Spin Planar Hall Effect

• Spin Planar Hall Effect is a phenomenon where spin textures and in-plane magnetization create transverse Hall signals, defined by angular dependencies and symmetry properties.
• Recent studies reveal its manifestation in topological systems, frustrated magnets, and spintronic heterostructures, with experimental challenges in distinguishing it from spin-pumping signals.
• The effect offers pathways for generating pure spin currents and controlling spin–orbit torques, paving the way for advanced spintronic devices and quantum sensing applications.

The spin planar Hall effect encompasses a range of Hall-like transport phenomena in which spin, magnetization, or spin texture is fundamentally intertwined with planar geometry, field direction, or spin-orbit coupling, resulting in transverse (Hall) signals that reflect spin and symmetry properties rather than solely charge and external field orientation. While the canonical planar Hall effect (PHE) originates from anisotropic magnetoresistance in ferromagnets, recent theoretical and experimental advances—in both crystalline materials and artificial structures—have revealed spin-driven planar Hall behaviors in topological systems, frustrated magnets, and spintronic heterostructures, including both charge and spin-current manifestations. Crucially, the spin planar Hall effect can masquerade as spin-pumping or inverse spin Hall signals in dynamical experiments, necessitating strict symmetry disentanglement in spin-pumping and spin-charge interconversion protocols.

1. Fundamentals and Angular Dependence

The planar Hall resistivity, arising from spin or magnetization texture, follows the general form

$$\rho_{xy}^{\mathrm{PHE}} = \Delta \rho \sin\theta \cos\theta,$$

where $\Delta\rho$ is the anisotropic magnetoresistance (AMR) amplitude and $\theta$ is the angle between the in-plane magnetization (or spin axis) and applied current. For itinerant ferromagnets such as permalloy or NiFe, the resistivity tensor is constructed as

$$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$

yielding PHE and angular magnetoresistance signals, both with sin2θ or cos2θ periodicity in field–current geometry. In spin-ice nanostructures, such as honeycomb Nd–Sn bilayers, the PHE emerges from the local moment configuration, specifically from chiral ‘two-in, one-out’ (2I1O) motifs, producing a net AMR and associated transverse voltage (Guo et al., 2020). In all cases, the PHE vanishes for field aligned parallel or perpendicular to current and is maximal at θ = ±45°.

2. Dynamical Regimes and Spin Rectification

When subjected to microwave or RF excitation, as in ferromagnetic resonance (FMR) or spin pumping, the planar Hall effect acts as a non-linear detector of spin dynamics via rectification: $$V_{\mathrm{PHE}} = \frac{\Delta R}{2} I_{\mathrm{RF}} \sin2\theta_0,$$ where $I_{\mathrm{RF}}$ is the current amplitude, and $\theta_0$ the equilibrium magnetization angle (He et al., 2021, Kobljanskyj et al., 2015). Dynamic magnetization precession modulates the instantaneous $\theta(t)$, and product mixing with the RF current yields a DC voltage reflecting the angular trajectory of the spin system. Notably, this spin-planar-Hall-induced rectification (PHE-SRE) can closely mimic the field symmetry of the inverse spin Hall effect (ISHE) voltages generated by pure spin current injection, especially under reversal of applied field $H$.

In microwave-driven FMR geometry, the measured DC voltage is typically decomposed into symmetric and antisymmetric Lorentzian shapes with respect to $H$: $\Delta\rho$0 where $\Delta\rho$1 is the output voltage, $\Delta\rho$2 the resonance field and $\Delta\rho$3 the linewidth. The field symmetry under $\Delta\rho$4 distinguishes true spin-pumping (odd) from PHE rectification (even) (He et al., 2021).

