The following article has been submitted to the Journal of Applied Physics. After it is published, it will be found at https://aip.scitation.org/journal/jap
Spin-orbit torques offer a promising mechanism for electrically controlling magnetization dynamics in nanoscale heterostructures. While spin-orbit torques occur predominately at interfaces, the physical mechanisms underlying these torques can originate in both the bulk layers and at interfaces. Classifying spin-orbit torques based on the region that they originate in provides clues as to how to optimize the effect. While most bulk spin-orbit torque contributions are well studied, many of the interfacial contributions allowed by symmetry have yet to be fully explored theoretically and experimentally. To facilitate progress, we review interfacial spin-orbit torques from a semiclassical viewpoint and relate these contributions to recent experimental results. Within the same model, we show the relationship between different interface transport parameters. For charges and spins flowing perpendicular to the interface, interfacial spin-orbit coupling both modifies the mixing conductance of magnetoelectronic circuit theory and gives rise to spin memory loss. For in-plane electric fields, interfacial spin-orbit coupling gives rise to torques described by spin-orbit filtering, spin swapping and precession. In addition, these same interfacial processes generate spin currents that flow into the non-magnetic layer. For in-plane electric fields in trilayer structures, the spin currents generated at the interface between one ferromagnetic layer and the non-magnetic spacer layer can propagate through the non-magnetic layer to produce novel torques on the other ferromagnetic layer.
Here we study the effect of an additional interfacial spin-transfer torque, as well as the well established spin-orbit torque and bulk spin-transfer torque, on skyrmion collections - group of skyrmions dense enough that they are not isolated from on another - in ultrathin heavy metal / ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show the experimen…
Interfacial orbital transmission, conversion, and mechanical torque in metals
Aix-Marseille Université（艾克斯-马赛大学）；Korea University（高丽大学）；Forschungszentrum Jülich（于利希研究中心）；Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学）；Norwegian University of Science and Technology（挪威科技大学）
We present measurements of spin orbit torques generated by Ir as a function of film thickness in sputtered Ir/CoFeB and Ir/Co samples. We find that Ir provides a damping-like component of spin orbit torque with a maximum spin torque conductivity 1.4e5 in SI unit and a maximum spin-torque efficiency of 0.04, which is sufficient to drive switching in an 0.8 nm film of CoFeB with perpendicular magnetic anisotropy. We also observe a surprisingly large field like spin orbit torque. Measurements as a function of Ir thickness indicate a substantial contribution to the FLT from an interface mechanism …
Skyrmions can be driven by spin-orbit torques as a result of the spin Hall effect. Here we model an additional contribution in ultra-thin multilayers, arising from the spin accumulation at heavy metal / ferromagnetic interfaces and observe the effects on a large range of skyrmion diameters. The combination of the interfacial spin-transfer torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles for skyrmion diameters less than 100 nm. We show that this additional term has a significant effect on the skyrmion dynamics and l…
In bilayer systems consisting of an ultrathin ferromagnetic layer adjacent to a metal with strong spin-orbit coupling, an applied in-plane current induces torques on the magnetization. The torques that arise from spin-orbit coupling are of particular interest. Here, we calculate the current-induced torque in a Pt-Co bilayer to help determine the underlying mechanism using first principles methods. We focus exclusively on the analogue to the Rashba torque, and do not consider the spin Hall effect. The details of the torque depend strongly on the layer thicknesses and the interface structure, pr…
We investigate an interfacial spin-transfer torque and $β$-term torque with alternating current (AC) parallel to a magnetic interface. We find that both torques are resonantly enhanced as the AC frequency approaches to the exchange splitting energy. We show that this resonance allows us to estimate directly the interfacial exchange interaction strength from the domain wall motion. We also find that the $β$-term includes an unconventional contribution which is proportional to the time derivative of the current and exists even in absence of any spin relaxation processes.
