Anisotropic property of magnetic dipole in bulk, surface, and overlayer systems

Magnetization-angle dependence of the magnetic dipole is extensively studied for bulk, surface, and overlayer systems by using first-principles electronic structure calculations. In most transition-metal ferromagnets, the magnetic dipole is described well in a weak spin-orbit-interaction (SOI) regime with the angle dependence of 3 cos(2)theta-1 and the existence of the so-called magic angle. In a system with relatively strong SOI, such as Pt overlayer on Fe substrate, however, the angle dependence deviates from the 3 cos(2)theta-1 variation. An actinide compound shows completely different angle dependence arising from a competition between l.s coupling and crystal-field effect.