3. Spin Planar Hall Current and Spin-Orbit Torques

Beyond static AMR-based signals, the spin planar Hall effect is a generator of pure spin current and induces spin–orbit torques with unique angular dependencies. In ferromagnet/nonmagnet bilayers, a planar Hall charge current, $\Delta\rho$5, drives a spin current polarized along $\Delta\rho$6 across the interface. The resultant spin flux $\Delta\rho$7 exerts a torque on the magnetization, with a “biaxial” $\Delta\rho$8 symmetry distinct from the conventional spin Hall torque’s uniaxial patterns (Safranski et al., 2017, Safranski et al., 2019). The strength of planar-Hall-induced anti-damping torque is of the same order as giant spin Hall torques in Pt or Ta, with estimated charge-to-spin efficiency $\Delta\rho$9–0.09 depending on stack geometry and magnetic parameters.

In multilayer devices (e.g., CoNi/Au/CoFeB), the angular dependence of spin-torque ferromagnetic resonance measured linewidth changes,

$\theta$0

demonstrates a maximum when the source magnetization is at $\theta$1 to the film plane (Safranski et al., 2019). The polarization direction of the spin current is tunable via the magnetization orientation, enabling field-free perpendicular switching schemes in spintronic memory applications.

4. Manifestations in Topological and Frustrated Magnets

The spin planar Hall effect is not limited to canonical metallic ferromagnets but appears in topological materials, noncoplanar magnets, and frustrated systems:

• Chiral and Solitonic Lattices: In Cr$\theta$2NbS$\theta$3, the giant PHE and concomitant giant topological Hall effect both originate from a tilted chiral soliton lattice, inducing a uniform in-plane magnetization component and a nonvanishing scalar spin chirality. The planar Hall resistivity amplitude can reach $\theta$4–$\theta$5 $\theta$6 cm—orders of magnitude above ordinary ferromagnets—accompanied by a direct link to Berry curvature effects (Mayoh et al., 2022).
• Artificial Spin Ice: In Nd–Sn honeycomb mesostructures, the PHE reflects the population imbalance and chirality of two-in, one-out domain configurations. The effect emerges only in a narrow temperature window (18–32 K) consistent with robust short-range ice rule order, disappears in the antiferromagnetic ground state, and is absent when thermal disorder dominates (Guo et al., 2020). The PHE thus serves as an electrical fingerprint for emergent topological textures in frustrated lattices.
• Antiferromagnets and SOC-driven Split Bands: In $\theta$7-MnTe thin films, spin–orbit coupling induces an anisotropic, zero-field planar Hall effect via four spin-polarized valence-band pockets. The angular dependence rigidly follows sin2θ, and the maximal PHE efficiency is bounded by band-structure symmetry to $\theta$831% (Yin et al., 2018).
• Topological Insulators: In surfaces of dual-gated Bi$\theta$9Sb$$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$0Te$$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$1, a spin-dependent planar Hall effect arises from in-plane field-induced time-reversal-symmetry breaking, enabling backscattering via spin-flip impurity resonances and amplifying resistivity anisotropy near the Dirac point. Notably, nonlinear “bilinear” contributions in response to both field and current reversal have been identified as fingerprints of inhomogeneous spin-momentum locking (Taskin et al., 2017, Zarezad et al., 2022).
• Topological Hall–Planar Hall Interplay: In Fe$$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$2Sn$$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$3, “planar topological Hall effect” emerges when a current is parallel to c axis and field rotates into the current axis, with the transverse signal peaking near magnetic saturation. The real-space Berry curvature, determined by spin spiral structure and finite scalar chirality, underlies this PTHE—distinguishable from both conventional planar and anomalous Hall effects (Li et al., 2021).

