Origin of four-fold anisotropy in square lattices of circular ferromagnetic dots

TL;DR

This paper investigates the origin of four-fold anisotropy in square lattices of circular ferromagnetic dots, attributing it to non-uniform magnetization caused by dipolar interactions, and provides a theoretical explanation for the observed anisotropy.

Contribution

It introduces a theoretical model explaining four-fold anisotropy in ferromagnetic dot lattices due to non-uniform magnetization from dipolar forces, validated by experimental observations.

Findings

Four-fold anisotropy observed in FMR fields of dot lattices.

Anisotropy magnitude varies with interdot distance and lattice orientation.

Non-uniform magnetization explains anisotropy, modeled by iterative variational method.

Abstract

We discuss the four-fold anisotropy of in-plane ferromagnetic resonance (FMR) field $H_r$, found in a square lattice of circular Permalloy dots when the interdot distance $a$ gets comparable to the dot diameter $d$. The minimum $H_r$, along the lattice $<11>$ axes, and the maximum, along the $<10>$ axes, differ by $\sim$ 50 Oe at $a/d$ = 1.1. This anisotropy, not expected in uniformly magnetized dots, is explained by a non-uniform magnetization $\bm(\br)$ in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variational procedure.