Nonadiabatic Spin-transfer Torque Research Articles

Spin transfer torque bias (STTB) due to domain wall resistance in an infinitely long ferromagnetic nanowire

The shift of a magnetization loop along the magnetic field axis for a ferromagnetic (FM)/anti-ferromagnetic (AFM) system when it is cooled through Néel temperature of AFM layer is called exchange anisotropy or exchange bias. Here, using micromagnetic simulations we propose that spin transfer torque (STT) mechanism would indeed be helpful in realizing the shift of the magnetization loop along magnetic field axis through domain wall (DW) resistance for an infinitely long FM nanowire without having AFM layer, which we call as spin transfer torque bias (STTB). Essentially, STTB is realized on both positive and negative magnetic field axes by varying the angle between spin polarized current and Zeeman field from 0° to 180° respectively and the origin is attributed to helical motion of the DW. However, we do not see STTB at 90° due to coherent rotation of domain. We also ascertain that STTB is also a function of magnetic anisotropy, current density, polarization strength and non-adiabatic STT term. Variation in STTB for different FM systems such as Fe2CoSi, Ni80Fe20 and Fe is attributed to a change in DW width. We believe that present results would lead to a new dimension in the field of spintronics.

Universality classes of the domain-wall creep motion driven by spin-transfer torques.

With the stochastic Landau-Lifshitz-Gilbert equation, we numerically simulate the creep motion of a magnetic domain wall driven by the adiabatic and nonadiabatic spin-transfer torques induced by the electric current. The creep exponent μ and the roughness exponent ζ are accurately determined from the scaling behaviors. The creep motions driven by the adiabatic and nonadiabatic spin-transfer torques belong to different universality classes. The scaling relation between μ and ζ based on certain simplified assumptions is valid for the nonadiabatic spin-transfer torque, while invalid for the adiabatic one. Our results are compatible with the experimental ones, but go beyond the existing theoretical prediction. Our investigation reveals that the disorder-induced pinning effect on the domain-wall rotation alters the universality class of the creep motion.

Current-induced spin-wave Doppler shift and attenuation in compensated ferrimagnets

We theoretically and numerically study current-induced modification of ferrimagnetic spin-wave dynamics when an electrical current generates adiabatic and nonadiabatic spin-transfer torques. We find that the sign of the Doppler shift depends on the spin-wave handedness because the sign of spin polarization carried by spin waves depends on the spin-wave handedness. It also depends on the sign of the adiabatic-torque coefficient, originating from unequal contributions from two sublattices. For a positive nonadiabaticity of spin current, the attenuation lengths of both right- and left-handed spin waves increase when electrons move in the same direction with spin-wave propagation. Our result establishes a way to simultaneously measure important material parameters of a ferrimagnet, such as angular momentum compensation point, spin polarization, and nonadiabaticity using current-induced control of ferrimagnetic spin-wave dynamics.

Numerical computation of spin-transfer torques for antiferromagnetic domain walls

We numerically compute current-induced spin-transfer torques for antiferromagnetic domain walls, based on a linear response theory in a tight-binding model. We find that, unlike for ferromagnetic domain wall motion, the contribution of adiabatic spin torque to antiferromagnetic domain wall motion is negligible, consistent with previous theories. As a result, the non-adiabatic spin-transfer torque is a main driving torque for antiferromagnetic domain wall motion. Moreover, the non-adiabatic spin-transfer torque for narrower antiferromagnetic domain walls increases more rapidly than that for ferromagnetic domain walls, which is attributed to the enhanced spin mistracking process for antiferromagnetic domain walls.

Three-Dimensional Dynamics of a Magnetic Hopfion Driven by Spin Transfer Torque.

