Boundary conditions for magnetization in magnetic nano-elements

TL;DR

This paper derives new effective boundary conditions for dynamic magnetization in thin magnetic nano-elements, accounting for inhomogeneous demagnetizing fields that influence boundary pinning, generalizing classical conditions.

Contribution

The work introduces generalized boundary conditions that incorporate inhomogeneous demagnetizing fields, extending the classical Rado-Weertman boundary conditions for nano-sized magnetic elements.

Findings

Boundary conditions account for inhomogeneous demagnetizing fields.

Effective boundary conditions reduce to Rado-Weertman in thin limit.

Demagnetizing fields dominate boundary pinning effects.

Abstract

We show that the dynamic magnetization at the edges of a thin magnetic element with finite lateral size can be described by new effective boundary conditions that take into account inhomogeneous demagnetizing fields near the element edges. These fields play a dominant role in the effective pinning of the dynamic magnetization at the boundaries of mesoscopic and nano-sized magnetic elements. The derived effective boundary conditions generalize well-known Rado-Weertman boundary conditions and are reduced to them in the limiting case of a very thin magnetic element.