Ab initio theory of exchange interactions and the Curie temperature of bulk Gd

An ab initio approach to the magnetic properties of bulk hexagonal Gd is developed that is based on the local spin-density approximation with the 4f electrons treated as localized core electrons. The effective one-electron problem is solved using the tight-binding linear muffin-tin orbital method in the atomic-sphere approximation with the valence basis consisting of s-, p- and d-type orbitals. The approach leads to a correct description of the ground-state properties like the stability of the ferromagnetic structure, the magnetic moment and the equilibrium lattice constant. Application of a real-space Green-function formalism yields the exchange pair interactions between distant neighbours that are inevitable for quantitative studies of magnetic excitations. The distance dependence and anisotropy of the exchange pair interactions are presented and the Curie temperature in the mean-field approximation is evaluated. The obtained value of 334 K is in much better agreement with the experimental value of 293 K than previous theoretical results. Depending on the atomic volume we find an unusually large dependence of the Curie temperature on the c/a ratio, which bears important consequences for the critical temperatures of thick strained Gd films as grown on various substrates.