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Edge spin galvanic effect in altermagnets

L. E. Golub

TL;DR

We address edge-based spin-charge interconversion in centrosymmetric d-wave altermagnets, where bulk spin galvanic coupling is symmetry-forbidden. By solving a Boltzmann kinetic equation for a spin-polarized semi-infinite plane with an edge along y, we show that a nonequilibrium spin along the Néel vector S_N yields an edge electric current J_edge = Xi S_N with Xi = beta k_F^2 (e tau^2)/(m tau_s) sin(2 theta), and that the current is localized within a stripe of width ~ v_F tau and reverses upon reversal of the Néel vector. The paper also predicts a pure spin edge photocurrent under polarized light, J_edge^s = -2 beta sin(2 theta) n (e tau)^3 [3+(omega tau)^2] / [m hbar^2 [1+(omega tau)^2]^2] E_x^2, which can be converted to an electric edge current by applying a magnetic field: J_edge = 2 B beta sin(2 theta) g mu_B (e tau)^3 [3+(omega tau)^2] / [pi hbar^4 [1+(omega tau)^2]^2] E_x^2. Together, these results establish edge-enabled spin-charge interconversion in altermagnets, offer concrete predictions for polarization- and frequency-dependent edge responses, and point to experimental routes via spin pumping and terahertz excitation.

Abstract

The edge spin galvanic effect (ESGE) in $d$-wave altermagnets is proposed. ESGE is a creation of an electrical current flowing along the edge of the sample, which is driven by the spin orientation of charge carriers. The ESGE current is formed owing to the altermagnetic spin splitting and the scattering of carriers by the edge of the sample. The current is sensitive to the orientation of the edge in respect to the main axes of the altermagnet. The edge spin galvanic current reverses its direction upon a reversal of the non-equilibrium spin direction or the Néel vector. We also propose the pure spin edge photocurrent excited by polarized radiation and formed at the edges of a sample. Its dependence on the radiation polarization and frequency is analyzed. The application of an external magnetic field converts this pure spin photocurrent into an electric current along the edge.

Edge spin galvanic effect in altermagnets

TL;DR

We address edge-based spin-charge interconversion in centrosymmetric d-wave altermagnets, where bulk spin galvanic coupling is symmetry-forbidden. By solving a Boltzmann kinetic equation for a spin-polarized semi-infinite plane with an edge along y, we show that a nonequilibrium spin along the Néel vector S_N yields an edge electric current J_edge = Xi S_N with Xi = beta k_F^2 (e tau^2)/(m tau_s) sin(2 theta), and that the current is localized within a stripe of width ~ v_F tau and reverses upon reversal of the Néel vector. The paper also predicts a pure spin edge photocurrent under polarized light, J_edge^s = -2 beta sin(2 theta) n (e tau)^3 [3+(omega tau)^2] / [m hbar^2 [1+(omega tau)^2]^2] E_x^2, which can be converted to an electric edge current by applying a magnetic field: J_edge = 2 B beta sin(2 theta) g mu_B (e tau)^3 [3+(omega tau)^2] / [pi hbar^4 [1+(omega tau)^2]^2] E_x^2. Together, these results establish edge-enabled spin-charge interconversion in altermagnets, offer concrete predictions for polarization- and frequency-dependent edge responses, and point to experimental routes via spin pumping and terahertz excitation.

Abstract

The edge spin galvanic effect (ESGE) in -wave altermagnets is proposed. ESGE is a creation of an electrical current flowing along the edge of the sample, which is driven by the spin orientation of charge carriers. The ESGE current is formed owing to the altermagnetic spin splitting and the scattering of carriers by the edge of the sample. The current is sensitive to the orientation of the edge in respect to the main axes of the altermagnet. The edge spin galvanic current reverses its direction upon a reversal of the non-equilibrium spin direction or the Néel vector. We also propose the pure spin edge photocurrent excited by polarized radiation and formed at the edges of a sample. Its dependence on the radiation polarization and frequency is analyzed. The application of an external magnetic field converts this pure spin photocurrent into an electric current along the edge.

Paper Structure

This paper contains 3 sections, 43 equations, 3 figures.

Table of Contents

  1. Edge spin galvanic current calculation
  2. ESGE current density
  3. Pure spin edge photocurrent calculation

Figures (3)

  • Figure 1: (a): Semi-infinite $d$-wave altermagnet with the edge along $y$ axis. Red and blue curves show the Fermi contours for two spin states with the main axes $(x_0,y_0)$ rotated by angle $\theta$ in respect to $(x,y)$. (b): Edge spin galvanic current formation. In the presence of a nonequilibrium spin $\bm S$ parallel to the Néel vector $\bm N$, electrons from each spin subband flow to the sample edge at some preferred angle. The asymmetry in the electron momentum distribution emerges due to scattering off the edge, thus forming the edge current. At opposite spin orientation the edge current reverses its direction.
  • Figure 2: Spatial distribution of the ESGE current density near the sample edge for specular and diffuse edge scattering. The current density is normalized by $J_{\rm edge}/(v_{\rm F}\tau)$, where $J_{\rm edge}$ is the total current at specular scattering Eq. \ref{['J_edge_result']}.
  • Figure 3: Pure spin edge photocurrent in a $d$-wave altermagnet. (a) The current is maximal at the radiation polarization perpendicular to the edge. It varies as $\propto \sin{2\theta}$ with the angle $\theta$ between the edge and the main axes of the $d$-wave altermagnet, Eq. \ref{['J_s']}. The spin-up and spin-down carriers shown by red and blue circles are accumulated at the corners of the sample. (b) Pure spin edge photocurrent dependence on the radiation frequency.