Finding efficient ways of manipulating magnetic bits is one of the core goals in spintronic research. Electrically-generated spin-orbit torques (SOTs) are good candidates for this and the search for materials capable of generating highly-efficient SOTs has gained a lot of traction in the recent years. While antiferromagnet/ferromagnet bilayer structures have been employed extensively for passive applications, e.g. by using exchange bias fields, their active properties are not yet widely employed. Here we show the presence of large interfacial SOTs in bilayer of a ferromagnet and the two-dimens…
Using the first-principles non-equilibrium Green's function technique with supercell disorder averaging, we study the influence of interfacial intermixing on the spin-orbit torque in Co$\mid$Pt bilayers. Intermixing is modeled by inserting one or more monolayers of a disordered CoPt alloy between Co and Pt. Dampinglike torque is moderately enhanced by interfacial intermixing, while the fieldlike torque, which is small for abrupt interfaces, is strongly enhanced and becomes comparable to the dampinglike torque. The enhancement of the fieldlike torque is attributed to the interface between Co an…
The ability of spin-orbit interactions to convert charge current into spin current, most often in the bulk of heavy metal thin films, has been the hallmark of spintronics in the last decade. In this study, we demonstrate how the insertion of light metal element interface profoundly affects both the nature of spin-orbit torque and its efficiency in terms of damping-like ($H_{\text{DL}}$) and field-like ($H_{\text{FL}}$) effective fields in ultrathin Co ferromagnet. Indeed, we measure unexpectedly large $H_{\text{FL}}$/$H_{\text{DL}}$ ratio ($\sim$2.5) upon inserting a 1.4 nm thin Al layer in Pt…
The thickness dependence of spin-orbit torque and magnetoresistance in ferromagnet/heavy-metal bilayers is studied using the first-principles non-equilibrium Green's function formalism combined with the Anderson disorder model. A systematic expansion in orthogonal vector spherical harmonics is used for the angular dependence of the torque. The damping-like torque in Co/Pt and Co/Au bilayers can be described as a sum of the spin-Hall contribution, which increases with thickness in agreement with the spin-diffusion model, and a comparable interfacial contribution. The magnetoconductance in the p…
In bilayer nanowires consisting of a ferromagnetic layer and a non-magnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, damping-like and field-like. The damping-like torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the field-like torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on…
We compute the spin-orbit torque in a transition metal heterostructure using Slater-Koster parameterization in the two-center tight-binding approximation and accounting for d-orbitals only. In this method, the spin-orbit coupling is modeled within Russel-Saunders scheme, which enables us to treat interfacial and bulk spin-orbit transport on equal footing. The two components of the spin-orbit torque, dissipative (damping-like) and reactive (field-like), are computed within Kubo linear response theory. By systematically studying their thickness and angular dependence, we were able to accurately …
Increasing dampinglike spin-orbit torque (SOT) is both of fundamental importance for enabling new research into spintronics phenomena and also technologically urgent for advancing low-power spin-torque memory, logic, and oscillator devices. Here, we demonstrate that enhancing interfacial scattering by inserting ultra-thin layers within a spin Hall metals with intrinsic or side-jump mechanisms can significantly enhance the spin Hall ratio. The dampinglike SOT was enhanced by a factor of 2 via sub-monolayer Hf insertion, as evidenced by both harmonic response measurements and current-induced swi…
Non-equilibrium spin transport in a magnetic tunnel junction comprising a single magnetic layer in the presence of interfacial spin-orbit interaction (SOI) is studied theoretically. The interfacial SOI generates a spin torque of the form {\bf T}=T_{||}{\bf M}x({\bf z}x{\bf M})+T_{\bot}{\bf z}x{\bf M}, even in the absence of an external spin polarizer. For thick and large tunnel barriers, the torque reduces to the perpendicular component, $T_{\bot}$, which can be electrically tuned by applying a voltage across the insulator. In the limit of thin and low tunnel barriers, the in-plane torque $T_{…
We investigate the effect of capping layer (CAP) on the interfacial magnetic anisotropy energy density (K_S), magnetic damping (α), and spin-orbit torques (SOTs) in heavy-metal (Pt) / ferromagnet (Co or Py) / CAP (MgO/Ta, HfOx, or TaN). At room temperature (RT) the CAP materials influence the effective magnitude of K_S, which is associated with a formation of interfacial magnetic oxides. The dynamical dissipation parameters of Co are considerably influenced by the CAP (especially MgO) while those of Py are not. This is possibly due to an extra magnetic damping via spin-pumping process across t…
