Relativistic theory for the nuclear spin-lattice relaxation rate in ferromagnetic metals with application to $5d$ impurities in bcc Fe

A relativistic theory for the nuclear spin-lattice relaxation rate ${(TT}_1{)}^{-1}$ in ferromagnetic metals is presented that includes in particular the electric quadrupolar and the core polarization contributions. Because it is formulated within the framework of the spin-polarized relativistic version of the Korringa-Kohn-Rostoker method of band structure calculations it can be applied in principle to any kind of system. Here an application of the theory to $5d$ impurities (Lu–Hg) in ferromagnetic bcc Fe is presented. While the core polarization contribution turned out to be negligible in all cases, the electric quadrupolar contribution was found to be of the same order of magnitude as the magnetic dipolar one in the case of Lu, Hf, Ir, and Au.