Thermal fluctuations and longitudinal relaxation of single-domain magnetic particles at elevated temperatures

We present numerical and analytical results for the swiching times of magnetic nanoparticles with uniaxial anisotropy at elevated temperatures, including the vicinity of $T_C$. The consideration is based in the Landau-Lifshitz-Bloch equation that includes the relaxation of the magnetization magnitude $M$. The resulting switching times are shorter than those following from the naive Landau-Lifshitz equation due to (i) additional barrier lowering because of the reduction of $M$ at the barrier and (ii) critical divergence of the damping parameters.

Figure 1

Switching times for a FePt particle with $8\text{−}\mathrm{nm}$ diameter calculated numerically from the LL-Langevin and LLB-Langevin equations and analytically from the approproate Fokker-Planck equations. While the integral relaxation time (IRT) works very well at all temperatures, the high-barrier asymptotes break down for $\sigma \lesssim 1$. The $1∕\sigma$ corrections improve the asymptotes for $\sigma \gtrsim 1$.