Spin transport in magnetic tunnel junctions comprising a single magnetic layer in the presence of interfacial spin-orbit interaction (SOI) is investigated theoretically. Due to the presence of interfacial SOI, a current-driven spin torque can be generated at the second order in SOI, even in the absence of an external spin polarizer. This torque possesses two components, in-plane and perpendicular to the plane of rotation, that can induce either current-driven {\em magnetization switching} from in-plane to out-of-plane configuration or {\em magnetization precessions}, similarly to Spin Transfer…
We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetis…
Current induced spin-orbit magnetic fields (iSOFs), arising either in single-crystalline ferromagnets with broken inversion symmetry1,2 or in non-magnetic metal/ferromagnetic metal bilayers3,4, can produce spin-orbit torques which act on a ferromagnet's magnetization,thus offering an efficient way for its manipulation.To further reduce power consumption in spin-orbit torque devices, it is highly desirable to control iSOFs by the field-effect, where power consumption is determined by charging/discharging a capacitor5,6. In particular, efficient electric-field control of iSOFs acting on ferromag…
Recent studies rediscovered the crucial role of field-like spin orbit torque (SOT) in nanosecond-timescale SOT dynamics. However, there is not yet an effective way to control its relative amplitude. Here, we experimentally modulate the field-like SOT in W/CoFeB/MgO trilayers through tuning the interfacial spin accumulation. By performing spin Hall magnetoresistance measurement, we find that the CoFeB with enhanced spin dephasing, either generated from larger layer thickness or from proper annealing, can distinctly boost the spin absorption and enhance the interfacial spin mixing conductance G_…
We study inserting Co layer thickness-dependent spin transport and spin-orbit torques (SOTs) in the Pt/Co/Py trilayers by spin-torque ferromagnetic resonance. The interfacial perpendicular magnetic anisotropy energy density ($K_s = 2.7~erg/cm^2$), which is dominated by interfacial spin-orbit coupling (ISOC) in the Pt/Co interface, total effective spin-mixing conductance ($G_{eff,tot} = 0.42 {\times} 10^{15}~Ω^{-1} m^{-2}$) and two-magnon scattering ($β_{TMS} = 0.46~nm^2$) are first characterized, and the damping-like torque ($ξ_{DL}$ = 0.103) and field-like torque ($ξ_{FL}$ = -0.017) efficienc…
Transition metal dichalcogenides (TMDs) are promising materials for efficient generation of current-induced spin-orbit torques on an adjacent ferromagnetic layer. Numerous effects, both interfacial and bulk, have been put forward to explain the different torques previously observed. Thus far, however, there is no clear consensus on the microscopic origin underlying the spin-orbit torques observed in these TMD/ferromagnet bilayers. To shine light on the microscopic mechanisms at play, here we perform thickness dependent spin-orbit torque measurements on the semiconducting WSe$_{2}$/permalloy bi…
Symmetry Breaking by Interfacial Dead Layers: Observation of Forbidden Self-Induced Spin-Orbit Torque in Symmetric Ferromagnets
Indian Institute of Technology Ropar（印度理工学院罗帕尔分校）；Virginia Commonwealth University（弗吉尼亚联邦大学）；Jaypee Institute of Information Technology（贾伊皮信息技术学院）；Université de Lorraine（洛林大学）；Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza（阿拉贡纳米科学与材料研究所 (INMA)，西班牙科学研究中心-萨拉戈萨大学）；Indian Institute of Technology Bhubaneswar（印度理工学院布巴内斯瓦尔分校）；Carnegie Mellon University（卡内基梅隆大学）
The spin-transfer torque (STT) in Co2MnSi(CMS)/Al/Co2MnSi spin-valve system with and without interfacial disorder is studied by a first-principles noncollinear wave-function-matching method. It is shown that in the case of clean interface the angular dependence of STT for CoCo/Al (the asymmetry parameter Lambda approx. 4.5) is more skewed than that for MnSi/Al (Lambda approx. 2.9), which suggests the clean CoCo/Al architecture is much more efficient for the application on radio frequency oscillation. We also find that even with interfacial disorder the spin-valve of half-metallic CMS still has…
Current-driven spin-orbit torques are investigated in a heterostructure composed of a ferromagnet deposited on top of a three dimensional topological insulator using the linear response formalism. We develop a tight-binding model of the heterostructure adopting a minimal interfacial hybridization scheme that promotes induced magnetic exchange on the topological surface states, as well as induced Rashba-like spin-orbit coupling in the ferromagnet. Therefore, our model accounts for spin Hall effect from bulk states together with inverse spin galvanic and magnetoelectric effects at the interface …
Future applications of spin-orbit torque will require new mechanisms to improve the efficiency for switching nanoscale magnetic tunnel junctions (MTJs), while also controlling the magnetic dynamics to achieve fast, nanosecond scale performance with low write error rates. Here we demonstrate a strategy to simultaneously enhance the interfacial magnetic anisotropy energy and suppress interfacial spin memory loss by introducing sub-atomic and monatomic layers of Hf at the top and bottom interfaces of the ferromagnetic free layer of an in-plane magnetized three-terminal MTJ device. When combined w…
