A Hall viscosity for skyrmion via magnon interaction

TL;DR

The study identifies a Hall viscosity term in skyrmion dynamics arising from parity-breaking Dzyaloshinskii-Moriya interaction after temporally averaging the magnon contributions, producing a transverse force proportional to the skyrmion circumference and dependent on the magnon density gradient. By combining a slow-mode Thiele equation with a circular-magnon ansatz, the authors show that the Hall viscosity term is rooted in the DM term and scales with skyrmion size and the ratio $J/D$, while the skyrmion Hall angle is governed by $J/D$, $P$, and damping $\alpha$, with opposite charges yielding opposite transverse deflections. They further introduce a velocity-dependent neutral Hall viscosity parameterized by $R$, which can create asymmetries between $+1$ and $-1$ skyrmions and even abrupt jumps in the Hall angle, suggesting experimentally detectable signatures. Overall, the work extends the concept of Hall viscosity to magnetic skyrmions in insulating magnets, highlighting a parity-violating transport mechanism mediated by magnon-skyrmion interactions and DM coupling, with potential implications for controlled skyrmion motion.

Abstract

We identify a Hall viscosity term directly from the Dzyaloshinskii-Moriya interaction (DMI), that breaks parity symmetry, in the skyrmion motion of insulating magnets by time-averaging the magnon contribution to all orders. The viscosity term is proportional to the skyrmion charge. Skyrmion Hall angle shows significant dependence on the skyrmion shape and size, the ratio of exchange over DMI parameters, while roughly independent of the Gilbert damping parameter. The Hall angles have the same magnitude for opposite skyrmion charges. We speculate a velocity-dependent Hall viscosity contribution to seek asymmetric Hall angles for the opposite charges.

Figures (2)

• Figure 1: Hall angle with Log-Log scales for $(J/D, \alpha)$
• Figure 2: Hall angles $\theta_\pm (R)$ for $-0.1 < R <0.1$