STRUCTURE AND ENERGY OF MOVING DOMAIN WALLS

Abstract

A rigorous solution of the micromagnetic equations for moving domain walls is presented assuming uniaxial anisotropy and uniform wall velocity. This solution applies for wall velocities smaller than a critical velocity v1 = γ(HaD)1/2 [ (1 + σ)1/2 − 1]. Here γ is the gyromagnetic ratio, Ha the anisotropy field, D the exchange constant, σ = 4πMo/Ha, and Mo the saturation magnetization. The wall energy E increases with increasing v according to E = Eoa(v), where Eo is the energy of the wall at rest, a(v) is proportional to the reciprocal of the wall width, and is given by v2/γ2HaD = − (1 + σ)a−2 + 2 + σ − a2. At the critical velocity the derivative of the wall energy with respect to v becomes infinite, the wall energy itself remains finite. The “tails” of the domain wall (the regions where the magnetization approaches alignment with the anisotropy axis) can be considered as spin waves of imaginary wavenumber and frequency but real phase velocity. The parameter a in Eq. (2) is (apart from a constant factor) the imaginary part of the wavenumber. The domain velocity v is the same as the phase velocity of these spin waves. The wall mobility is velocity dependent, being inversely proportional to the wall energy in this velocity range. The structure of domain walls moving at speeds exceeding v1 is discussed.