Current-Induced Spin-Wave Doppler Shift in Antiferromagnets

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 (${\mathbf{v}}_n$) and staggered (${\mathbf{v}}_{\ell }$) electron spin densities. While the former is well recognized, the latter is often overlooked. We show that both ${\mathbf{v}}_n$ and ${\mathbf{v}}_{\ell }$ 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 ($t^{\prime }$) hopping, which interpolate two opposite transport regimes of strongly-coupled AF ($t^{\prime }/t\ll 1$) and two weakly coupled ferromagnets ($t^{\prime }/t\gg 1$). In the AF transport regime ($t^{\prime }/t\ll 1$), ${\mathbf{v}}_n$ and ${\mathbf{v}}_{\ell }$ have opposite signs, and the sign of the Doppler shift depends on band filling; ${\mathbf{v}}_n$ (${\mathbf{v}}_{\ell }$) is dominant near the AF gap (near the band bottom or the top). As $t^{\prime }/t$ is increased, ${\mathbf{v}}_n$ undergoes a sign change whereas ${\mathbf{v}}_{\ell }$ does not. In the limit of vanishing $t$, ${\mathbf{v}}_n$ and ${\mathbf{v}}_{\ell }$ coincide and the spin-transfer torque reduces to that of ferromagnets.

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