Spin-Splitter Magnonic Torque

• Spin-splitter magnonic torque is a phenomenon where spin-wave currents with nonzero angular momentum, produced by symmetry-breaking mechanisms, exert controllable torques on magnetic textures.
• It uses methods such as interfacial spin–orbit torque, magnon band splitting in altermagnets, and domain-wall spin splitters to enable nonreciprocal switching and domain motion.
• Experimental techniques like Brillouin light-scattering and inverse spin Hall voltage detection validate performance metrics, supporting innovations in nano-magnonic and spin-caloritronic devices.

Spin-splitter magnonic torque refers to the class of magnon-mediated torques that arise when a spin-split magnon current—i.e., a flow of spin waves (magnons) with angular-momentum polarization that is not globally zero—interacts with magnetic textures or interfaces to exert a strongly symmetry-selective and directionally controllable torque. This effect is central to a range of newly engineered magnonic devices and materials platforms, including nano-magnonic waveguides, altermagnets, Y-junctions, and domain-wall logic elements. Spin-splitter magnonic torque provides a framework for nonreciprocal signal routing, all-magnonic switching, and spin-caloritronic control of magnetic order at the nanoscale.

1. Underlying Mechanisms and Model Systems

Spin-splitter magnonic torque typically emerges in systems supporting either (a) symmetry-induced spin-splitting of magnon bands, (b) interfacial spin-polarization by adjacent ferromagnetic order, or (c) engineered inhomogeneities (e.g., domain walls) acting as “perfect spin splitters” for propagating magnons.

The principal classes of systems and mechanisms include:

• Nano-magnonic spin-splitters via interfacial spin–orbit torque (SOT): In Pt/Py nanowire devices, a localized reduction in ferromagnetic layer thickness creates a “nano-oscillator” where SOT, induced by a transverse charge current (via spin Hall effect in Pt), drives spin-wave auto-oscillations that emit magnons asymmetrically into the waveguide. The notch position and excitation profile set the splitter efficiency (Divinskiy et al., 2018).
• Collinear altermagnets with magnon band spin splitting: In insulating altermagnetic lattices (e.g., honeycomb or square-lattice AFM with sublattice-exchange anisotropy), spin–rotation symmetry is broken such that spin-up and spin-down magnon bands split throughout the Brillouin zone, enabling magnonic spin currents under a thermal gradient (spin Seebeck effect) and yielding a torque with strong crystal anisotropy (Sarkar et al., 6 Jul 2025, Schwartz et al., 16 Dec 2025).
• Domain wall spin splitters: In one-dimensional ferromagnetic wires, a transverse 180° domain wall acts as a “perfect” spin splitter: magnons incident from one side flip their spin upon transmission, transferring two quantum units of angular momentum to the wall per magnon, resulting in a robust domain-wall velocity (Yan et al., 2011).
• F/AF/F trilayers under thermal gradient: In ferromagnet/antiferromagnet/ferromagnet stacks, interfacial exchange at the first F layer splits the magnon branches in the AF, rendering spin currents thermally and spatially polarized (via local Zeeman splitting), which can then switch the downstream F magnetization through a pure magnonic torque (Cheng et al., 2018).

2. Theoretical Framework and Torque Structure

Spin-splitter magnonic torque is grounded in the decomposition of the total torque on a magnetic background due to a nonequilibrium spin-wave flow:

• Landau–Lifshitz–Gilbert (LLG) with SOT/magnonic torque: The LLG equation is extended by torque terms originating from either spin-orbit coupling (for SOT) or magnonic spin current (for texture–magnon interaction). For example, the SOT-induced damping modification is

$$\alpha_\text{eff} = \alpha_0 (1 - J_c / J_\text{th}),$$

where $J_c$ is current density and $J_\text{th}$ a material/geometric threshold (Divinskiy et al., 2018). In magnon-transport-driven cases,

$$\tau_\text{mag} = \tau_\text{STT} + \tau_\text{DM} + \tau_\text{GL} + \tau_\text{PL}$$

with $\tau_\text{STT} = (j \cdot \nabla) m_0$ the key adiabatic spin-transfer torque, and others encoding DMI and magnon-density effects (Lan et al., 2022).

• Spin-drift and spin-splitter torque in altermagnets: In d-wave altermagnets, sublattice-resolved spin currents $j_{1,i}, j_{2,i}$ combine into “spin-drift” velocities $u, u'$, with $u' \ne 0$ due to magnon band splitting:

$$\tau_{\text{ss}} = 2\, \mathbf{n} \times (u' \cdot \nabla) \mathbf{n}.$$

Here $u'_i = (\alpha_0^s/s) (\sigma_z)_{ij} \nabla_j T$ proportional to the crystal tensor structure (Schwartz et al., 16 Dec 2025).

These torque terms enable highly directional and symmetry-selective transfer of angular momentum from magnon currents to the magnetic background, critically distinguishing spin-splitter torques from conventional (charge-based) spin-transfer mechanisms.

3. Physical Origin and Role of Symmetry

The physical emergence of spin-splitter magnonic torque is controlled by the symmetry of the host lattice, interface, or imposed magnetic texture:

Mechanism/Platform	Key Symmetry Breaking	Physical Origin of $\Delta$spin
Altermagnets (honeycomb/square)	Anisotropic NNN exchange, DMI	Non-degenerate magnon bands ($\epsilon_{↑,k} \ne \epsilon_{↓,k}$) (Sarkar et al., 6 Jul 2025, Schwartz et al., 16 Dec 2025)
F/AF Interface	Local Zeeman field, fixed F order	Exchange splitting at F/AF boundary (Cheng et al., 2018)
Domain Wall in 1D Ferromagnet	Spatially varying $m(z)$	Reversal of $S_z$ via wall, perfect spin splitter (Yan et al., 2011)
Nano-magnonic Notch Device	Geometric (notch), SOT	Lateral shift of auto-oscillator, emission asymmetry (Divinskiy et al., 2018)

Spin splitting of magnon channels renders otherwise canceling $\uparrow$/$\downarrow$ contributions finite and direction-selected, as required for efficient spin-current-driven switching, signal routing, or nonreciprocal logic.

