Modeling of Motion of the Domain Walls in Ferromagnetic Materials (A Survey)

We analyze basic approaches to the mathematical modeling of motion of the domain walls in ferromagnetics under the influence of external magnetic fields. According to the results of synthesis of the literature data, we present an equation for the displacement of a domain wall with regard for the Brownian distribution of the field. We also describe the available mathematical models constructed on the basis of the dependences of the thickness of domain walls on mechanical stresses, which enable us to determine the maximum displacements of a domain wall and estimate the amplitude of magnetoelastic acoustic emission.