Magnetic exchange interactions in the gadolinium pnictides from first principles

The magnetic exchange interactions in the Gd-pnictide series are analyzed from various points of view. First, a Heisenberg Hamiltonian between the 4f induced local moments on the Gd only is used and the corresponding exchange interactions between first and second-nearest neighbors are derived from total-energy differences between the ferromagnetic (FM) and antiferromagnetic AFM-I and AFM-II configurations, as calculated from a full-potential-linearized muffin-tin orbital method in the local-density approximation with Hubbard-U corrections (LSDA+U). The induced magnetic moments on Gd d and N in the different configurations are found to differ and to favor the AFM-II for the P-Bi compounds while the FM configurations is favored for GdN. The extracted J(2) parameter determines the Neel temperature of the AFM-II compounds in good agreement with experimental values. The Curie-Weiss temperature involves both J(1) and J(2) in this model and is also in good agreement with experiment. The FM state of GdN can be viewed as an antiferromagnetic arrangement of the small moments induced on Gd d and N on the rocksalt lattice, which in this case happen to cancel each other exactly because of the semiconducting nature of GdN. This locks the Gd 4f moments into a FM arrangement through the on-site f-d coupling. Linear response calculations in the atomic sphere approximation, including empty sphere sites, provide an alternative decomposition of the magnetic ordering energy in Gd-Gd, Gd-N, and Gd-empty sphere exchange interactions. The latter can be viewed as representing the tails of the t(2g) orbitals on Gd. This analysis shows that the magnetic ordering arises from the small induced moments on the Gd d, N, and empty sphere sites rather than from direct interactions between 4f moments. The Curie temperature for GdN is found to be significantly smaller than previous calculations estimated and than experimental values and may indicate that the latter are influenced by defects. For GdP, GdAs, GdSb, and GdBi, the linear-response calculations around the AFM-II ground state give results in good agreement with the full-potential linearized muffin-tin orbital calculations. The linear-response approach also gives a reasonable value for the Curie temperature of metallic Gd.