Effect of spin disorder on the specific loss power of a nanomagnet

Abstract

Spin non-collinearities in magnetic nanostructures arise from a variety of sources, including structural defects, finite-size effects, boundary or surface effects, Dzyaloshinskii-Moriya exchange coupling, and magnetic vortex formation. While strong forms of spin disorder generally require a numerical treatment, relatively weak non-collinearities induced by surface anisotropy are amenable to the analytical framework of the effective one-spin problem (EOSP). In this work, we exploit this framework to present a qualitative, semi-analytical study of the effect of spin disorder on the specific loss power (SLP) of a single nanomagnet within linear-response theory. Surface-induced spin misalignment mainly manifests as an additional quartic (cubic-symmetry) contribution to the anisotropy energy, parametrized by the ratio $\zeta \equiv K_4/K_2$. We derive a semi-analytical expression for the SLP as a function of $\zeta$ by combining the $\zeta$-dependent equilibrium susceptibility and the relaxation rate obtained within Langer's approach. Our results show that, for systems in the slow-relaxation regime, the SLP is enhanced by spin misalignment, predominantly through the increase of the relaxation rate caused by the lowering of the effective energy barrier. Retaining the full Debye factor reveals that for moderate reduced barriers $\sigma$, where the system is close to the superparamagnetic regime, the SLP can actually \emph{decrease} with increasing spin disorder. The enhancement is asymmetric with respect to the sign of $\zeta$ and depends on the nanomagnet shape (sphere versus cube) through the geometric prefactors in the EOSP mapping.