SciPost Phys. 12, 159 (2022) ·
published 12 May 2022
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.
SciPost Phys. 11, 108 (2021) ·
published 21 December 2021
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.
SciPost Phys. 10, 078 (2021) ·
published 29 March 2021
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.
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