Magnonic USMR in Spin-Hall Heterostructures

• Magnonic USMR is a nonlinear magnetoresistance effect where electron–magnon interactions create an odd resistance response upon reversing current or magnetization.
• It is characterized via second-harmonic transport measurements that separate magnon contributions from spin-orbit torque and thermal effects in various HM/FM and HM/FI systems.
• Optimization through material thickness, interfacial engineering, and spin Hall angle tuning enhances the magnon-mediated response, benefiting ultrafast and antiferromagnetic device applications.

Magnonic unidirectional spin-Hall magnetoresistance is the magnon-mediated component of unidirectional spin Hall magnetoresistance (USMR), a nonlinear magnetoresistive response in spin-orbit-coupled heterostructures for which the longitudinal resistance changes upon reversal of either the applied current or the magnetic order. In the systems discussed in the literature, a charge current in a heavy metal or topological spin source generates spin accumulation or a spin current through the spin Hall effect, or in some topological-insulator heterostructures through spin-momentum locking and possibly the Rashba-Edelstein effect; when that nonequilibrium spin angular momentum creates, annihilates, or accumulates magnons, the resistance acquires an odd-in-current, odd-in-magnetization contribution that is commonly isolated in second-harmonic transport. The resulting phenomenology spans metallic HM/FM bilayers, HM/FM/HM trilayers, ferromagnetic-insulator and antiferromagnetic-insulator bilayers, topological-insulator heterostructures, and terahertz-driven ultrafast devices (Avci et al., 2018, Sterk et al., 2018, Cheng et al., 2022, Salikhov et al., 2024).

1. Definition, symmetry, and observables

USMR is a nonlinear magnetoresistance effect rather than a reciprocal magnetoresistance. In HM/FM heterostructures it arises from spin accumulation at the HM/FM interface generated by the spin Hall effect, and the signal is unidirectional in the sense that it is linear in both the magnetization $\mathbf m$ and the applied charge current density $j$. In harmonic transport language, the USMR-related resistance scales as $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$ (Moskaltsova et al., 2021).

For magnonic USMR, the essential distinction is that the resistance asymmetry is tied to magnons rather than only to spin-dependent electronic conduction. In metallic bilayers this may appear through electron-magnon scattering or spin current-driven magnon generation; in HM/FI bilayers it can arise even when the magnetic layer is insulating; and in antiferromagnetic systems it can be governed by antiferromagnetic magnon populations or by a nonequilibrium magnon chemical potential (Avci et al., 2018, Sterk et al., 2018, Cheng et al., 2022, He et al., 12 Dec 2025).

A standard dimensionless definition used in the theoretical literature is

$$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$

which makes explicit that USMR is odd under reversal of the driving field or current (Sterk et al., 2018). This odd symmetry distinguishes it from SMR, AMR, and other reciprocal magnetoresistances, while also explaining why second-harmonic longitudinal and Hall measurements are central to its detection (Yin et al., 2017, Prok et al., 23 Apr 2025).

2. Microscopic mechanisms

The baseline electronic theory was formulated by Zhang and Vignale for HM/FM bilayers: spin accumulation generated by the bulk spin Hall current in the heavy metal modifies the in-plane conductivity of the ferromagnetic metal through the spin-polarization dependence of the electron mobility, yielding a nonlinear magnetoresistance that appears at first order of the spin Hall angle (Zhang et al., 2016). This mechanism is sufficient to explain some metallic results, particularly where thickness dependence follows drift-diffusion expectations (Yin et al., 2017).

Magnonic USMR introduces additional channels. In Co/Pt and CoCr/Pt bilayers, three competing mechanisms were identified: interface spin-dependent electron scattering, bulk spin-dependent scattering, and electron-magnon scattering. The magnonic term, denoted spin-flip UMR or SF-UMR, is strongly field dependent, increases with temperature and current through the magnon population, and can dominate at low field and high current (Avci et al., 2018). In W/CoFeB, the current dependence was separated into a spin-dependent-scattering regime at small current densities $J \sim 10^{9}\,\mathrm{A/m^2}$ with UMR $\propto J$, a spin-magnon-interaction regime at intermediate $J \sim 10^{10}\,\mathrm{A/m^2}$ with UMR $\propto J^3$, and a spin-transfer torque regime at $J \sim 10^{11}\,\mathrm{A/m^2}$ where the UMR ratio becomes current independent (Chang et al., 2021).

