Dipole-dipole interaction in arrays of Fe/Fe$_x$O$_y$ core/shell nanocubes probed by ferromagnetic resonance

TL;DR

This study investigates how long-range magnetic dipole-dipole interactions influence ferromagnetic resonance spectra in arrays of Fe/Fe$_x$O$_y$ nanocubes, revealing size-dependent stability and a threshold distance for negligible interactions.

Contribution

It provides a detailed theoretical analysis of dipole-dipole interactions in nanoparticle arrays and identifies the critical array size and inter-particle distance affecting FMR spectra.

Findings

Array size controls system stability and suppresses low-field excitations.

Dipole-dipole interactions become negligible beyond 80-100 nm inter-particle distance.

Simulation results align with experimental FMR spectra of irregularly placed nanocubes.

Abstract

This paper represents a detailed theoretical study of the role of the longrange magnetic dipole-dipole interaction evidenced by the ferromagnetic resonance (FMR) spectra for the ordered arrays of cubic nanoparticles. We show that the size of the array essentially controls the stability of the system, allowing to suppress the intermittent low-field excitations starting from the arrays formed by 6x6 nanoparticles. Our numerical simulations allow to determine the threshold inter-particle distance (around 80 {\div} 100 nm), after which the dipole-dipole interaction becomes negligible so that the FMR spectrum of the nanoparticle arrays becomes the same as the spectrum featured by a single nanoparticle. We also compare our simulations with experimental FMR-spectra of 24 Fe/Fe$_x$O$_y$-nanocubes irregularly placed on a substrate.