Roles of Electrically Excited Magnons in Unidirectional Magnetoresistance of Metallic Magnetic Bilayers

TL;DR

This work develops a nonlinear, coupled electron–magnon diffusion framework to elucidate unidirectional magnetoresistance in metallic FM|NM bilayers. By solving coupled kinetic equations with explicit electron–magnon interactions and interfacial spin convertances, it shows nonequilibrium magnons can drain spin angular momentum from conduction electrons, thereby suppressing UMR and renormalizing spin-diffusion lengths. The theory predicts distinct fingerprints in magnetic-field dependence, FM thickness, and temperature, including a magnon-mediated reduction of spin accumulation near the interface and a peak in UMR at a characteristic FM thickness tied to a dressed diffusion length. The framework offers a unified approach to magnonic contributions to nonlinear spin transport and points to extensions involving momentum-relaxation renormalization and interfacial effects in broader heterostructures.

Abstract

Unidirectional magnetoresistance (UMR) in metallic bilayers arises from nonlinear spin-charge transport mediated by broken time-reversal and inversion symmetries, yet the role of magnons remains unsettled. We develop a theoretical framework that incorporates coupled electron-magnon dynamics, revealing cross diffusion and spin-angular-momentum transfer between the two subsystems, which renormalize the characteristic electron and magnon spin-diffusion lengths. We show that nonequilibrium magnons, indirectly excited by the electric field, can suppress UMR by absorbing spin angular momentum from conduction electrons. We also analyze the magnetic-field, thickness, and temperature dependencies and identify distinct features that constitute experimental fingerprints of magnonic contributions to UMR in metallic bilayers, providing qualitative to semiquantitative guidance for elucidating the underlying physical mechanisms.

Figures (6)

• Figure 1: Feynman diagrams of electron-magnon scattering processes. (a) Spin-flip scattering of an electron from a spin-down state $(\mathbf{k+q},\downarrow)$ to a spin-up state $(\mathbf{k},\uparrow)$, accompanied by the emission of a magnon with momentum $\mathbf{q}$ that carries an angular momentum quantum of $-\hbar$. (b) Spin-flip scattering of an electron from a spin-up state $(\mathbf{k},\uparrow)$ to a spin-down state $(\mathbf{k+q},\downarrow)$, accompanied by the absorption of a magnon with momentum $\mathbf{q}$ with angular momentum of $-\hbar$.
• Figure 2: Schematic illustration of spin transport carried by conduction electrons and magnons in an NM$|$FM bilayer. (a) Without electron–magnon interaction: spin-Hall spin current generated in the NM layer is injected into the FM, where both spin accumulation (as represented by dark blue arrows near the interface) and spin current are continuous across the interface, resulting solely in electron spin diffusion in the FM layer. (b) With electron–magnon interaction: the spin current at the NM side of the interface is partially converted into magnon accumulation, producing diffusive magnon spin current in the FM. This leads to a discontinuity in spin accumulation (reduced value at the FM interface) and coexistence of electron and magnon spin currents in the FM layer.
• Figure 3: Spatial profiles of spin accumulation and spin current in an FM$|$NM bilayer, with and without electron–magnon interactions. (a) Spin accumulation $\delta n_{\mathrm{s}}(z)$: for $J_{\mathrm{sd}}=0$ the profile is continuous across the interface (dashed red curve), while for $J_{\mathrm{sd}}\neq 0$ a discontinuity appears at the boundary and the spin accumulation inside the FM is reduced (solid black curve). (b) Electron spin current density $j_{\mathrm{s},z}(z)$: without electron--magnon interactions, the current is continuous across the interface at $z=0$ (dashed red curve); with electron--magnon interactions, $j_{\mathrm{s},z}$ shows a discontinuity at $z=0$ and is reduced in the FM (solid black curve), reflecting conversion into magnon currents. Inset shows the continuity of total spin angular momentum current across the interface when $J_{\mathrm{sd}} \neq 0$. The calculations were performed using $J_{\mathrm{sd}}^0 = 0.1\,\text{eV}$, $E_x=10^{-4}$ V/nm, and fixed layer thicknesses $d_N=d_F=50$ nm.
• Figure 4: UMR coefficient $\zeta_{\mathrm{UMR}}$ as a function of exchange coupling. The solid curves show results for different magnon thermal relaxation times $\tau_{\mathrm{th}}$ ($\tau^0_{\mathrm{th}}=100\, \text{ps}$). Inset: dependence of $\zeta_{\mathrm{UMR}}$ on exchange coupling for different magnon momentum-relaxation times $\tau_{\mathrm{m}}$ ($\tau^0_{\mathrm{m}}=10\, \text{ps}$).
• Figure 5: UMR coefficient $\zeta_{\mathrm{UMR}}$ as a function of external magnetic field $B$. The solid red curve corresponds to $B$ applied parallel to the magnetization, and the dashed red curve to $B$ applied antiparallel. Inset: $\zeta_{\mathrm{UMR}}$ as a function of intrinsic magnon gap $\Delta_\mathrm{g}$ (scaled with $\Delta^0_\mathrm{g}=1 \, \text{meV}$).