Vortex wall dynamics and pinning in helical magnets

Abstract

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.

Stiffness in vortex—like structures due to chirality-domains within a coupled helical rare-earth superlattice

“…It was predicted earlier that the helical background screens the vortex fields over large length scales. This screening perpetuates weak vortex—vortex interaction in the domain wall 5 .…”

“…The ± sign designates the handedness of the spiral. Domain walls, developed due to a change in chirality, are predicted to be generically characterized by two-dimensional pattern with regular lattice of vortex singularities, in contrast to more commonly found Bloch or Néel walls 2 5 .…”

Current induced vortex wall dynamics in helical magnetic systems

“…As the result for example in Ho at temperatures below 133 K a helical order is developed with the helical axis perpendicular to the basal planes and below 19 K the moments cant away from the planes to form a conical phase [2].The ground state of this helical system is degenerate with respect to the sense of rotation of the helices or chirality of the structure. Recently observation of chiral domains in these systems[2] has triggered novel ideas and predictions about the interface between chiral domains in a general perspective [3][4][5]. The most striking one is the prediction that these interfaces posses vorticity totally unrelated to the boundary effects contrary to what is seen for example in the case of vortex domain walls (consisting of a single vortex) in certain ferromagnetic nanowires [6].…”

“…Because of strong screening of the vortices by helical background (the vortex effect on local magnetic moments vanishes very fast away from the wall into the helical phase) [5] the vortex energy density vanishes at distances longer than π/q consequently we can use an approximate exponential model for the energy density of vortex lines and find the above correlation function:…”

“…Early studies have shown that the peculiar structure of these walls leads to a different static and dynamic behavior. The interaction between the vortex lines have been predicted to be weak [5] which implies the elasticity must originate from a vicinal behavior [4]. On the other hand the movement of the vortex lines inside the plane of the interface leads to the mobility enhancement [5].…”