Spin Hall Torque Research Articles

Boundary conditions for micromagnetism with spin currents

In this paper we show how the spin current in insulating ferromagnets can be treated in the micromagnetic framework by generalizing the boundary conditions in order to allow for the transport of magnetic moment and energy at the interface with other spin carrying media. As specific examples we demonstrate the spin Hall torque and spin pumping effects for a ferromagnetic layer in contact with a spin Hall metallic layer. In particular we show how by this method we can reproduce the known literature result in the case of thin films and make predictive examples for thick ferromagnets.

Topological nature of the proper spin current and the spin-Hall torque

Topological nature of the proper spin current and the spin-Hall torque

Detection of long-range orbital-Hall torques

We report and quantify a large orbital-Hall torque generated by Nb and Ru, which we identify from a strong dependence of torques on the ferromagnets. This is manifested as a sign reversal and strong enhancement in the damping-like torques measured in Nb (or Ru)/Ni bilayers as compared to Nb (or Ru)/FeCoB bilayers. The long-range nature of orbital transport in the ferromagnet is revealed by the thickness dependences of Ni in Nb (or Ru)/Ni bilayers which are markedly different from the regular spin absorption in the ferromagnet that takes place within a few angstroms and thus it uniquely distinguishes the orbital Hall torque from the spin Hall torque.

Enhancement of spin-charge conversion efficiency for Co3Sn2S2 across transition from paramagnetic to ferromagnetic phase

Co$_{3}$Sn$_{2}$S$_{2}$ (CSS) is one of the shandite compounds and becomes a magnetic Weyl semimetal candidate below the ferromagnetic phase transition temperature ($\textit{T}_\textrm{C}$). In this paper, we investigate the temperature ($\textit{T}$) dependence of conversion between charge current and spin current for the CSS thin film by measuring the spin-torque ferromagnetic resonance (ST-FMR) for the trilayer consisting of CSS / Cu / CoFeB. Above $\textit{T}_\textrm{C}$ ~ 170 K, the CSS / Cu / CoFeB trilayer exhibits the clear ST-FMR signal coming from the spin Hall effect in the paramagnetic CSS and the anisotropic magnetoresistance (AMR) of CoFeB. Below $\textit{T}_\textrm{C}$, on the other hand, it is found that the ST-FMR signal involves the dc voltages ($\textit{V}_\textrm{dc}$) not only through the AMR but also through the giant magnetoresistance (GMR). Thus, the resistance changes coming from both AMR and GMR should be taken into account to correctly understand the characteristic field angular dependence of $\textit{V}_\textrm{dc}$. The spin Hall torque generated from the ferromagnetic CSS, which possesses the same symmetry as that for spin Hall effect, dominantly acts on the magnetization of CoFeB. A definite increase in the spin-charge conversion efficiency ($\xi$) is observed at $\textit{T}$ < $\textit{T}_\textrm{C}$, indicating that the phase transition to the ferromagnetic CSS promotes the highly efficient spin-charge conversion. In addition, our theoretical calculation shows the increase in spin Hall conductivity with the emergence of magnetic moment at $\textit{T}$ < $\textit{T}_\textrm{C}$, which is consistent with the experimental observation.

Intrinsic spin Hall torque in a moiré Chern magnet

In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a non-magnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin–orbit torque. Here we demonstrate a spin–orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moiré superlattice site. We observe hysteretic switching of the resistivity as a function of applied current. Magnetic imaging reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns with spin accumulation measured near the Hubbard band edges with high Berry curvature. This suggests that intrinsic spin or valley Hall torques drive the observed current-driven magnetic switching in both MoTe2/WSe2 and other moiré materials. The switching current density is substantially less than those reported in other platforms, suggesting that moiré heterostructures are a suitable platform for efficient control of magnetic order. Switching of magnetic behaviour is one of the main ideas that drives spintronics. Now, magnetic switching via spin-orbit torque is shown in a moiré bilayer, introducing a platform for spintronic applications.