We report that current-induced spin-orbit torques (SOTs) in heavy-metal/ferromagnetic-metal bilayers are strongly altered by the oxidation of the ferromagnetic layer near the interface. We measured damping-like (DL) and field-like (FL) SOTs for Pt/Co and Pt/Ni$_{81}$Fe$_{19}$ (Pt/Py) films using spin-torque ferromagnetic resonance. In the Pt/Co film, we found that the oxidation of the Co layer near the interface enhances both DL and FL SOTs in spite of the insulating nature of the CoO$_x$ layer. The enhancement of the SOTs disappears by inserting a thin Ti layer at the Pt/CoO$_x$ interface, in…
An efficient first principles method was developed to calculate spin transfer torques in layered system with noncollinear magnetization. The complete scattering wave function is determined by matching the wave function in the scattering region with the Bloch states in the leads. The spin transfer torques are obtained with aid of the scattering wave function. We applied our method to the ferromagnetic spin valve and found that the material (Co, Ni and Ni80Fe20) dependence of the spin transfer torques could be well understood by the Fermi surface. Ni has much longer spin injection penetration le…
A free electron description of spin-dependent tranport in magnetic tunnel junctions with non collinear magnetizations is presented. We investigate the origin of transverse spin density in tunnelling transport and the quantum interferences which give rise to oscillatory torques on the local magnetization. Spin transfer torque is also analyzed and an important bias asymmetry is found as well as a damped oscillatory behaviour. Furthermore, we investigate the influence of the s-d exchange coupling on torque in particular in the case of half-metallic MTJ in which the spin transfer torque is due to …
Spin-dependent transport at heavy metal/magnetic insulator interfaces is at the origin of many phenomena at the forefront of spintronics research. A proper quantification of the different interfacial spin conductances is crucial for many applications. Here, we report the first measurement of the spin Hall magnetoresistance (SMR) of Pt on a purely ferromagnetic insulator (EuS). We perform SMR measurements in a wide range of temperatures and fit the results by using a microscopic model. From this fitting procedure we obtain the temperature dependence of the spin conductances ($G_s$, $G_r$ and $G…
We propose a mechanism of torque generation by injection of an orbital current, which we call $\textit{orbital torque}$. In a magnetic bilayer consisting of a nonmagnet (NM) and a ferromagnet (FM), we consider a situation where the spin-orbit coupling (SOC) is present only in the FM. Although the SOC is absent in the NM, the orbital Hall effect can arise in the NM. When the resulting orbital Hall current is injected to the FM, the SOC of the FM converts the orbital angular momentum into spin, which exerts torque to the magnetization of the FM. Remarkably, even for small SOC strength comparable…
We calculate the spin-transfer torque in Fe/MgO/Fe tunnel junctions and compare the results to those for all-metallic junctions. We show that the spin-transfer torque is interfacial in the ferromagnetic layer to a greater degree than in all-metallic junctions. This result originates in the half metallic behavior of Fe for the $Δ_1$ states at the Brillouin zone center; in contrast to all-metallic structures, dephasing does not play an important role. We further show that it is possible to get a component of the torque that is out of the plane of the magnetizations and that is linear in the bias…
Spin-orbit torques due to interfacial Rashba and spin Hall effects have been widely considered as a potentially more efficient approach than the conventional spin-transfer torque to control the magnetization of ferromagnets. We report a comprehensive study of spin-orbit torque efficiency in Ta(O)/Ni81Fe19 bilayers by tuning low-oxidation of \b{eta}-phase tantalum, and find that the spin Hall angle θDL increases from ~ -0.18 of the pure Ta/Py to the maximum value ~ -0.30 of Ta(O)/Py with 7.8% oxidation. Furthermore, we distinguish the efficiency of the spin-orbit torque generated by the bulk sp…
Current-induced spin-orbit torque (SOT) in normal metal/ferromagnet (NM/FM) bilayers bears great promise for technological applications, but the microscopic origin of purely interfacial SOTs in ultra-thin systems is not yet fully understood. Here, we show that a linear response theory with a nonperturbative treatment of spin-dependent interactions and impurity scattering potential predicts damping-like SOTs that are strictly absent in perturbative approaches. The technique is applied to a two-dimensional Rashba-coupled ferromagnet (the paradigmatic model of a NM/FM interface), where higher-ord…
Current-induced torques in ultrathin Co/Pt bilayers were investigated using an electrically driven FMR technique. The angle dependence of the resonances, detected by a rectification effect as a voltage, were analysed to determine the symmetries and relative magnitudes of the spin-orbit torques. Both anti-damping (Slonczewski) and field-like torques were observed. As the ferromagnet thickness was reduced from 3 to 1 nm, the sign of the field-like torque reversed. This observation is consistent with the emergence of a Rashba spin orbit torque in ultra-thin bilayers.
