TY - JOUR

T1 - Magnon band structure of skyrmion crystals and stereographic projection approach

AU - Aristov, D. N.

N1 - Publisher Copyright: © 2022 American Physical Society.

PY - 2022/1/28

Y1 - 2022/1/28

N2 - Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The magnetization configuration is described in stereographic projection by the complex valued function f, both for the static equilibrium background and the spin-wave excitations on top of it. The topologically nontrivial ground state of SkX corresponds to simple poles of f at skyrmions' positions. We use the earlier proposed ansatz for this ground-state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Numerical analysis yields the magnon band structure in accordance with previously known results. At low energies there are two sets of bands, one set with a flat dispersion, topologically trivial, and rapidly evolving with magnetic field. Despite similarity to Landau levels scheme, the underlying equations have a different structure, making this set of bands somewhat enigmatic. Another set of bands is robust to magnetic field and is characterized by pronounced dispersion and by the Berry curvature which may be sign reversal in the Brillouin zone. We demonstrate that the dispersion is of tight-binding form and well described by nearest-neighbor hopping, which seems unexpected for smooth superlattice potential and strong nonuniform gauge field. The developed theory can be easily generalized to other types of topological spin structures and used for calculation of the dynamical susceptibility tensor and thermal transport in magnets with skyrmion lattice background.

AB - Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The magnetization configuration is described in stereographic projection by the complex valued function f, both for the static equilibrium background and the spin-wave excitations on top of it. The topologically nontrivial ground state of SkX corresponds to simple poles of f at skyrmions' positions. We use the earlier proposed ansatz for this ground-state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Numerical analysis yields the magnon band structure in accordance with previously known results. At low energies there are two sets of bands, one set with a flat dispersion, topologically trivial, and rapidly evolving with magnetic field. Despite similarity to Landau levels scheme, the underlying equations have a different structure, making this set of bands somewhat enigmatic. Another set of bands is robust to magnetic field and is characterized by pronounced dispersion and by the Berry curvature which may be sign reversal in the Brillouin zone. We demonstrate that the dispersion is of tight-binding form and well described by nearest-neighbor hopping, which seems unexpected for smooth superlattice potential and strong nonuniform gauge field. The developed theory can be easily generalized to other types of topological spin structures and used for calculation of the dynamical susceptibility tensor and thermal transport in magnets with skyrmion lattice background.

KW - STATES

UR - http://www.scopus.com/inward/record.url?scp=85124145818&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/15a6194f-ced3-3a02-9dda-e5b62ec45115/

U2 - 10.1103/PhysRevB.105.024422

DO - 10.1103/PhysRevB.105.024422

M3 - Article

AN - SCOPUS:85124145818

VL - 105

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 2

M1 - 024422

ER -