Parametric resonance of spin waves in ferromagnetic nanowires tuned by spin Hall torque

We present a joint experimental and theoretical study of parametric resonance of spin wave eigenmodes in Ni$_{80}$Fe$_{20}$/Pt bilayer nanowires. Using electrically detected magnetic resonance, we measure the spectrum of spin wave eigenmodes in transversely magnetized nanowires and study parametric excitation of these eigenmodes by a microwave magnetic field. We also develop an analytical theory of spin wave eigenmodes and their parametric excitation in the nanowire geometry that takes into account magnetic dilution at the nanowire edges. We measure tuning of the parametric resonance threshold by antidamping spin Hall torque from a direct current for the edge and bulk eigenmodes, which allows us to independently evaluate frequency, damping and ellipticity of the modes. We find good agreement between theory and experiment for parametric resonance of the bulk eigenmodes but significant discrepancies arise for the edge modes. The data reveals that ellipticity of the edge modes is significantly lower than expected, which can be attributed to strong modification of magnetism at the nanowire edges. Our work demonstrates that parametric resonance of spin wave eigenmodes is a sensitive probe of magnetic properties at edges of thin-film nanomagnets.

Spin Currents at the Interface and Spin Hall Torque

We compare two different approaches to compute the spin Hall torque at the interface between a spin Hall metallic layer and a ferromagnet. In one approach, one attributes a spin mixing conductance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{\uparrow \downarrow }$ </tex-math></inline-formula> to the interface, while the other employs the thermodynamic theory for the magnetic moment currents. The main difference between the outcomes of the two approaches is the field-like torque term that, in the first approach, is due to the imaginary part of the spin mixing conductance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {Im}[g_{\uparrow \downarrow }]$ </tex-math></inline-formula> and, in the second one, is proportional to the effective damping <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha ^{\prime }$ </tex-math></inline-formula> of the ferromagnet.

Collective spin dynamics under dissipative spin Hall torque

Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets but also more complex noncollinear spin systems. We develop a general Lagrangian–Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of the order and, in particular, on whether there is a net magnetic moment. The latter endows the system with a unipolar switching capability, while magnetically compensated materials tend to evolve toward limit cycles, at large torques, with chirality dependent on the torque sign. Apart from the ferromagnetic and antiferromagnetic cases, we discuss ferrimagnets, which display an intricate competition between switching and limit cycles. As a simple case for compensated noncollinear order, we consider isotropic spin glasses and a scenario of their coexistence with a collinear magnetic order.

Controlled Localized Domain Wall Writing in Antiferromagnetic Nano Stripes With In-Plane Transverse Currents

In order for textures in intrinsic antiferromagnets to be applied in proposed spintronics devices, localized and controllable writing is required. Here, the feasibility of a simple scheme for spin-Hall torque driven localized writing of chiral antiferromagnetic (AFM) domain wall (DW) pairs at a chosen location in AFM nano stripes is investigated. Short voltage pulses causing in-plane current-injection across transverse contacts in the heavy metal trigger a localized horizontal boundary-nucleated reverse AFM domain that propagates throughout the width to the opposite boundary, defining a locally written DW pair without affecting information in other parts of the device. The nucleation mechanism is examined, indicating exchange torque governing. A diagram of the number of DW-pairs written as a function of applied writing pulse amplitude and pulse duration is shown for a generic antiferromagnet, illustrating the degree of control required of the excitation protocol. Simulations of write and drive pulses are also presented, showing that the slight current bending around the writing contacts does not impose any significant pinning nor nucleation of unwanted textures for a typical driving amplitude. The advantages of this simple scheme are that it does not require any component for vertical spin-polarized current injection nor lasers for writing as in previous proposals.

Temperature-dependent anisotropic magnetoresistance and spin-torque-driven vortex dynamics in a single microdisk

Spin–orbit-torque-driven dynamics have recently gained interest in the field of magnetism due to the reduced requirement of current densities and an increase in efficiency, as well as the ease of implementation of different devices and materials. From a practical point of view, the low-frequency dynamics below 1 GHz is particularly interesting since dynamics associated with magnetic domains lie in this frequency range. While spin-torque excitation of high-frequency modes has been extensively studied, the intermediate low-frequency dynamics have received less attention, although spin torques could potentially be used for both manipulation of the spin texture and the excitation of dynamics. In this work, we demonstrate that it is possible to drive magnetic vortex dynamics in a single microdisk by spin-Hall torque at varying temperatures and relate the results to transport properties. We find that the gyrotropic mode of the core couples to the low-frequency microwave signal and produces a measurable voltage. The dynamic measurements are in agreement with magnetic transport measurements and are supported by micromagnetic simulations. Our results open the door for integrating magnetic vortex devices in spintronic applications.