A distinct magnonic theory applies to HM/FI bilayers. For Pt|YIG, diffusive transport of Holstein-Primakoff magnons leads to an interfacial spin accumulation and a magnoresistance that is not invariant under inversion of current direction. Because the interfacial spin current is nonlinear in the electron and magnon accumulations, the magnonic USMR is, to leading order, cubic in the spin Hall angle, in contrast to the linear spin Hall angle dependence of the electronic contribution (Sterk et al., 2018).

Recent work has further split magnonic USMR into two physically different categories. One is the conventional fluctuation-driven mechanism, in which spin current-induced magnetization fluctuations or magnon creation-annihilation processes control the resistance and are suppressed at high magnetic field and low temperature. The other is a nonequilibrium magnon-accumulation mechanism characterized by a finite magnon chemical potential. In CrPS$_4$/Pt, the latter produces a large magnonic USMR that persists under strong magnetic fields and low temperatures and peaks near the spin-flip transition; the quadratic term in the magnon chemical potential dominates the USMR (He et al., 12 Dec 2025).

A further theoretical refinement is the coupled electron-magnon diffusion framework for metallic bilayers. There, nonequilibrium magnons are indirectly excited by the electric field through spin Hall injection and electron-magnon scattering, and they can suppress UMR by absorbing spin angular momentum from conduction electrons. In that description, cross diffusion and spin-angular-momentum transfer renormalize the characteristic electron and magnon spin-diffusion lengths, so magnonic participation is not only an additive channel but also a renormalization of the electronic one (Gupta et al., 11 Oct 2025).

Mechanism	Core process	Representative platforms
Electronic USMR	SHE-induced spin accumulation modulates spin-dependent mobility	HM/FM bilayers
SF-UMR / fluctuation-driven magnonic USMR	Electron-magnon scattering or current-induced magnon creation-annihilation	Co/Pt, CoCr/Pt, Py/Pt, W/CoFeB
Chemical-potential-driven magnonic USMR	Nonequilibrium magnon accumulation with finite magnon chemical potential	CrPS$j$0/Pt
Diffusive magnonic USMR in insulators	Holstein-Primakoff magnons and nonlinear interfacial spin transfer	Pt

3. Metallic heterostructures

Metallic HM/FM bilayers supplied the first systematic evidence that magnonic and electronic contributions coexist. In Pt/Co/AlO$j$1, USMR shows a non-monotonic dependence on both Pt and Co thicknesses: the normalized USMR reaches a maximum at around $j$2 Pt and at about $j$3 Co, and the data are well fitted by a drift-diffusion theory with transport parameters extracted using the Fuchs-Sondheimer model. Under those room-temperature conditions, the agreement was taken to attribute USMR to spin-Hall-induced spin accumulation and metallic diffusion in the ferromagnetic layer (Yin et al., 2017).

That conclusion is not universal. In Permalloy/Pt, simultaneous electronic measurements and micro-focus Brillouin light scattering established that the current dependence of USMR closely follows the dipolar magnon density and that both dependencies exhibit the same scaling over a large temperature range of $j$4–$j$5. The measured USMR could be fitted by the same nonequilibrium kinetic form used for the BLS magnon intensity,

$j$6

with the same critical current $j$7, which was interpreted as direct evidence that the same magnon population underlies both observables (Borisenko et al., 2018).

The metallic literature also shows that the magnonic contribution is highly tunable. In Co/Pt and CoCr/Pt, both positive and negative UMR can be obtained by tuning the interface and bulk spin-dependent scattering terms relative to the magnon population, and the field-dependent magnonic part follows a power law in field because a stronger field suppresses the magnon population (Avci et al., 2018). In W/CoFeB at room temperature, the UMR ratio reaches approximately $j$8, and the high-current saturation regime is correlated with spin-transfer torque-induced tilting of the magnetization; nonetheless, the intermediate regime retains the explicit spin-magnon-interaction signature $j$9 (Chang et al., 2021).

