Current-Induced Chiral SOTs

• Current-induced chiral spin–orbit torques are relativistic torques arising from strong spin–orbit coupling and broken inversion symmetry, essential for manipulating magnetization with defined chirality.
• These torques are engineered via interfacial effects such as the Rashba phenomenon and Dzyaloshinskii–Moriya interaction, and can be finely tuned using material parameters, doping, and gating.
• Experimental realizations in transition-metal heterostructures and two-dimensional systems demonstrate their effectiveness in achieving field-free switching and low current density domain wall motion for memory applications.

Current-induced chiral spin–orbit torques (SOTs) are a class of relativistic torques exerted on magnetic moments in condensed matter systems when an electric current is applied, with the defining feature that the torque direction or symmetry is dictated by the chirality—i.e., the handedness—of the underlying magnetic, crystallographic, or interfacial structure. These torques arise from the interplay of spin–orbit coupling (SOC), broken spatial inversion symmetry, and the electronic band structure, and exhibit a pronounced sensitivity to material parameters, interface engineering, and external control fields. Chiral SOTs are central to the operation of contemporary spintronic devices including memory, logic, and domain wall-based technologies.

1. Theoretical Foundations and General Mechanisms

In the absence of spin–orbit coupling, current-induced spin-transfer torque (STT) is described by the divergence of the spin current and its absorption by the magnetization, typically expressed as

$$\tau_{\text{STT}}(\mathbf{r}) = -(\Delta/\hbar^2)\left[\mathbf{M}(\mathbf{r}) \times \mathbf{s}(\mathbf{r})\right]$$

where $\Delta$ is the exchange splitting, $\mathbf{M}$ the magnetization, and $\mathbf{s}$ the spin density (Haney et al., 2010). Spin angular momentum conservation underlies this relation.

With strong SOC, the spin current is not conserved independently. The total electronic angular momentum $\mathbf{J} = \mathbf{L} + \mathbf{s}$ (spin and orbital components) must be considered. The angular momentum flow and the generalized conservation law become

$$\frac{d\mathbf{J}}{dt} - \nabla \cdot \mathbf{Q}_J = -(\tau_{\text{STT}} + \tau_{\text{lat}})$$

where $\mathbf{Q}_J$ is the total angular momentum current (including orbital and spin), and $\tau_{\text{lat}}$ is a mechanical torque transmitted to the lattice via the orbital angular momentum channel.

This framework accounts for key chiral phenomena: (a) persistent torques that do not decay in the bulk of systems with strong SOC, such as ferromagnetic semiconductors, and (b) mechanical torques at nonmagnetic interfaces, both stemming from the nonconservation of spin versus total angular momentum (Haney et al., 2010).

2. Microscopic Models and Phenomenology

A variety of theoretical approaches have clarified the origin, symmetry, and tunability of chiral SOTs:

a. Rashba and Interfacial Effects:

The Rashba effect, due to interfacial inversion symmetry breaking and strong SOC, creates Rashba-like torques proportional to $\mathbf{m} \times (\hat{j} \times \hat{z})$ (where $\hat{j}$ is the current direction and $\hat{z}$ the interface normal). These torques include “field-like” and “damping-like” components—sometimes both of comparable magnitude and with chiral dependence on magnetic and structural details (Haney et al., 2013, Skinner et al., 2013, Kim et al., 2017).

b. Dzyaloshinskii–Moriya Interaction (DMI):

In noncentrosymmetric systems or at interfaces, DMI introduces an antisymmetric exchange, favoring chiral spin textures and stabilizing Néel walls with a specified handedness. DMI both stabilizes chiral configurations and enables the emergence of chiral SOTs that are deterministic in the absence of an external symmetry-breaking field (Martinez et al., 2015, An et al., 2022, Dao et al., 2020).

c. Spin and Orbital Hall Effects:

Heavy metals exhibit both spin Hall effects (SHE)—generating transverse spin currents—and, in some cases, orbital Hall effects (OHE), generating orbital angular momentum currents (Go et al., 2020, Lee et al., 2021). Orbital torques (requiring conversion of orbital current to spin current by SOC in the adjacent ferromagnet or via an interfacial layer) can dominate the SOT depending on the material system (Tazaki et al., 2020, Lee et al., 2021).

d. Quantum Kinetic and Boltzmann Approaches:

Kinetic models, incorporating band structure, spin-dependent scattering, and SOC, yield analytic expressions for SOTs in various regimes. For instance, in Rashba ferromagnets with spin-dependent impurity scattering,

$$\mathbf{H}_{\mathrm{eff}}^\mathrm{S} \propto (\alpha m j_\mathrm{tr} / |e| M_S) \frac{(\tau_\uparrow - \tau_\downarrow)}{(\tau_\uparrow + \tau_\downarrow)} \cdots (\hat{y} \times \mathbf{m})$$

captures the essential chiral mechanism—disparity in scattering times in the presence of SOC (Pesin et al., 2012).

3. Material Systems and Experimental Realizations

a. Transition-Metal/Ferromagnet Heterostructures:

Co/Pt, Pd/Co, and similar bilayers demonstrate that both field-like and damping-like SOTs arise from interfacial or Rashba phenomena, with the sign, magnitude, and angular dependence of the torque determined by interface structure, heavy-metal SOC strength, and layer thickness (Haney et al., 2013, Ghosh et al., 2017). Thinner FM layers emphasize interfacial (and therefore chiral) contributions, as observed by sign reversals in field-like torque with decreasing thickness (Skinner et al., 2013).

b. Chiral Magnetic Textures—Domain Walls and Skyrmions:

Domain wall (DW) dynamics in the presence of SOTs are intricately controlled by the interplay between field-like and Slonczewski-like torques. Proper tuning of these competing contributions, often linked to DMI strength and domain wall structure, allows control of both velocity and directionality of DW motion—key for racetrack memories (Boulle et al., 2013, Hals et al., 2013, Dao et al., 2020). In chiral magnets (e.g., helimagnets, skyrmion crystals), SOC-induced torques give rise to both drift and transverse (Magnus-type) velocities, highly sensitive to the underlying symmetry and the damping tensor anisotropy (Hals et al., 2013, Hals et al., 2013).

c. Two-Dimensional and Interfacial Systems:

NbSe$_2$/Permalloy and TMDC/CrI$_3$ heterostructures illustrate the emergence of SOTs in 2D materials. In TMDC/CrI$_3$, both intra-band (field-like) and inter-band (damping-like) torques depend strongly on carrier doping, twist angle, and gating, offering external control over both the strength and symmetry (sign) of the chiral SOTs (Guimaraes et al., 2018, Majidi et al., 31 Jul 2025). The appearance of additional SOT components, forbidden by bulk symmetries but activated through strain or interface engineering, highlights the role of symmetry breaking (Guimaraes et al., 2018).

d. Orbital Torque and Spin–Orbit Interconversion:

Naturally oxidized Cu/ferromagnet bilayers and Cr/ferromagnet stacks with Gd or Pt interfacial layers demonstrate current-induced torques originating from orbital currents rather than spin currents, with conversion efficiency dictated by the FM’s SOC. This leads to unconventional torque sign reversal with FM composition and high spin Hall conductivity even in weak-SOC materials (Tazaki et al., 2020, Lee et al., 2021). In these systems, engineering the orbital–spin conversion parameter $\eta_{LS}$ via rare-earth FMs or heavy-metal interlayers enables control of the overall SOT.