We study the role of thermal magnons in the spin and heat transport across a normal-metal/insulating-ferromagnet interface, which is beyond an elastic electronic spin transfer. Using an interfacial exchange Hamiltonian, which couples spins of itinerant and localized orbitals, we calculate spin and energy currents for an arbitrary interfacial temperature difference and misalignment of spin accumulation in the normal metal relative to the ferromagnetic order. The magnonic contribution to spin current leads to a temperature-dependent torque on the magnetic order parameter; reciprocally, the coher…
In systems with strong spin-orbit coupling, the relationship between spin-transfer torque and the divergence of the spin current is generalized to a relation between spin transfer torques, total angular momentum current, and mechanical torques. In ferromagnetic semiconductors, where the spin-orbit coupling is large, these considerations modify the behavior of the spin transfer torques. One example is a persistent spin transfer torque in a spin valve: the spin transfer torque does not decay away from the interface, but approaches a constant value. A second example is a mechanical torque at sing…
The spin-torque ferromagnetic resonance (ST-FMR) in a bilayer system consisting of a magnetic insulator such as Y3Fe5O12 and a normal metal with spin-orbit interaction such as Pt is addressed theoretically. We model the ST-FMR for all magnetization directions and in the presence of field-like spin-orbit torques based on the drift-diffusion spin model and quantum mechanical boundary conditions. ST-FMR experiments may expose crucial information about the spin-orbit coupling between currents and magnetization in the bilayers.
Proposals for novel spin-orbitronic logic1 and memory devices2 are often predicated on assumptions as to how materials with large spin-orbit coupling interact with ferromagnets when in contact. Such interactions give rise to a host of novel phenomena, such as spin-orbit torques3,4 , chiral spin-structures5,6 and chiral spin-torques. These chiral properties are related to the anti-symmetric exchange, also referred to as the interfacial Dzyaloshinskii-Moriya interaction (DMI)9,10. For numerous phenomena, the relative strengths of the symmetric Heisenberg exchange and the DMI is of great importan…
We report that spin current transport across Pt-ferromagnet (FM) interfaces is strongly dependent on the type and the thickness of the FM layer and on post-deposition processing protocols. By employing both harmonic voltage measurements and spin-torque ferromagnetic resonance measurements, we find that the efficiency of the Pt spin Hall effect in exerting a damping-like spin torque on the FM ranges from < 0.05 to > 0.10 under different interfacial conditions. We also show that the temperature dependence of the spin torque efficiencies for both the damping-like torque and field-like torque is d…
The topological force and torque are investigated in the systems with spin-orbit coupling. Our results show that the topological force and torque appears as a pure relativistic quantum effect in an electromagnetic field. The origin of both topological force and torque is the Zitterbewegung effect. Considering nonlinear behaviors of spin-orbit coupling, we address possible phenomena driven by the topological forces.
