Rare-earth contribution to the magnetocrystalline anisotropy energy inR2Fe14B

The zero-temperature value of the magnetocrystalline anisotropy (MCA) energy of trivalent rare-earth ions and its temperature dependence have been calculated for the whole series of the $R_2$ ${\mathrm{Fe}}_{14}$B compounds. The computations, performed with a single-ion origin of the anisotropy and within a molecular-field approximation, reveal a large local anisotropy of the rare-earth ion, 2 orders of magnitude larger than the iron anisotropy. The crystal field acting on the rare-earth ions is of comparable magnitude as the molecular field. As a consequence, the internal ferro- and ferrimagnetic structures are very sensitive to applied external magnetic fields leading to large bending angles between the rare-earth and iron sublattice magnetizations. The calculated values for the intrinsic anisotropy constants of ${\mathrm{Dy}}_2$ ${\mathrm{Fe}}_{14}$B reproduce, within a two-sublattice model, the observed value of 20 T for the apparent anisotropy field at 4.2 K. The calculated values of the local MCA energy at zero temperature and room temperature are in good agreement with the experimentally determined data.