Surface effects on ferromagnetic resonance in magnetic nanocubes

TL;DR

This paper investigates how surface anisotropy influences spin-wave excitations and ferromagnetic resonance in magnetic nanocubes, developing a numerical method to analyze surface and core contributions and predicting specific resonance features.

Contribution

The authors introduce a numerical approach based on the Landau-Lifshitz equation to analyze surface effects on spin-wave spectra in nanoclusters, validated against spin-wave theory.

Findings

Surface anisotropy affects the spin-wave spectrum and resonance peaks.

Predicted low-energy resonance around 10 GHz for 8 nm iron nanocubes.

High-frequency exchange-mode peaks near 60 GHz.

Abstract

We study the effect of surface anisotropy on the spectrum of spin-wave excitations in a magnetic nanocluster and compute the corresponding absorbed power. For this, we develop a general numerical method based on the (undamped) Landau-Lifshitz equation, either linearized around the equilibrium state leading to an eigenvalue problem or solved using a symplectic technique. For box-shaped clusters, the numerical results are favorably compared to those of the finite-size linear spin-wave theory. Our numerical method allows us to disentangle the contributions of the core and surface spins to the spectral weight and absorbed power. In regard to the recent developments in synthesis and characterization of assemblies of well defined nano-elements, we study the effects of free boundaries and surface anisotropy on the spin-wave spectrum in iron nanocubes and give orders of magnitude of the expected spin-wave resonances. For an 8 nm iron nanocube, we show that the absorbed power spectrum should exhibit a low-energy peak around 10 GHz, typical of the uniform mode, followed by other low-energy features that couple to the uniform mode but with a stronger contribution from the surface. There are also high-frequency exchange-mode peaks around 60 GHz.