Trilayer engineering extends the same logic. In Pt/Co/Ta and Ta/Co/Pt, introducing a second heavy metal with the opposite sign of the spin Hall angle enhances both SOTs and USMR because spin currents injected from the two heavy metals into the central Co layer can add constructively. For Pt/Co/Ta, the maximum effective spin Hall angle reaches $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$0, and the normalized USMR reaches $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$1 per $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$2, which is up to $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$3 higher than in the best bilayer comparator. W/Co and W/Co/Pt do not show similar enhancement, which was attributed to mixed $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$4-phase W and possible oxidation (Moskaltsova et al., 2021). This suggests that interfacial engineering, current partitioning, and spin Hall angle sign are as important as the presence of magnons themselves.

4. Insulating and antiferromagnetic systems

A common misconception is that USMR requires a conductive ferromagnet. The HM/FI theory for Pt|YIG shows the opposite: a magnonic contribution can occur in ferromagnetic insulators because the nonlinearity resides in interfacial spin transfer and magnon diffusion rather than in charge transport within the magnetic layer. For realistic Pt|YIG parameters the maximal magnonic USMR is estimated to be on the order of $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$5, but it may reach values of up to $R^{2\omega}_{USMR} \sim |j \times \mathbf m|$6 if the magnon gap is suppressed; the signal can also be enhanced by an order of magnitude when the magnon diffusion length is reduced to an optimal value (Sterk et al., 2018).

Antiferromagnetic insulators bring a different symmetry structure. In Pt/$R^{2\omega}_{USMR} \sim |j \times \mathbf m|$7-Fe$R^{2\omega}_{USMR} \sim |j \times \mathbf m|$8O$R^{2\omega}_{USMR} \sim |j \times \mathbf m|$9, USMR was observed even though the magnetic layer is an antiferromagnetic insulator, and systematic field- and temperature-dependent measurements were used to confirm its magnonic origin. The mechanism was described as an imbalance of creation and annihilation of antiferromagnetic magnons by spin-orbit torque due to thermal random field. Unlike ferromagnetic magnonic USMR, the field dependence is non-monotonic: the USMR increases with field, peaks at about $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$0, and then decreases at higher fields; at $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$1 it rapidly drops to zero below $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$2 (Cheng et al., 2022).

CrPS$$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$3/Pt introduces yet another antiferromagnetic regime. There, the nonequilibrium magnon accumulation characterized by a finite magnon chemical potential leads to a large and robust magnonic USMR that survives strong magnetic fields and low temperatures and displays a pronounced peak near the spin-flip transition, roughly $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$4 at $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$5. The figure of merit is reported as $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$6, which exceeds that of YIG/Pt by more than two orders of magnitude and is twice as large as the electrical USMR in Ta/Co bilayers. The field and temperature dependences were interpreted as evidence that spin transport is dominated by magnon chemical-potential gradients rather than thermal- or fluctuation-driven magnon generation (He et al., 12 Dec 2025).

These insulating and antiferromagnetic results materially broaden the subject. Magnonic USMR is not a small correction to metallic USMR alone; it can be the primary effect, and in antiferromagnets it can encode the Néel-state response, field-induced canting, and phase transitions in a two-terminal geometry (Cheng et al., 2022, He et al., 12 Dec 2025).

5. Enhancement strategies and materials platforms

One route to enhancement is to increase spin injection while preserving the conditions for magnon generation. In HM/FM/HM trilayers, using heavy metals with opposite spin Hall angles produces constructive spin-current injection into the central ferromagnet, thereby increasing both SOT and USMR (Moskaltsova et al., 2021). In metallic bilayers, thickness optimization relative to spin diffusion lengths is equally important, because USMR decreases for layers that are too thin or too thick due to insufficient spin current, current shunting, or spin relaxation (Yin et al., 2017).

A second route is to exploit materials with efficient spin-charge conversion and strong spin-disorder scattering. In topological-insulator/ferromagnetic-metal heterostructures such as BST/CoFeB and BS/CoFeB, USMR was observed in a technologically relevant device geometry, and the reported figure of merit is comparable to the highest values in Ta/Co bilayers. The best reported figure of merit is $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$7 and $$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$8 for BS($$\mathcal{U} \equiv \left| \frac{\rho(E)-\rho(-E)}{\rho(E)} \right|,$$9 QL)/CoFeB at $J \sim 10^{9}\,\mathrm{A/m^2}$0 (Lv et al., 2017).

