Exchange Interaction in Gd$_4$Bi $_3$ and Gd From First-Principles Calculations

Electronic structure and exchange interaction have been calculated for the Gd
₄
Bi
₃
magnetocaloric compound and Gd metal by a local-spin-density- approximation + Hubbard U (LSDA+U) method. In Gd
₄
Bi
₃
and Gd, the 4f states have little direct contribution to the ferromagnetic coupling. The higher Curie temperature is ascribed to the strong interaction between the Gd 5
d
and the Bi 6
p
electrons in the Gd
₄
Bi
₃
compound. The estimated Curie temperatures from the calculated effective exchange coupling constants based on mean-field approximation are 337 K and 403 K for Gd metal and Gd
₄
Bi
₃
, respectively. These calculated values are comparable with the experimental values of Gd (
T

_C
= 294 K) and Gd
₄
Bi
₃
compound (
T

_C
= 332 K).