Evidence of magnetization switching by anomalous spin Hall torque in NiFe

Recently the anomalous Hall effect was predicted as a possible mechanism to produce magnetization-dependent spin current. Here we have applied NiFe/Ru/perpendicular magnetic multilayers and a specific geometry to demonstrate magnetization switching driven by anomalous spin-orbit torque resulting from the bulk anomalous Hall effect. The anomalous spin Hall torque of NiFe is strong enough not only to switch the magnetization of perpendicular Co but also leads to opposite switching chirality compared with the ordinary spin Hall torque. This work confirmed the existence of a strong anomalous spin Hall torque due to anomalous Hall effect, which may lay a foundation to develop spin-orbit torque devices free of heavy metals.

The positive correlation between interface Dzyaloshinskii–Moriya interaction and damping-like spin Hall torque in the Ta/Pt/CoFeB/MgO/Ta system

Interfacial Dzyaloshinskii–Moriya interaction (iDMI) receives a lot of attention due to its potential for spintronics devices. The physical understanding of the artificial approaches that control the strength of iDMI remains complicated. In the Ta/Pt/CoFeB/MgO/Ta system, the strength of the iDMI D and the efficiency of the damping-like spin Hall torque (DL-SHT) have been quantified utilizing Brillouin light scattering, spin-torque ferromagnetic resonance, and spin Hall magnetoresistance. A linear relationship between D and DL-SHT efficiency was obtained, indicating that DL-SHT efficiency governed by itinerant electron spin is a comprehensive parameter for iDMI study.

Observation of the magnetization metastable state in a perpendicularly magnetized nanopillar with asymmetric potential landscape

The effect of spin torque on magnetization is investigated in an MgO/CoFeB/W perpendicularly magnetized nanopillar with an asymmetric bistable potential landscape. While conventional pulse-current-induced magnetization switching has been implemented, a metastable switched state is observed under direct current (DC). The mean dwell time of the metastable state depends not only on the DC amplitude but also on the current direction. These results suggest that the damping spin Hall torque suppresses the magnetization fluctuation and realizes the metastable state.

Anisotropic spin-orbit torque generation in epitaxial SrIrO3 by symmetry design

Spin-orbit coupling (SOC), the interaction between the electron spin and the orbital angular momentum, can unlock rich phenomena at interfaces, in particular interconverting spin and charge currents. Conventional heavy metals have been extensively explored due to their strong SOC of conduction electrons. However, spin-orbit effects in classes of materials such as epitaxial 5d-electron transition-metal complex oxides, which also host strong SOC, remain largely unreported. In addition to strong SOC, these complex oxides can also provide the additional tuning knob of epitaxy to control the electronic structure and the engineering of spin-to-charge conversion by crystalline symmetry. Here, we demonstrate room-temperature generation of spin-orbit torque on a ferromagnet with extremely high efficiency via the spin-Hall effect in epitaxial metastable perovskite SrIrO3 We first predict a large intrinsic spin-Hall conductivity in orthorhombic bulk SrIrO3 arising from the Berry curvature in the electronic band structure. By manipulating the intricate interplay between SOC and crystalline symmetry, we control the spin-Hall torque ratio by engineering the tilt of the corner-sharing oxygen octahedra in perovskite SrIrO3 through epitaxial strain. This allows the presence of an anisotropic spin-Hall effect due to a characteristic structural anisotropy in SrIrO3 with orthorhombic symmetry. Our experimental findings demonstrate the heteroepitaxial symmetry design approach to engineer spin-orbit effects. We therefore anticipate that these epitaxial 5d transition-metal oxide thin films can be an ideal building block for low-power spintronics.

Switching-current shift in spin Hall effect with perpendicular magnetic field

The spin Hall torque induced by DC current was studied experimentally. A Pt/Co/Pt structure with perpendicular magnetic anisotropy was grown, and magnetization reversal due to the spin Hall effect was observed. An extra magnetic field perpendicular to the sample was applied in addition to a constant bias field. It was found that the switching current shifted in proportion to the additional perpendicular field. The spin Hall angle was estimated from this relation, and the small perpendicular magnetic field can be measured accurately based on this effect.