The most dramatic enhancement in the supplied literature appears in the BiSb/GaMnAs topological-insulator/ferromagnetic-semiconductor heterostructure, where a giant UMR ratio of $J \sim 10^{9}\,\mathrm{A/m^2}$1 was reported. The dominant mechanism was identified not as GMR-like spin-dependent scattering but as magnon emission/absorption together with strong spin-disorder scattering in the GaMnAs layer. The magnonic term shows a nonlinear current dependence proportional to $J \sim 10^{9}\,\mathrm{A/m^2}$2, increases with sample temperature, and is suppressed by high field, all of which are consistent with a magnonic origin. Conductivity matching between BiSb and GaMnAs is decisive: when the current bypasses GaMnAs, magnonic effects are quenched and thermally driven pseudo-UMR signals remain (Khang et al., 2019).

A third route is to alter the magnetic excitation spectrum itself. The Pt|YIG theory identifies low magnon gap, short magnon diffusion length, and large spin Hall angle as favorable conditions for increasing magnonic USMR (Sterk et al., 2018). The CrPS$J \sim 10^{9}\,\mathrm{A/m^2}$3/Pt results add that nonequilibrium magnon chemical-potential engineering in van der Waals antiferromagnets can produce large, field-robust nonlinear magnetoresistance (He et al., 12 Dec 2025). Taken together, these results suggest that “magnonic USMR” is best viewed as a family of spin-charge conversion phenomena whose magnitude is controlled by the efficiency of spin injection, the magnon density of states, and the relaxation channels available to the magnetic subsystem.

6. Measurement, analysis, and dynamical regimes

Because USMR is nonlinear and often comparable in symmetry to thermoelectric and torque-induced signals, metrology is central to the subject. Second-harmonic Hall and longitudinal measurements are used to separate damping-like and field-like SOTs, Oersted fields, and thermal effects such as SSE and ANE from USMR. In Pt/Co/Ta and related trilayers, the second-harmonic Hall signal is decomposed into DL-SOT, FL-SOT, Oersted, and thermal terms, while longitudinal $J \sim 10^{9}\,\mathrm{A/m^2}$4 with proper background subtraction yields the USMR (Moskaltsova et al., 2021). In Pt/Co/AlO$J \sim 10^{9}\,\mathrm{A/m^2}$5, second-harmonic Hall measurements were specifically used to distinguish USMR caused by spin-Hall-driven spin accumulation from thermal contributions with similar symmetry (Yin et al., 2017).

More recent work shows that UMR is itself a source of systematic error in SOT analysis. In Py/Pt bilayers, unidirectional magnetoresistance that was known from the second-harmonic longitudinal resistance was shown also to appear in second-harmonic Hall data. Describing the data over a wide field range with these UMR contributions was found to be essential for accurate torque extraction; in the reported example, the antidamping SOT field $J \sim 10^{9}\,\mathrm{A/m^2}$6 was reduced from $J \sim 10^{9}\,\mathrm{A/m^2}$7 without UMR to approximately $J \sim 10^{9}\,\mathrm{A/m^2}$8 when UMR was included (Prok et al., 23 Apr 2025). This clarifies that “USMR versus SOT artifact” is not the right dichotomy: UMR is an intrinsic nonlinear transport channel that must be modeled simultaneously with torques.

The dynamical range of the phenomenon has also expanded. A terahertz study demonstrated that USMR is active at THz frequencies for picosecond-time readout and can be initiated with light fields. In FM/HM thin-film heterostructures, ultrafast USMR was detected through THz second-harmonic generation, and the temperature dependence indicated a significant contribution from electron-magnon spin-flip scattering. In the Ta(2)/Py(3)/Pt(2) sample, the USMR-SHG contribution was about $J \sim 10^{9}\,\mathrm{A/m^2}$9 of the ISHE-SHG amplitude, the signal dropped nearly threefold on cooling from $\propto J$0 to $\propto J$1, and the resistance asymmetry was estimated as approximately $\propto J$2 (Salikhov et al., 2024).

The adjacent AC SMR theory reinforces the same conceptual direction. In the terahertz regime, SMR develops pronounced singularities at magnon frequencies and acquires a longitudinal magnonic contribution to spin transport across the interface, establishing all-electric magnon spectroscopy as a realistic prospect (Reiss et al., 2021). A plausible implication is that future work on magnonic USMR will increasingly treat nonlinear magnetoresistance not only as a memory-readout mechanism but also as a spectroscopic probe of nonequilibrium magnon populations, mode structure, and spin-transport conversion across metallic, insulating, and antiferromagnetic interfaces.