Magnetic hopfion is a three-dimensional (3D) topological soliton with novel spin structure that would enable exotic dynamics. Here, we study the current-driven 3D dynamics of a magnetic hopfion with a unit Hopf index in a frustrated magnet. Attributed to the spin Berry phase and symmetry of the hopfion, the phase space entangles multiple collective coordinates, thus the hopfion exhibits rich dynamics including longitudinal motion along the current direction, transverse motion perpendicular to the current direction, rotational motion, and dilation. Furthermore, the characteristics of hopfion dynamics is determined by the ratio between the nonadiabatic spin transfer torque parameter and the damping parameter. Such peculiar 3D dynamics of magnetic hopfion could shed light on understanding the universal physics of hopfions in different systems and boost the prosperous development of 3D spintronics.

Spin-transfer torques for domain wall motion in antiferromagnetically coupled ferrimagnets

Antiferromagnetic materials are outstanding candidates for next generation spintronic applications, because their ultrafast spin dynamics makes it possible to realize several orders of magnitude higher-speed devices than conventional ferromagnetic materials1. Though spin-transfer torque (STT) is a key for electrical control of spins as successfully demonstrated in ferromagnetic spintronics, experimental understanding of STT in antiferromagnets has been still lacking despite a number of pertinent theoretical studies2-5. Here, we report experimental results on the effects of STT on domain-wall (DW) motion in antiferromagnetically-coupled ferrimagnets. We find that non-adiabatic STT acts like a staggered magnetic field and thus can drive DWs effectively. Moreover, the non-adiabaticity parameter {\beta} of STT is found to be significantly larger than the Gilbert damping parameter {\alpha}, challenging our conventional understanding of the non-adiabatic STT based on ferromagnets as well as leading to fast current-induced antiferromagnetic DW motion. Our study will lead to further vigorous exploration of STT for antiferromagnetic spin textures for fundamental physics on spin-charge interaction as wells for efficient electrical control of antiferromagnetic devices.

A new twist for spin torques in antiferromagnets

A large non-adiabatic spin-transfer torque in an antiferromagnetically coupled ferrimagnet can provide fast and efficient control of spin textures — and challenges current understanding of such effects.

Electrically-driven Domain Wall Motion in Quantum Anomalous Hall States

We theoretically study domain wall motion induced by an electric field in the quantum anomalous Hall states on a two-dimensional Kagome lattice with ferromagnetic order and spin-orbit coupling. We show that an electric charge is accumulated near the domain wall which indicates that the electric field drives both the accumulated charge and the domain wall with small energy dissipation. Using the linear response theory we compute the non-equilibrium spin density which exerts a non-adiabatic spin transfer torque on textures of the local magnetization. This torque emerges even when the bulk is insulating and does not require the longitudinal electric current. Finally, we estimate the velocity of domain wall motion in this system, which is faster than that in conventional metals.

Scaling of the Rashba spin-orbit torque in magnetic domain walls

Spin-orbit torque in magnetic domain walls was studied by solving the Pauli-Schrödinger equation for the itinerant electrons. The Rashba interaction considered is derived from the violation of inversion symmetry at interfaces between ferromagnets and heavy metals. In equilibrium, the Rashba spin-orbit interaction gives rise to a torque corresponding to the Dzyaloshinskii-Moriya interaction. When there is a current flowing, the spin-orbit torque experienced by the itinerant electrons in short domain walls has both field-like and damping-like components. However, when the domain wall width is increased, the damping-like component, which is the counterpart of the non-adiabatic spin transfer torque, decreases rapidly at the domain wall center. In contrast to the non-adiabatic spin transfer torque, the damping-like spin-orbit torque does not approach to zero far away from the domain wall center, even in the adiabatic limit. The scattering of spin-up and spin-down wave functions, which is caused by the Rashba spin-orbit interaction and the spatial variation of magnetization profile in the domain walls, gives rise to the finite damping-like spin-orbit torque.

Depinning phase transitions of current- and field-driven domain wall motion

With the Landau–Lifshitz–Gilbert (LLG) equation, we investigate critical dynamic behaviors of the domain wall driven by the electric current and the magnetic field in disordered magnetic films. Based on the dynamic scaling form far from stationary, the critical points, and both the static and dynamic exponents of the depinning phase transition are accurately determined. The phase diagram is comprehensively depicted, which agrees with and goes beyond that of the experiments. The adiabatic and non-adiabatic spin-transfer torques induced by the electric current play distinct roles in the depinning phase transition. The novel dynamic approach to the numerical simulations of the LLG equation shows its great efficiency.

