Current-Induced Spin-Wave Doppler Shift in Antiferromagnets

TL;DR

This paper theoretically investigates how electric currents induce a Doppler shift in spin waves within antiferromagnets, revealing the roles of uniform and staggered electron spin densities and their impact across different transport regimes.

Contribution

It identifies and analyzes the contributions of both uniform and staggered spin densities to spin-wave Doppler shifts in antiferromagnets, including microscopic calculations across various transport regimes.

Findings

Both ${oldsymbol v}_n$ and ${oldsymbol v}_ extell$ contribute equally to the Doppler shift.

The sign of the Doppler shift depends on band filling and transport regime.

${oldsymbol v}_n$ and ${oldsymbol v}_ extell$ can change sign as parameters vary.

Abstract

We theoretically study the spin dynamics in antiferromagnets (AFs)under the influence of an electric current. We identify two different sources of spin-transfer torques that stem from uniform (${\boldsymbol v}_n$) and staggered (${\boldsymbol v}_\ell$) electron spin densities. While the former is well recognized, the latter is often overlooked. We show that both ${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ contribute equally to the spin-wave Doppler shift. Microscopic calculations are presented for electrons on a two-dimensional square lattice with nearest-neighbor ($t$) and next-nearest-neighbor ($t'$) hopping, which interpolate two opposite transport regimes of strongly-coupled AF ($t'/t \ll 1$) and two weakly coupled ferromagnets ($t'/t \gg 1$). In the AF transport regime ($t'/t \ll 1$), ${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ have opposite signs, and the sign of the Doppler shift depends on band filling; ${\boldsymbol v}_n$ (${\boldsymbol v}_\ell$) is dominant near the AF gap (near the band bottom or the top). As $t'/t$ is increased, ${\boldsymbol v}_n$ undergoes a sign change whereas ${\boldsymbol v}_\ell$ does not. In the limit of vanishing $t$, ${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ coincide and the spin-transfer torque reduces to that of ferromagnets.