5. Experimental Disentanglement and Symmetry Protocols

A significant challenge is the unambiguous separation between spin Hall, planar Hall, and spin-pumping-induced signals in experiment. Practical recipes to distinguish them are:

• Field-Symmetry Analysis: Measure $$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$4 and $$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$5 at fixed magnetization angle. The ISHE (spin-pumping) voltage is odd in field, $$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$6; the PHE rectification is even, $$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$7 (He et al., 2021).
• Angular Geometry Selection: Set device and field geometry such that AMR rectification vanishes (e.g., angle $$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$8 in the CPW gap). Under this condition, pure PHE rectification and ISHE reach maximal contrast.
• Lorentzian Decomposition: Fit voltage as a sum of symmetric and antisymmetric Lorentzians; analyze their field symmetry according to material and stack parameters.
• Harmonic Detection: In non-magnetic, low-symmetry materials (e.g., IrO$$\hat{\rho} = \rho_0\,I + \Delta\rho\,\hat{m} \hat{m}^T,$$9), antisymmetric planar Hall and spin Hall effects can coexist. Harmonic Hall measurements, decomposed into parts even (conventional PHE) and odd (APHE) in B, enable clear separation. Lorentz-force contributions (odd in field) are symmetry-allowed only in specific crystal orientations (Yang et al., 2024).

6. Microscopic Mechanisms and Theory

Several microscopic routes underpin the spin planar Hall effect:

• Anisotropic Magnetoresistance (AMR): Conventional mechanism involving spin-dependent scattering rates and current deflection by in-plane magnetization.
• Noncoplanar Spin Chirality and Berry Curvature: In chiral magnets and frustrated lattices, the finite scalar spin chirality establishes emergent gauge fields, imparting Berry phases to conduction electrons and producing both planar and topological Hall signals (Guo et al., 2020, Li et al., 2021, Mayoh et al., 2022).
• Spin-Orbit Coupling and Band Topology: SOC-driven splitting and band anisotropy in antiferromagnets and TIs can produce angularly modulated transverse spin/charge currents, with upper efficiency bounds determined by symmetry (e.g., D$$V_{\mathrm{PHE}} = \frac{\Delta R}{2} I_{\mathrm{RF}} \sin2\theta_0,$$0 in MnTe, low-symmetry mirror planes in IrO$$V_{\mathrm{PHE}} = \frac{\Delta R}{2} I_{\mathrm{RF}} \sin2\theta_0,$$1) (Yin et al., 2018, Yang et al., 2024).
• Planar Spin Hall Effect (Spin Current Variant): Analogous to the conventional SHE but with spin current and polarization within the plane of electric field and Hall response; characterized by a Berry-phase–controlled “spin-repulsion” vector $$V_{\mathrm{PHE}} = \frac{\Delta R}{2} I_{\mathrm{RF}} \sin2\theta_0,$$2 existing only in specific crystal point groups (Pan et al., 2021).

7. Applications and Outlook

The spin planar Hall effect, in both its charge and spin-current forms, is now a key probe for spin texture, chirality, and symmetry in quantum materials:

• Spintronic Devices: Exploiting PHE as an integrated spin current source or selector in MRAM, spin transfer oscillators, and field-free switching architectures (Safranski et al., 2017, Safranski et al., 2019).
• Quantum Sensing: Harnessing giant PHE signals in metamagnetic and topological antiferromagnets (e.g., EuAl$$V_{\mathrm{PHE}} = \frac{\Delta R}{2} I_{\mathrm{RF}} \sin2\theta_0,$$3Si$$V_{\mathrm{PHE}} = \frac{\Delta R}{2} I_{\mathrm{RF}} \sin2\theta_0,$$4) for high-precision angle-sensitive magnetic-field sensors and magnetic-noise detection (Liu et al., 27 Aug 2025).
• Topological Characterization: Using PHE and its spin analogs to diagnose chiral anomalies, topological phase transitions, and domain-wall configurations in Weyl semimetals, topological insulators, and artificial spin ice systems (Zarezad et al., 2022, Guo et al., 2020).
• Material Discovery: Symmetry-based screening protocols, leveraging Berry curvature and spin-repulsion analysis, enable theoretical prediction and search for high-efficiency planar spin Hall materials, with explicit materials design rules set by crystal point group classification (Pan et al., 2021).

The spin planar Hall effect thus functions as both a sensitive diagnostic and an active component in emerging spintronic and quantum electronic platforms, with ongoing research focused on optimizing magnitude, tunability, and disentanglement of multiple Hall-like contributions for next-generation devices.