Is the magnetic anisotropy proportional to the orbital moment?

The relation between orbital moment and magnetic anisotropy is investigated by model calculations, which show that only a part of the spin-orbit coupling contributes to the anisotropy. A large part of the anisotropy energy, about 50% for iron series elements and nearly 100% for rare-earths, is stored in the nonrelativistic part of the Hamiltonian. A feature important for x-ray magnetic circular dichroism is that the orbital moment of heavy atoms rotates with the spin moment, whereas in light atoms, the orbital moment is recreated in each different direction. In the discussion, we consider three examples of current interest in different areas of magnetism, namely, spin-orbit coupling in Gd 3+ and Eu 2+ , surface anisotropy of Nd 2 Fe 14 B, and multiferroic magnetization switching using rare-earths.