending a classic result of Yafet & Gyorgy (YG) and using Monte Carlo simulations we calculate the complete zero temperature phase diagram of the model. Through this calculation we analyze the correlation between domain walls structure and stripe width variation, as the perpendicular anisotropy changes.…
Through First-Principles real-time Density-Matrix (FPDM) dynamics simulations, we investigate spin relaxation due to electron-phonon and electron-impurity scatterings with spin-orbit coupling in two-dimensional Dirac materials - silicene and germanene, at finite temperatures and under external fields. We discussed the applicability of conventional descriptions of spin relaxation mechanisms by Elliott-Yafet (EY) and D'yakonov-Perel' (DP) compared to our FPDM method, which is determined by a complex interplay of intrinsic spin-orbit coupling, external fields, and electron-phonon coupling strengt…
The ultra-fast magnetisation relaxation rates during the laser-induced magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB) equation for different values of spin $S$. The LLB equation is equivalent in the limit $S \rightarrow \infty$ to the atomistic Landau-Lifshitz-Gilbert (LLG) Langevin dynamics and for $S=1/2$ to the M3TM model [B. Koopmans, {\em et al.} Nature Mat. \textbf{9} (2010) 259]. Within the LLB model the ultra-fast demagnetisation time ($τ_{M}$) and the transverse damping ($α_{\perp}$) are parameterized by the intrinsic coupling-to-the-bath parameter $λ$,…
The Fermi-surfaces and Elliott-Yafet spin-mixing parameter (EYP) of several elemental metals are studied by \emph{ab initio} calculations. We focus first on the anisotropy of the EYP as a function of the direction of the spin-quantization axis [Phys.~Rev.~Lett.\ \textbf{109}, 236603 (2012)]. We analyze in detail the origin of the gigantic anisotropy in $5d$ hcp metals as compared to $5d$ cubic metals by band-structure calculations and discuss the stability of our results against an applied magnetic field. We further present calculations of light (4$d$ and 3$d$) hcp crystals, where we find a hu…
We have studied spin relaxation characteristics in a Ag nanowire covered with various oxide layers of Bi2O3, Al2O3, HfO2, MgO or AgOx by using non-local spin valve structures. The spin-flip probability, a ratio of momentum relaxation time to spin relaxation time at 10 K, exhibits a gradual increase with an atomic number of the oxide constituent elements, Mg, Al, Ag and Hf. Surprisingly the Bi2O3 capping was found to increase the probability by an order of magnitude compared with other oxide layers. This finding suggests the presence of an additional spin relaxation mechanism such as Rashba eff…
Designing new quantum materials with long-lived electron spin states urgently requires a general theoretical formalism and computational technique to reliably predict intrinsic spin relaxation times. We present a new, accurate and universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate spin-phonon relaxation time ($τ_s$) of solids with arbitrary spin mixing and crystal symmetry. This method describes contributions of Elliott-Yafet (EY) and D'yakonov-Perel' (DP) mechanisms to spin relaxation for systems with and without inversion symmetry on an equa…
We report an anomalous scaling of the D'yakonov-Perel' spin relaxation with the momentum relaxation in semiconductor quantum wells under a strong magnetic field in the Voigt configuration. We focus on the case that the external magnetic field is perpendicular to the spin-orbit-coupling--induced effective magnetic field and its magnitude is much larger than the later one. It is found that the longitudinal spin relaxation time is proportional to the momentum relaxation time even in the strong scattering limit, indicating that the D'yakonov-Perel' spin relaxation shows the Elliott-Yafet-like beha…
Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film
Kyoto University（京都大学）；The Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Kobe University（神户大学）；Saitama University（埼玉大学）；Center for Spintronics Research Network (CSRN), Kyoto University（京都大学自旋电子学研究网络中心）；Osaka Metropolitan University（大阪公立大学）
We report a computational theoretical investigation of electron spin-flip scattering induced by the electron-phonon interaction in the transition-metal ferromagnets bcc Fe, fcc Co and fcc Ni. The Elliott-Yafet electron-phonon spin-flip scattering is computed from first-principles, employing a generalized spin-flip Eliashberg function as well as ab initio computed phonon dispersions. Aiming at investigating the amount of electron-phonon mediated demagnetization in femtosecond laser-excited ferromagnets, the formalism is extended to treat laser-created thermalized as well as nonequilibrium, nont…
We investigate the spin-dependent electron-phonon scatterings of the $L$ and $Γ$ valleys and the band structure near the conduction band minima in germanium. We first construct a $16\times16$ ${\bm k}\cdot{\bm p}$ Hamiltonian in the vicinity of the $L$ point in germanium, which ensures the correctness of the band structure of the lowest three conduction bands and highest two valence bands. This Hamiltonian facilitates the analysis of the spin-related properties of the conduction electrons. We then demonstrate the phonon-induced electron scatterings of the $L$ and $Γ$ valleys, i.e., the intra-$…
We present a microscopic calculation of magnetization damping for a magnetic "toy model." The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchan…
We present a generally applicable parameter-free first-principles method to determine electronic spin relaxation times and apply it to the technologically important group-IV materials silicon, diamond and graphite. We concentrate on the Elliott-Yafet mechanism, where spin relaxation is induced by momentum scattering off phonons and impurities. In silicon, we find a $\sim T^{-3}$ temperature dependence of the phonon-limited spin relaxation time T$_1$ and a value of 4.3 ns at room temperature, in agreement with experiments. For the phonon-dominated regime in diamond and graphite, we predict a st…
Spatiotemporal spin transport from first principles
Rensselaer Polytechnic Institute（伦斯勒理工学院）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；nOhm Devices, Inc.（nOhm 设备有限公司）；Catalan Institute of Nanoscience and Nanotechnology (ICN2)（加泰罗尼亚纳米科学与技术研究所）
The temperature evolution of spin relaxation time, τsf, in degenerate silicon (Si)-based lateral spin valves is investigated by means of the Hanle effect measurements. τsf at 300 K is estimated to be 1.68+-0.03 ns and monotonically increased with decreasing temperature down to 100 K. Below 100 K, in contrast, it shows almost a constant value of ca. 5 ns. The temperature dependence of the conductivity of the Si channel shows a similar behavior to that of the τsf, i.e., monotonically increasing with decreasing temperature down to 100 K and a weak temperature dependence below 100 K. The temperatu…
The ability to controllably manipulate the laser-induced ultrafast magnetic dynamics is a prerequisite for future high speed spintronic devices. The optimization of devices requires the controllability of the ultrafast demagnetization time, , and intrinsic Gilbert damping, . In previous attempts to establish the relationship between and , the rare-earth doping of a permalloy film with two different demagnetization mechanism is not a suitable candidate. Here, we choose Co/Ni bilayers to investigate the relations between and by means of time-resolved magneto-optical Kerr effect (TRMOKE) via adju…
Understanding the evolution of spin-orbit torque (SOT) with increasing heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical for the development of magnetic memory based on SOT. However, several experiments have revealed an apparent discrepancy between damping enhancement and damping-like SOT regarding their dependence on NM thickness. Here, using linewidth and phase-resolved amplitude analysis of vector network analyzer ferromagnetic resonance (VNA-FMR) measurements, we simultaneously extract damping enhancement and both field-like and damping-like inverse SOT in Ni$_…
