Hall Effect of Spin Waves in Frustrated Magnets

We examine a possible spin Hall effect for localized spin systems with no charge degrees of freedom. In this scenario, a longitudinal magnetic field gradient induces a transverse spin current carried by spin wave excitations with an anomalous velocity which is caused by a topological Berry-phase effect associated with spin chirality, in analogy with anomalous Hall effects in itinerant electron systems. Our argument is based on semiclassical equations of motion applicable to general spin systems. Also, a microscopic model of frustrated magnets which exhibits the anomalous spin Hall effect is presented.

Figure 1

(a) Schematic view of the origin of the Hall effect of spin waves. Short arrows represent spin structures. Long arrows represent spin current flows. See the text. (b) Examples of plots of ${\sigma }_{xy}^{\mathrm{SHE}}/K^2$ (solid line) and ${\sigma }_{xy}^D/\tau J_1^3$ (broken line) versus $T/J_1$ for several values of $\sin {\phi }_1$. ${\Delta }_1={\Delta }_2=0.8$, $J_1=1.0$, $J_2=1.5$. $\sin {\phi }_1=0.3,0.5,0.8$ (from bottom to top). (c) Plots of ${\sigma }_{xy}^{\mathrm{SHE}}/K^2$ (solid line) and ${\sigma }_{xy}^D/\tau J_1^3$ (broken line) versus $\sin {\phi }_1$ for ${\Delta }_1={\Delta }_2=0.8$, $J_1=1.0$, $J_2=1.5$, and $T/J_1=0.8$.