Magnetic states in multiply-connected flat nano-elements

TL;DR

This paper extends a mathematical approach to describe magnetic states in flat nano-elements with holes, revealing how holes restrict possible magnetic configurations, which is important for spintronic device design.

Contribution

It introduces a conformal mapping-based method for analyzing magnetic states in multiply-connected nano-elements, advancing understanding of their magnetic behavior.

Findings

Holes impose restrictions on magnetic states

Extended mathematical framework for multiply-connected geometries

Potential implications for spintronic device engineering

Abstract

Flat magnetic nano-elements are an essential component of current and future spintronic devices. By shaping an element it is possible to select and stabilize chosen metastable magnetic states, control its magnetization dynamics. Here, using a recent significant development in mathematics of conformal mapping, complex variable based approach to the description of magnetic states in planar nano-elements is extended to the case when elements are multiply-connected (that is, contain holes or magnetic anti-dots). We show that presence of holes implies a certain restriction on the set of magnetic states of nano-element.