The ability of spintronic devices to utilize an electric current for manipulating the magnetization has resulted in large-scale developments, such as, magnetic random access memories and boosted the spintronic research area. In this regard, over the last decade, magnetization manipulation using spin-orbit torque has been devoted a lot of research attention as it shows a great promise for future ultrafast and power efficient magnetic memories. In this review, we summarize the latest advancements in spin-orbit torque research and highlight some of the technical challenges for practical spin-orbi…
An antiferromagnet is a promising material for spin-orbit torque generation. Earlier studies of the spin-orbit torque in an antiferromagnet are limited to collinear spin configurations. We calculate the spin-orbit torque in an antiferromagnet whose spin ordering is weakly noncollinear. Such noncollinearity may be induced spontaneously during the magnetization dynamics even when the equilibrium spin configuration is perfectly collinear. It is shown that deviation from perfect collinearity can modify properties of the spin-orbit torque since noncollinearity generates extra Berry phase contributi…
We investigate the current-induced spin-orbit torque in antiferromangnetic materials in the presence of Rashba spin orbit coupling using both the linear response theory and the non-equilibrium Green's function technique implemented on a tight-binding model. We show that a staggered spin density arises from interband contributions. The effect of the disorder is restricted to the diminution of the torque magnitude and does not bring any anomalous behavior to the dependences of the torque on the spin orbit strength and the exchange interaction between the antiferromagnetic local moments and the i…
Heavy metal/ferromagnet interfaces feature emergent spin-orbit effects absent in the bulk materials. Because of their inherent strong coupling between spin, charge and orbital degrees of freedom, such systems provide a platform for technologically sought-after spin-orbit torques (SOTs). However, the microscopic origin of purely interfacial antidamping SOT, especially in the ultimate atomically thin limit, has proven elusive. Here, using two-dimensional (2D) van der Waals materials as a testbed for interfacial phenomena, we address this problem by means of a microscopic framework accounting for…
We study spin-orbit torques in two dimensional hexagonal crystals such as graphene, silicene, germanene and stanene. The torque possesses two components, a field-like term due to inverse spin galvanic effect and an antidamping torque originating from Berry curvature in mixed spin-$k$ space. In the presence of staggered potential and exchange field, the valley degeneracy can be lifted and we obtain a valley-dependent Berry curvature, leading to a tunable antidamping torque by controlling the valley degree of freedom. The valley imbalance can be as high as 100\% by tuning the bias voltage or mag…
We study the optically induced torques in thin film ferromagnetic layers under excitation by circularly polarized light. We study cases both with and without Rashba spin-orbit coupling using a 4-band model. In the absence of Rashba spin-orbit coupling, we derive an analytic expression for the optical torques, revealing the conditions under which the torque is mostly derived from optical spin transfer torque (i.e. when the torque is along the direction of optical angular momentum), versus when the torque is derived from the inverse Faraday effect (i.e. when the torque is perpendicular to the op…
The influence of structural asymmetries (barrier height and exchange splitting), as well as inelastic scattering (magnons and phonons) on the bias dependence of the spin transfer torque in a magnetic tunnel junction is studied theoretically using the free electron model. We show that they modify the "conventional" bias dependence of the spin transfer torque, together with the bias dependence of the conductance. In particular, both structural asymmetries and bulk (inelastic) scattering add {\em antisymmetric} terms to the perpendicular torque ($\propto V$ and $\propto j_e|V|$), while the interf…
Spin-orbit torque in magnetic domain walls was investigated 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 …
This paper presents the boundary conditions needed for drift-diffusion models to treat interfaces with spin-orbit coupling. Using these boundary conditions for heavy metal/ferromagnet bilayers, solutions of the drift-diffusion equations agree with solutions of the spin-dependent Boltzmann equation and allow for a much simpler interpretation of the results. A key feature of these boundary conditions is their ability to capture the role that in-plane electric fields have on the generation of spin currents that flow perpendicularly to the interface. The generation of these spin currents is a dire…
As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these…
We report on $\vec{k}\cdot\vec{p}$ calculations of Rashba spin-orbit coupling controlled by external gates in InAs/InAsP core-shell nanowires. We show that charge spilling in the barrier material allows for a stronger symmetry breaking than in homoegenous nano-materials, inducing a specific interface-related contribution to spin-orbit coupling. Our results qualitatively agree with recent experiments [S. Futhemeier \textit{et al.}, Nat. Commun. \textbf{7}, 12413 (2016)] and suggest additional wavefunction engineering strategies to enhance and control spin-orbit coupling.
