Contributor info: Prof. Oleg Tchernyshyov

Oleg Tchernyshyov

SciPost Phys. Lect. Notes 85 (2024) · published 5 September 2024 | Toggle abstract · pdf

These lecture notes from the 2023 Summer School "Principles and applications of symmetry in magnetism" introduce the reader to the classical field theory of ferromagnets and antiferromagnets.

Xiaofan Wu, Oleg Tchernyshyov

SciPost Phys. 12, 159 (2022) · published 12 May 2022 | Toggle abstract · pdf

When a magnetic skyrmion is modeled as a point particle, its dynamics depends on the precise definition of the skyrmion center. The guiding-center position, defined as the first moment of the skyrmion density, exhibits Thiele's massless dynamics; position based on the first moment of magnetization component $m_z$ shows Larmor oscillations characteristic of a massive particle. We show that, even with the latter definition, the Larmor oscillations may be absent for certain types of external forces such as adiabatic spin torque. We offer an alternative mechanical model of a skyrmion featuring two coupled massless particles.

Xingjian Di, Oleg Tchernyshyov

SciPost Phys. 11, 108 (2021) · published 21 December 2021 | Toggle abstract · pdf

The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This makes canonical momenta gauge-dependent and requires a careful application of Noether's theorem. We show that Cartan's theory of differential forms is a natural language for this task. We use it to derive conserved momenta of the Belavin--Polyakov skyrmion, whose symmetries include translation, global spin rotation, and dilation.

Daniel Hill, Valeriy Slastikov, Oleg Tchernyshyov

SciPost Phys. 10, 078 (2021) · published 29 March 2021 | Toggle abstract · pdf

We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.