Abstract
Magnetic skyrmions are topologically stable objects that are made with a bunch of spins tightly arranged in a smooth fashion. Their topological nature provides unusual and complex transport properties, such as the skyrmion Hall effect. Extensive Hall data have further revealed asymmetry between skyrmion and antiskyrmion Hall angles, which cannot be accounted by known mechanisms. Here, we explain this asymmetry by utilizing another universal transport coefficient called `Hall viscosity,' extensively studied in quantum Hall systems. Hall viscosity is modeled in steady-state skyrmions motion by generalizing the Thiele equation with a transverse velocity component and is independent of the skyrmion charge. Our analyses, based on available asymmetric Hall angle data, reveal this transverse force amounts 3\% - 5.4\% of the force due to the skyrmion Hall effect. Further clarification of Hall viscosity will be essential for designing next generation storage devices properly, not to mention for our deeper understanding of fundamental properties of nature.
Highlights
Skyrmions are particlelike extended spin textures that are found in magnetic materials and characterized by a topological number [1,2,3]
We study the properties of Hall viscosity using hydrodynamics and model them in a Thiele equation [16] that describes the center of motion of a skyrmion
We show that Hall viscosity can resolve the asymmetric Hall angles between skyrmions and antiskyrmions
Summary
Universal hydrodynamics for a system with skyrmions suggests the existence of Hall viscosity ηH , antisymmetric viscosity tensor in addition to the symmetric one [11]. D2x q with q = n · (∂xn × ∂yn), is an odd function of n and changes its sign Hall viscosity is parallel to the direction of fluid motion, T yy ay = −2ηH (∂xvy ) x, while shear viscosity is transverse to it, T yx ax = −2η(∂xvy ) y These results can be confirmed in cylindrical coordinates with a finite area element. We demonstrate that Hall viscosity and the corresponding transverse force only depend on the direction of flow and are independent of skyrmion charge. The combination QR from the skyrmion Hall effect and Hall viscosity accelerates skyrmions and decelerates antiskyrmions, or vice versa, depending on the sign of R This is in contrast to the transverse force (10). Generalized Thiele equation (7), which includes (10) and (11), describes drastically different Hall transport phenomena
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