Macrospin approximation and quantum effects in models for magnetization reversal

The thermal activation of magnetization reversal in magnetic nanoparticles is controlled by the anisotropy-energy barrier. Using perturbation theory, exact diagonalization and stability analysis of the ferromagnetic spin-s Heisenberg model with coupling or single-site anisotropy, we study the effects of quantum fluctuations on the height of the energy barrier. Opposed to the classical case, there is no critical anisotropy strength discriminating between reversal via coherent rotation and via nucleation/domain-wall propagation. Quantum fluctuations are seen to lower the barrier depending on the anisotropy strength, dimensionality and system size and shape. In the weak-anisotropy limit, a macrospin model is shown to emerge as the effective low-energy theory where the microscopic spins are tightly aligned due to the ferromagnetic exchange. The calculation provides explicit expressions for the anisotropy parameter of the effective macrospin. We find a reduction of the anisotropy-energy barrier as compared to the classical high spin-s limit.Comment: 10 pages, 11 figure

Fractional Fokker-Planck equation for anomalous diffusion in a potential: Exact matrix continued fraction solutions

Methods for the exact solution of fractional Fokker-Planck equations for anomalous diffusion in an external potential are discussed using both ordinary and matrix continued fractions, whereby the scalar multi-term recurrence relations generated by such fractional diffusion equations are reduced to three-term matrix ones. The procedure is illustrated by solving various problems concerning the anomalous translational diffusion in both periodic and double-well potentials