Vortex Wall Dynamics and Pinning in Helical Magnets

Domain walls formed by one dimensional array of vortex lines have been recently predicted to exist in disordered helical magnets and multiferroics. These systems are on one hand analogues to the vortex line lattices in type-II superconductors while on the other hand they propagate in the magnetic medium as a domain boundary. Using a long wavelength approach supported by numerical optimization we lay out detailed theory for dynamics and structure of such topological fluctuations at zero temperature in presence of weak disorder. We show the interaction between vortex lines is weak. This is the direct consequence of the screening of the vorticity by helical background in the system. We explain how one can use this result to understand the elasticity of the wall with a vicinal surface approach. Also we show the internal degree of freedom of this array leads to the enhancement of its mobility. We present estimates for the interaction and mobility enhancements using the microscopic parameters of the system. Finally we determine the range of velocities/force densities in which the internal movement of the vortex wall can be effective in its dynamics.