Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films

Abstract

We analyze the electric current and magnetic field driven domain wall motion in perpendicularly magnetized ultrathin ferromagnetic films in the presence of interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and in-plane uniaxial anisotropies. We obtain exact analytical Walker-type solutions in the form of one-dimensional domain walls moving with constant velocity due to both spin-transfer torques and out-of-plane magnetic field. These solutions are embedded into a larger family of propagating solutions found numerically. Within the considered model, we find the dependencies of the domain wall velocity on the material parameters and demonstrate that adding in-plane anisotropy may produce domain walls moving with velocities in excess of 500 m/s in realistic materials under moderate fields and currents.

Analytical computation of the demagnetizing energy of thin-film domain walls

“…Additional boundary integrals will need to be included in Eqs. (11)(12). More severely, the technique of deforming the integration contour to integrate term by term in Eqs.…”

“…From an analytical perspective, a class of widely used reduced models of DW dynamics is given by the so-called 1D models, describing the DW in terms of a smoothly * audun.skaugen@tuni.fi varying one-dimensional magnetization profile parameterized by the DW position, width, and an angular variable describing the orientation of the magnetization inside the DW. Dynamical equations for these variables are derived from the LLG equation [9][10][11][12]. As a general feature, such models (as well as the corresponding micromagnetic simulations) exhibit a regime of steady DW dynamics for small applied fields B a with the DW velocity increasing with the field.…”

Dynamics of ferromagnetic domain walls under extreme fields

“…The model ( 1)-( 2) has been extensively analysed in the literature (see e.g. [17,18,[23][24][25][26][27][28]). We will restrict our attention to the case of near-uniaxial wires, for which K K 2 (eventually, we will take K 2 = 0).…”

Unidirectional tilt of domain walls in equilibrium in biaxial stripes with Dzyaloshinskii–Moriya interaction

“…The orientation of the domain wall with respect to the stripe main axis has major impact on its dynamics including the maximum velocity [16] and Walker limit [17,18]. In equilibrium, the domain wall is oriented perpendicular to the main axis of the stripe.…”

“…The easy axis direction of the in-plane anisotropy can be given by a crystalline structure of the ferromagnet [29]. In contrast to the shape anisotropy [17,30] with an easy axis along the stripe, any misalignment between the in-plane anisotropy and the stripe axes breaks the symmetry of the magnetic texture and tilts (i) the magnetization inside the domain wall as well as (ii) the domain wall. The motion a domain wall in a biaxial magnetic with DMI has strong impact on the Walker field and the domain wall velocity.…”