Mechanics of magnetic solitons*

The dynamics of magnetization in a ferromagnet is governed by the Landau-Lifshitz equation, a nonlinear PDE that is rarely solvable exactly. To approximate soliton dynamics, we introduced a method of collective coordinates [1] generalizing Thiele's rigid-translation approximation [2] by including arbitrary deformations. The method has been applied to a variety of solitons (domain walls, skyrmions, vortices), extended to include the effects of spin-transfer torque, and adopted to antiferromagnetic solitons [3]. I will describe our recent applications of the method to several new problems: an extended domain wall in a thin ferromagnetic film behaves as a nonreciprocal string with transverse waves propagating on it with unequal speeds; annihilation of a vortex-antivortex pair in a thin film; and the propulsion of antiferromagnetic solitons under combined magnetic field and spin-polarized current.

[1] O. A. Tretiakov et al., Phys. Rev. Lett. 100, 127204 (2008).
[2] A. A. Thiele, Phys. Rev. Lett. 30, 230 (1973).
[3] E. G. Tveten et al., Phys. Rev. Lett. 110, 127208 (2013).