4. Quantitative Description and Performance Metrics

Crucial device parameters and torque strengths are determined via microscopic models, incorporating material constants and geometry:

• Splitter ratio $R$ in nano-magnonic devices: $R = P_+/P_-$ captures the power asymmetry in left/right emission; e.g., $R \sim 3$ at optimal current and field, tunable by controlling the lateral shift $\Delta x$ of the oscillator mode and the spin Hall angle $\theta_\text{SH}$ (Divinskiy et al., 2018).
• Domain wall motion in 1D: The velocity is set by $v_{\text{DW}} = - (\rho^2 / 2) V_g$ with $V_g$ the magnon group velocity and $\rho$ the spin-wave amplitude squared; wall velocities of $10$–$100$ m/s are attainable in YIG for moderate input power (Yan et al., 2011, Lan et al., 2022).
• Spin-splitter torque in altermagnets: The effective field exerted on an adjacent F layer is $B_\text{eff} = J_s/(M_s \ell)$, yielding $2$ mT fields for $1$ K/nm thermal gradients and standard nanoscale F thickness—well above typical anisotropy fields (Sarkar et al., 6 Jul 2025).

Typical thresholds for efficient spin-splitter torque action are well below $1$ K/nm for magnon-Seebeck-induced switching, and required charge currents for SOT-based devices stay within feasible limits for Pt/Py geometries.

5. Experimental Signatures and Detection

Characteristic observable signatures include:

• Brillouin light-scattering imaging: Microfocus BLS resolves propagation and amplitude contrast between split magnon channels, confirming both directionality and splitting ratios, as shown by spatially resolved emission maps in nano-notched devices (Divinskiy et al., 2018).
• Inverse Spin Hall voltage detection: For heavy-metal/magnetic-insulator interfaces, the asymmetry and quadratic nonlinearity of the resultant ISH voltage corroborate the nonlinear spin-splitter magnon emission predicted by SOT theory (Wang et al., 2017).
• Nonreciprocal switching in F/AF/F stacks: The threshold and polarization dependence of magnon-mediated F switching under $\nabla T$ provides a direct probe of spin-split, pure magnonic currents (Cheng et al., 2018).
• Angular dependence in altermagnets: Crystal-axis–dependent spin-splitter torque yields strongly anisotropic domain-wall precession and skyrmion motion under $\nabla T$, providing experimental handles for both detection and control (Schwartz et al., 16 Dec 2025).

6. Materials Platforms and Device Applications

Candidate materials and device architectures include:

• Altermagnets: Layered hexagonal AFMs (e.g., MnTe, MnSe, MnPSe$_3$, CrSb), and twisted MnBi$_2$Te$_4$ bilayers, with strong exchange anisotropy, support robust spin-splitter effects and are compatible with thermal spin-current injection (Sarkar et al., 6 Jul 2025, Schwartz et al., 16 Dec 2025).
• Magnetic insulators for all-magnonic logic: YIG nanowire and waveguide structures enable domain-wall–mediated spin-splitter functionality without Joule heating, supporting low-dissipation data routing and switching (Yan et al., 2011, Lan et al., 2022).
• Spin–orbitronic magnonics: Pt/YIG/Py trilayers and nanowire stacks combine the tunability of SOT with magnonic channel nonreciprocity, robustly reconfigurable by field, current, or device geometry (Divinskiy et al., 2018, Wang et al., 2017).

Device applications span:

• Nonreciprocal magnonic logic elements and splitters.
• Spintronic racetrack memories using thermal-gradient-driven, highly anisotropic domain-wall and skyrmion motion (Schwartz et al., 16 Dec 2025).
• Microwave oscillators and spin-caloritronic logic exploiting all-magnonic switching.

7. Outlook, Optimization, and Challenges

Optimization strategies for maximizing spin-splitter magnonic torque include:

• Material engineering: Employing low-damping insulators (YIG, $\alpha \sim 10^{-4}$) to extend magnon propagation length ($L_\text{prop}$) and lower switching thresholds; selecting large $\theta_\text{SH}$ heavy metals (W, $\beta$-Ta, topological insulators) to boost SOT efficiency (Divinskiy et al., 2018).
• Geometric tuning: Tailoring nano-notch shape, domain wall width, and injection position for precise control of splitter ratio and magnon polarization.
• Crystal orientation: In altermagnets, exploiting $d$-wave symmetry to direct domain-wall/skyrmion motion and suppress undesired precession or deflection.

Limitations include:

• Gilbert damping–induced loss in metallic ferromagnets, leading to high excitation currents or rapid decay.
• Joule heating in metallic SOT devices, which imposes operational limits.
• Experimental challenges in isolating purely magnonic currents from charge or phononic contributions in device measurements.

Spin-splitter magnonic torque unifies the conceptual framework for magnon-based manipulation of magnetic textures and order, defining both a class of symmetry-encoded micromagnetic phenomena and a roadmap for their technological exploitation in dissipationless, scalable spintronic circuits (Divinskiy et al., 2018, Cheng et al., 2018, Schwartz et al., 16 Dec 2025, Sarkar et al., 6 Jul 2025, Yan et al., 2011, Lan et al., 2022, Wang et al., 2017).