4. Control Parameters and Chiral Modulation

The magnitude, directionality, and symmetry of chiral SOTs can be systematically controlled via:

• Crystallographic and Interfacial Engineering: Interface symmetry, ratio of spin Hall to Rashba torque contributions, and DMI can all be tuned to manipulate the domain wall chirality, stabilize specific magnetic states, and determine the efficiency and sign of SOTs (Hals et al., 2013, Haney et al., 2013, Martinez et al., 2015).
• Carrier Density and Doping: In TMDC/CrI$_3$ heterostructures, both field-like and damping-like torques, as well as their sign, show strong asymmetry between n- and p-type regimes, with dramatic three-order-of-magnitude enhancements observed for specific doping (Majidi et al., 31 Jul 2025).
• Twist Angle and Electrostatic Gating: Twisted bilayer systems and gating allow for continuous, even reversible, control of proximity exchange parameters in TMDC/CrI$_3$, thereby changing chiral SOT amplitude and sign (Majidi et al., 31 Jul 2025).
• Applied Field or Strain: The chiral nature of SOTs can be harnessed for field-free deterministic switching using engineered spin textures (e.g., through local spin current injection) or via symmetry breaking from device-induced strain (An et al., 2022, Guimaraes et al., 2018).
• Orbital-to-Spin Conversion Engineering: Substitution of conventional FMs by rare-earth materials (e.g., Gd) or adding ultrathin Pt interlayers at NM/FM interfaces supports efficient L–S conversion, thus enhancing SOTs originating from orbital Hall effects (Lee et al., 2021).

5. Functional Consequences in Magnetization Dynamics

a. Domain Wall Motion and Memory Applications:

Chiral SOTs generate deterministic and directionally selective domain wall injection and propagation, essential for logic and racetrack memory devices. The DMI-stabilized chirality allows for lower current densities in DW injection (e.g., ∼$4×10^{11}$ A/m$^2$) and robust sequence generation of alternating magnetic domains (Dao et al., 2020, Martinez et al., 2015).

b. Skyrmion and Helimagnet Control:

In skyrmion lattices or chiral magnets, reactive and dissipative SOTs provide distinct contributions to longitudinal and transverse velocities. Dissipative SOTs can dominate motion under certain scaling regimes, while anisotropic damping and the matching of DMI to spin–orbit strength enable nuanced control over the topological magnetization texture (Hals et al., 2013, Hals et al., 2013).

c. Field-Free Switching and Oscillatory Dynamics:

Engineering nonuniform chiral spin configurations (e.g., via local spin current injection) eliminates the need for in-plane assist fields for deterministic switching. Also, appropriately tuned ratios of field-like to damping-like SOTs enable oscillatory switching, supporting unipolar, deterministic operation advantageous for device scaling (Lee et al., 2017, An et al., 2022).

6. Outlook and Implications for Spintronic Technologies

Chiral current-induced spin–orbit torques underpin the next generation of low-power, high-speed, and field-free spintronic technologies:

• Energy-Efficient Memory and Logic: Chiral SOTs provide deterministic magnetization switching at lower current densities and support reconfigurable domain wall-based devices.
• Material Design Principles: Both orbital and spin current channels can be exploited—materials devoid of heavy-element SOC can exhibit strong torques via orbital mechanisms if the orbital Rashba effect and orbital-to-spin conversion are optimized (Tazaki et al., 2020, Lee et al., 2021).
• Interface and Device Engineering: Strategies involving atomic-layer control, twist angle tuning, or interface-embedded rare-earth/heavy-metal layers offer pathways to maximize both torque magnitude and control (Majidi et al., 31 Jul 2025, Lee et al., 2021, Ghosh et al., 2017).
• Symmetry and Topology as Functional Handles: Systematic symmetry breaking (e.g., through DMI, strain, or structural design) enables the creation and stabilization of novel chiral spin textures and tailored magneto-electric responses.
• Ultrafast and Multifunctional Operation: Chiral SOTs support ultrafast, robust switching and a range of dynamical behaviors (oscillatory, deterministic, or memory-retentive), paving the way for integration in neuromorphic and quantum information platforms.

Chiral spin–orbit torques, realized and tuned via a spectrum of microscopic mechanisms—from interfacial Rashba coupling and DMI, to orbital–spin interconversion and symmetry engineering—constitute a central tenet in modern spintronics, providing experimentally accessible, versatile, and efficient means to control magnetization at the nanoscale.