Spin Splitter and Inverse Effects in Altermagnetic Hybrid Structures

TL;DR

This work develops a generalized drift–diffusion framework for diffusive charge and spin transport in altermagnets, introducing spin–momentum coupling via $T_{jk}$ and anisotropic relaxation through $oldsymbol{2amma}$. It derives and analyzes the spin–splitter effect, where charge currents generate spin currents (e.g., $j_x^s=T_{xy}j_y$), and its inverse, yielding transverse voltages in AM strips under spin injection, with closed-form results in both extended and localized injection scenarios. The authors apply the theory to hybrid multiterminal geometries, predicting nonlocal voltages and Hanle-type responses in AM–normal metal–ferromagnet devices, controlled by the Néel vector orientation. Overall, the work positions altermagnets as robust, electrically controllable spin sources in nanoscale, multiterminal spintronic devices, with clear experimental signatures and practical guidance for device design.

Abstract

We provide a theoretical description of diffusive charge and spin transport in hybrid devices containing altermagnets. Based on recently derived drift--diffusion equations for coupled charge and spin dynamics and general boundary conditions, our approach provides a unified description of the spin-splitter effect, i.e., the conversion of charge currents into spin currents, and its inverse in terms of experimentally accessible parameters. We analyze, analytically and numerically, the spin-splitter effect, demonstrating that an injected spin accumulation generates a measurable voltage difference across the transverse direction in the altermagnet. Motivated by a recent experiment, we also analyze a nonlocal spin-valve geometry in which an altermagnetic strip injects spin into a diffusive normal metal. We derive the resulting nonlocal voltage detected by a ferromagnetic electrode as a function of the relative orientation of the N'eel vector and the ferromagnetic polarization, accounting for the main experimental findings. For this setup, we further address spin precession during diffusive transport by analyzing the spin Hanle effect. Our results provide theoretical explanations and predictions for several altermagnet hybrid structures.

Figures (7)

• Figure 1: Model geometries considered for the spin–splitter effect in an altermagnetic (AM) strip. (a) Transverse voltage bias configuration, where electrochemical potentials $\pm V/2$ are applied at the edges $y = \pm \frac{L_y}{2}$. (b) Longitudinal electric field configuration, with a uniform field $E_x$ applied along the strip axis. (c) Finite rectangular geometry of dimensions $L_x \times L_y$, combining a transverse voltage bias and open lateral boundaries. These configurations serve as the basis for modeling spin–charge coupling in diffusive altermagnets.
• Figure 2: Spin accumulation in a finite altermagnetic strip induced by a longitudinal voltage difference, see Fig. \ref{['fig:spinsplitter_geometries']}(c). The dimensions of the strip are $L_x/\ell_s = L_y/\ell_s = 4$. The plot is obtained from Eq. (\ref{['eq:mus_finite_correct']}) for $G_B\ell_s/\sigma_D = 1.5$, illustrating the spatial profile of the spin accumulation.
• Figure 3: Geometries considered for transverse spin injection in an altermagnetic (AM) strip. (a) Uniform spin injection at the upper transverse boundary of an infinite strip, assuming translational invariance along the longitudinal direction. (b) Spin injection at the upper transverse edge of a finite strip, with transverse boundaries located at $y=\pm L_y/2$. (c) Spin injection localized over a finite region of the upper transverse edge of a finite strip.
• Figure 4: Normalized electrochemical potential $\mu(x,y)/\max|\mu|$ together with the induced charge current streamlines generated by localized Gaussian spin injection at the upper edge of a finite altermagnetic strip. Spatial coordinates are given in units of the spin relaxation length $\ell_s$. The parameters used are $L_x/\ell_s=10$, $L_y/\ell_s=2$ and a Gaussian injection profile of width $W=0.25\,\ell_s$ centered at $x=0$.
• Figure 5: Induced inverse spin--splitter voltage $V_{\mathrm{ISS}}$ as a function of the transverse strip length $L_y$. Symbols correspond to the numerical results obtained from the full diffusive calculation, while the solid line shows the semi--analytical prediction given by Eq. (\ref{['eq:VISS_tanh']}). Parameters used are $G_B W/\sigma=0.15$, $T_{xy}=1$, and $L_x/\ell_s=40$.