Current-Driven Dynamics of Frustrated Skyrmions in a Synthetic Antiferromagnetic Bilayer

We report the current-driven dynamics of frustrated skyrmions in an antiferromagnetically exchange coupled bilayer system, where the bilayer skyrmion consists of two monolayer skyrmions with opposite skyrmion numbers $Q$. We show that the in-plane current-driven bilayer skyrmion moves in a straight path, while the out-of-plane current-driven bilayer skyrmion moves in a circular path. It is found that the in-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one at a large ratio of $\beta/\alpha$, where $\alpha$ and $\beta$ denote the damping parameter and non-adiabatic spin transfer torque strength, respectively. Besides, the out-of-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one when $\alpha$ is small. We also reveal that one bilayer skyrmion (consisting of monolayer skyrmions with $Q=\pm 2$) can be separated to two bilayer skyrmions (consisting of monolayer skyrmions with $Q=\pm 1$) driven by an out-of-plane current. Our results may be useful for designing skyrmionic devices based on frustrated multilayer magnets.

Unified theory of magnetization dynamics with relativistic and nonrelativistic spin torques

Spin torques play a crucial role in operative properties of modern spintronic devices. To study current-driven magnetization dynamics, spin-torque terms providing the action of spin-polarized currents have previously often been added in a phenomenological way to the Landau-Lifshitz-Gilbert equation describing the local spin dynamics, yet without derivation from fundamental principles. Here, starting from the Dirac-Kohn-Sham theory and incorporating nonlocal spin transport we rigorously derive the various spin-torque terms that appear in current-driven magnetization dynamics. In particular we obtain an extended magnetization dynamics equation that precisely contains the nonrelativistic adiabatic and relativistic nonadiabatic spin-transfer torques (STTs) of the Berger and Zhang-Li forms as well as relativistic spin-orbit torques (SOTs). We derive in addition a previously unnoticed relativistic spin-torque term and moreover show that the various obtained spin-torque terms do not appear in the same mathematical form in both the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations of spin dynamics.

Evaluating the nonadiabatic spin-transfer torque using coupled oscillation of magnetic vortices

In this paper, we detect the coupled oscillation of magnetic vortices in ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ gourd-shaped thin films electrically to evaluate the nonadiabatic spin-transfer torque (STT) coefficient $\ensuremath{\beta}$, which is important for understanding a variety of STT-related phenomena. We excite a translational mode in coupled magnetic vortices by applying an alternating electrical current that causes both STT and Oersted field torque. Since the coupled oscillation modes due to the STT and Oersted field torque have totally different eigenfrequencies, the coupled oscillation spectrum can be used to evaluate $\ensuremath{\beta}$, which is generally difficult to distinguish from the Oersted field contributions. Based on the ratio between the amplitudes of the spectrum's Lorentzian and anti-Lorentzian components, the value of $\ensuremath{\beta}$ is found to be $0.085\ifmmode\pm\else\textpm\fi{}0.016$, which is 4.3 times larger than the Gilbert damping constant $\ensuremath{\alpha}$.

Emergence of Huge Negative Spin-Transfer Torque in Atomically Thin Co layers.

Current-induced domain wall motion has drawn great attention in recent decades as the key operational principle of emerging magnetic memory devices. As the major driving force of the motion, the spin-orbit torque on chiral domain walls has been proposed and is currently extensively studied. However, we demonstrate here that there exists another driving force, which is larger than the spin-orbit torque in atomically thin Co films. Moreover, the direction of the present force is found to be the opposite of the prediction of the standard spin-transfer torque, resulting in the domain wall motion along the current direction. The symmetry of the force and its peculiar dependence on the domain wall structure suggest that the present force is, most likely, attributed to considerable enhancement of a negative nonadiabatic spin-transfer torque in ultranarrow domain walls. Careful measurements of the giant magnetoresistance manifest a negative spin polarization in the atomically thin Co films which might be responsible for the negative spin-transfer torque.

