Skyrmions and Hall Transport

Abstract

We derive a generalized set of Ward identities that captures the effects of topological charge on Hall transport. The Ward identities follow from the 2+1 dimensional momentum algebra, which includes a central extension proportional to the topological charge density. In the presence of topological objects like Skyrmions, we observe that the central term leads to a direct relation between the thermal Hall conductivity and the topological charge density. We extend this relation to incorporate the effects of a magnetic field and an electric current. The topological charge density produces a distinct signature in the electric Hall conductivity, which is identified in existing experimental data, and yields further novel predictions. For insulating materials with translation invariance, the Hall viscosity can be directly determined from the Skyrmion density and the thermal Hall conductivity to be measured as a function of momentum.

6+1 pages including Supplemental Material. Version to appear in Physical Review Letters

References in corpus (13)

• Spontaneous Skyrmion Ground States in Magnetic Metals
• Theory of current-driven motion of Skyrmions and spirals in helical magnets
• Robust formation of skyrmions and topological Hall effect in epitaxial thin films of MnSi
• Thermally Driven Ratchet Motion of Skyrmion Microcrystal and Topological Magnon Hall Effect
• Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi
• Rotating skyrmion lattices by spin torques and field or temperature gradients
• Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu2OSeO3
• Spacetime Symmetries of the Quantum Hall Effect
• Theory of helical spin crystals: phases, textures and properties
• Crystalline phases in chiral ferromagnets: Destabilization of helical order
• Noncommuting Momenta of Topological Solitons
• Dynamics of magnon fluid in Dzyaloshinskii-Moriya magnet and its manifestation in magnon-Skyrmion scattering
• Ward Identities for Hall Transport

Cited by in corpus (9)

• Skyrmions in Magnetic Multilayers
• Colloquium: Quantum skyrmionics
• Topical Review on Skyrmions and Hall Transport
• Quantum skyrmion Hall effect
• Modeling Hall viscosity in magnetic-skyrmion systems
• Skyrmions and Hall viscosity
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Generalizing Thiele Equation
• Skyrmion vs. antiskyrmion Hall angles