ac Current Generation in Chiral Magnetic Insulators and Skyrmion Motion induced by the Spin Seebeck Effect

We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic Skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the Skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of Skyrmion motion on the ac current generation and demonstrate that Skyrmions in insulators are a promising route for spin caloritronics applications.

Figure 1

Schematic view of the motion of a Skyrmion in the presence of a temperature gradient. The temperature gradient excites a magnon current flowing from the hot to the cold region, which drives the Skyrmion opposite to the magnon current direction. The Skyrmion motion changes the electric polarization, which generates an ac current when the insulating magnet is embedded in a closed circuit.

Figure 2

(a) Trajectory of the Skyrmion center of mass in the presence of a temperature gradient. Here, $\mathrm{\Delta }T/(L_{x}d)=0.003$ and $\alpha =0.1$. (b) Average drift velocity as a function of temperature gradient. The curves are obtained by averaging over 8 independent runs. (c) Schematic view of the magnonic spin transfer torque and the dynamics of the Skyrmion.

Figure 3

(a) Oscillation of the Skyrmion velocity with a nonzero dc component in the presence of a magnon current. (b)—(d) Dependence of the Skyrmion velocity on the amplitude $A$ and frequency ${\omega }_m$ of the ac magnetic field applied at the right edge of the sample $x=L_x$, which acts as a source of magnon current, and on the Gilbert damping $\alpha$. The inset in (d) is the Hall angle as a function of $\alpha$. The line is a fit to $\tan {\theta }_H$ in the main text.

Figure 4

ac current induced by the Skyrmion motion and magnon current, according to (a) the $d\text{−}p$ hybridization and (b) the inverse DM mechanism. Here $\alpha =0.03$, $A=1.0D^2/J_{\mathrm{ex}}$, ${\omega }_m=1.0\gamma D^2/J_{\mathrm{ex}}$,