Surface contribution to the anisotropy of magnetic nanoparticles

We calculate the contribution of the Neel surface anisotropy to the effective anisotropy of magnetic nanoparticles of spherical shape cut out of a simple cubic lattice. The effective anisotropy arises because deviations of atomic magnetizations from collinearity and thus the energy depends on the orientation of the global magnetization. The result is second order in the Neel surface anisotropy, scales with the particle's volume, and has cubic symmetry with preferred directions [+/-1, +/-1, +/-1].