Spin–orbit torque-driven current-induced domain wall motion in Gd–Fe magnetic wires

We fabricated Gd–Fe/Ta/sub. and W/Gd–Fe/Ta/sub. perpendicular magnetized magnetic wires and investigated current-induced domain wall motion (CIDWM) in them. The propagation field of the Gd–Fe wires is low (∼3 mT), and the wires were found to have a low threshold current density (∼3.1 × 1010 A m−2) of CIDWM. The directions of the CIDWM in Gd–Fe/Ta and W/Gd–Fe/Ta wires are opposite to each other, indicating that the CIDWM in both wires is driven by spin–orbit torque because the spin Hall torque generated by the Ta underlayer and W cap layer oppose each other.

Real-space and pulse-by-pulse analysis of domain wall creep induced by spin-Hall torque

This study aims to investigate the creep motion of a magnetic domain wall (DW) induced by spin-Hall torque (SHT) in a Ta/Co–Ni/Pt hetero-structured thin wire using photoemission electron microscopy. The displacement of the DW was recorded every time after the duration of an electric current pulse. Results revealed that the existence of pinning centers and the inhomogeneity of the thermal diffusion property of the wire may result in an unstable DW motion. On the contrary, this data also suggested that the SHT induced from both the Ta and Pt layers can significantly improve the DW velocity, which was found to be three orders of magnitude larger than that previously reported for the MgO/Co–Ni/Pt system (Taniguchi et al., Appl. Phys. Exp. 7, 053005 (2014)).

Control of magnetization dynamics by spin-Nernst torque

Control of magnetization dynamics is one of the primary goals in spintronics. It has been demonstrated using spin Hall effect i.e charge current to spin current conversion in non-magnetic metal which has large spin-orbit coupling such as Pt, W etc. Recently different groups have shown generation of spin current in Pt, W while thermal gradient is created by virtue of spin Nernst effect. In this work we show the evidence of magnetization control by spin Nernst torque in Pt/Py bi-layer. We compared relative strength of spin Nernst Torque and spin Hall torque by measuring the systematic variation of magnetic linewidth on application of constant heat or charge current. Spin-torque ferromagnetic resonance (ST-FMR) technique is adopted to excite the magnet and to measure line-width precisely from the symmetric and anti-symmetric voltage component. Control of magnetization dynamics by spin Nernst torque will emerge as an alternative way to manipulate nano-magnets.

Chiral skyrmions in an anisotropy gradient

A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin Hall effect has recently been demonstrated. Here, we study the fundamental properties of this type of motion by combining micromagnetic simulations and a generalized Thiele equation. We find that the anisotropy gradient drives the skyrmion mainly along the direction perpendicular to the gradient, due to the conservative part of the torque. There is some slower motion along the direction parallel to the anisotropy gradient due to damping torque. When an appropriate spin Hall torque is added, the skyrmion velocity in the direction of the anisotropy gradient can be enhanced. This motion gives rise to acceleration of the skyrmion as this moves to regions of varying anisotropy. This phenomenon should be taken into account in experiments for the correct evaluation of the skyrmion velocity. We employ a Thiele like formalism and derive expressions for the velocity and the acceleration of the skyrmion that match very well with micromagnetic simulation results.

Reorientable Spin Direction for Spin Current Produced by the Anomalous Hall Effect

We show experimentally that the spin direction of the spin current generated by spin-orbit interactions within a ferromagnetic layer can be reoriented by turning the magnetization direction of this layer. We do this by measuring the field-like component of spin-orbit torque generated by an exchange-biased FeGd thin film and acting on a nearby CoFeB layer. The relative angle of the CoFeB and FeGd magnetic moments is varied by applying an external magnetic field. We find that the resulting torque is in good agreement with predictions that the spin current generated by the anomalous Hall effect from the FeGd layer depends on the FeGd magnetization direction $\hat{m}_{FeGd}$ according to $\vec{\sigma}\propto\left ( \hat{y}\cdot \hat{m}_{FeGd} \right )\hat{m}_{FeGd}$, where $\hat{y}$ is the in-plane direction perpendicular to the applied charge current. Because of this angular dependence, the spin-orbit torque arising from the anomalous Hall effect can be non-zero in a sample geometry for which the spin Hall torque generated by non-magnetic materials is identically zero.