Stable topological textures in a classical two-dimensional Heisenberg model

Abstract

We show that stable localized topological soliton textures ͑skyrmions͒ with 2 topological charge Ն 1 exist in a classical two-dimensional Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exists only if the number of bound magnons exceeds some threshold value N cr depending on and the effective anisotropy constant K eff . We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both = 1 and Ͼ 2 while the solitons with = 2 reveal peculiar nonmonotonous behavior, determining the transition regime from low to high topological charges. In particular, the soliton energy per topological charge ͑topological energy density͒ achieves a minimum neither for = 1 nor high charges but rather for intermediate values =2 or = 3. We show that this peculiarity is related to the character of convergence of integrals defining soliton energy and number of bound magnons at different .

Thermal creation of skyrmions in ferromagnetic films with perpendicular anisotropy and Dzyaloshinskii-Moriya interaction

“…Perpendicular magnetic anisotropy, dipole-dipole interaction, magnetic field, and confined geometry can stabilize significantly large magnetic bubbles with skyrmion topology [34][35][36][37][38][39][40] . The stability of small skyrmions requires other than Heisenberg exchange coupling [41][42][43][44][45] , more complex magnetic anisotropy [46][47][48] , static disorder 49,50 , or a non-centrosymmetric system with large Dzyaloshinskii-Moriya interaction 5,[51][52][53][54][55] .…”

Collapse of skyrmions in two-dimensional ferromagnets and antiferromagnets

“…The nature of the exchange interaction on a lattice makes the skyrmion energy decreasing with its size, that leads to skyrmion collapse. A number of authors looked for interactions that could stabilize skyrmions in 2d ferromagnets [24][25][26] .…”

Helicity of magnetic vortices and skyrmions in soft ferromagnetic nanodots and films biased by stray radial fields

“…For a uniform magnetization distribution, naturally, Q = 0, meaning that it is topologically trivial. More complex states with higher topological charge, e.g., biskyrmions having Q = ±2, have been observed recently in experiments and attract also significant research interest [60][61][62][63]. The skyrmion number, of course, can be calculated for any magnetization texture, not obviously having uniform magnetization far from the origin.…”