Spin transfer and spin-orbit torques in in-plane magnetized (Ga,Mn)As tracks

Current-driven domain wall motion is investigated experimentally in in-plane magnetized (Ga,Mn)As tracks. The wall dynamics is found to differ in two important ways with respect to perpendicularly magnetized (Ga,Mn)As: the wall mobilities are up to ten times higher and the walls move in the same direction as the hole current. We demonstrate that these observations cannot be explained by spin-orbit field torques (Rashba and Dresselhaus types) but are consistent with nonadiabatic spin transfer torque enhanced by the strong spin-orbit coupling of (Ga,Mn)As. This mechanism opens the way to domain wall motion driven by bulk rather than interfacial spin-orbit coupling as in ultrathin ferromagnet/heavy metal multilayers.

Domain wall motion in ultrathin Co70Fe30/Pd multilayer nanowires with perpendicular anisotropy

We report the investigation of spin polarized current induced domain wall (DW) displacement in the perpendicularly magnetized nanowires patterned on ultrathin CoFe/Pd multilayer films by anomalous Hall-effect measurement. We find that DWs can be driven to propagate in the nanowire by the threshold current density (Jth) as low as 5.2 × 1010 A/m2 under a bias field H = 115 Oe. The spin-torque efficiency ε = (1.68 ± 0.09) × 10−14 T·m2/A is derived by measuring the effective field (HJ) generated by the pulsed current as well as through the dependency of Jth on H from the DW depinning field experiment. Our result indicates that the current induced DW motion is essentially dominated by the non-adiabatic spin transfer torque effect and the non-adiabaticity factor β is estimated to be as high as 0.96 ± 0.04.

In-line spin-torque nano-oscillators in perpendicularly magnetized nanowires

We propose a scheme for an in-line spin-torque nano-oscillator (iSTNO) composed of a single nanowire. The oscillating element is an in-plane magnetized region of an otherwise out-of-plane magnetized nanowire, which supports a spin-wave mode. Analytical exploration reveals that the nonadiabatic spin-transfer torque can cancel out the damping and thus induce sustained precession in response to a direct current. Moreover, it predicts that the frequency scales linearly with current and that the wave vector depends only on geometry. Simulations with single iSTNO cells confirm that oscillations occur, and simulations with two iSTNO cells show that they frequency lock to each other roughly in antiphase, even with mismatches in geometry. iSTNO devices can be easily fabricated by irradiating regions of a perpendicular magnetic anisotropy nanowire with ions, do not require an external field, inherently support multiple iSTNOs, and thus form an attractive alternative STNO.

Magnetic Skyrmion Transport in a Nanotrack With Spatially Varying Damping and Non-adiabatic Torque

Reliable transport of magnetic skyrmions is required for any future skyrmion-based information processing devices. Here we present a micromagnetic study of the in-plane current-driven motion of a skyrmion in a ferromagnetic nanotrack with spatially sinusoidally varying Gilbert damping and/or non-adiabatic spin-transfer torque coefficients. It is found that the skyrmion moves in a sinusoidal pattern as a result of the spatially varying Gilbert damping and/or non-adiabatic spin-transfer torque in the nanotrack, which could prevent the destruction of the skyrmion caused by the skyrmion Hall effect. The results provide a guide for designing and developing the skyrmion transport channel in skyrmion-based spintronic applications.

Impact of current on static and kinetic depinning fields of domain wall in ferromagnetic nanostrip

The impact of current on static and kinetic depinning fields of a domain wall in a one- dimensional ferromagnetic nanostrip is investigated analytically and numerically by solving the Landau–Lifshitz–Gilbert equation with adiabatic and non-adiabatic spin-transfer torques. The results show that in the absence of current, the static depinning field is greater than the kinetic depinning field. Both the depinning fields decrease by increasing the current applied in a direction opposite to the direction of the applied field. Both the depinning fields can also be tuned by the current to make them equal.

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.