Dynamics of Domain Walls in Chiral Magnets

The motion of domain walls in chiral magnets with symmetry broken relative to spatial inversion is investigated theoretically. It was found experimentally that such walls, which are known as the Dzyaloshinskii domain walls [22], exhibit unique dynamic properties. For chiral ferromagnets and antiferromagnets, nonlinear regimes of the motion of such a wall with the velocity up to its critical value have been investigated. The dynamics of walls in antiferromagnets can be described analytically, while for ferromagnets, numerical analysis must be used. Simple approximate expressions derived for ferromagnets describe dynamic characteristics of walls to a high degree of accuracy in the entire domain of their existence. The dispersion relations (i.e., the dependences of the energy of a wall on its linear momentum) are determined. For ferromagnets with purely uniaxial anisotropy, the critical velocity of a wall is determined exclusively by the chiral interaction and vanishes in the absence of this interaction. For antiferromagnetic, the role of the chiral interaction is not so obvious: like in the standard models for antiferromagnets, the structure of a moving wall can be obtained with the help of the Lorentz transformation with a chosen speed equal to the velocity of magnons in the linear part of the spectrum; however, the dispersion relation is more complicated and cannot be described by Lorentz-invariant expressions.