Mesoscopic bound on anisotropy in itinerant ferromagnets

We calculate the anisotropy energy of a single-domain ferromagnetic particle in which the only source of anisotropy is the presence of non-magnetic impurities. We find that such anisotropy takes the form of combined easy-axis and easy-plane anisotropies, with random orientations of the axes. Typically the anisotropy energy is of order $N^{1/2} \hbar/tau_{so}$, where $N$ is the number of electrons in the ferromagnetic particle and $\tau_{so}$ is the spin-orbit time.