Specific absorption rate of uniaxial single-domain nanomagnets: stochastic spin dynamics versus linear response theory

Abstract

We compute the specific absorption rate of a uniaxial single-domain nanomagnet driven by an alternating magnetic field by two methods: i) direct numerical integration of the stochastic (Langevin) Landau--Lifshitz--Gilbert equation (the LLL approach), and ii) linear response theory (LRT) based on the Debye susceptibility with the N\'eel relaxation time $\tau_\mathrm{N}$. We first analytically show that both methods are equivalent for small magnetic field amplitude, and then compute their deviation $\Lambda\equiv \mathrm{SAR}_{\mathrm{LLL}}/\mathrm{SAR}_{\mathrm{LRT}}-1$ as a function of the magnetic field amplitude for two temperatures chosen on opposite sides of the Debye resonance. One of the main results is that the sign and magnitude of $\Lambda$ are governed by the dimensionless product $\omega\tau_\mathrm{N}$, in addition to the linearity parameter $\xi=\mu_{s}B_{0}/k_{B}T$ for the easy-axis geometry considered here. Indeed, below resonance ($\omega\tau_\mathrm{N}<1$), linear response theory overestimates the specific absorption rate. In contrast, above resonance ($\omega\tau_\mathrm{N}>1$, the regime typical of blocked nanoparticles), linear response theory can underestimate the specific absorption rate by up to $\sim70\%$ at $\xi\sim2$. We expect this work to provide quantitative guidance for the use of linear response theory in magnetic hyperthermia and related nanoscale heat-transport problems, and to serve as a single-particle benchmark for extensions to many-spin and interacting systems.