Calculation of exchange integrals and Curie temperature for La-substituted barium hexaferrites

As the macro behavior of the strength of exchange interaction, state of the art of Curie temperature Tc, which is directly proportional to the exchange integrals, makes sense to the high-frequency and high-reliability microwave devices. Challenge remains as finding a quantitative way to reveal the relationship between the Curie temperature and the exchange integrals for doped barium hexaferrites. Here in this report, for La-substituted barium hexaferrites, the electronic structure has been determined by the density functional theory (DFT) and generalized gradient approximation (GGA). By means of the comparison between the ground and relative state, thirteen exchange integrals have been calculated as a function of the effective value Ueff. Furthermore, based on the Heisenberg model, the molecular field approximation (MFA) and random phase approximation (RPA), which provide an upper and lower bound of the Curie temperature Tc, have been adopted to deduce the Curie temperature Tc. In addition, the Curie temperature Tc derived from the MFA are coincided well with the experimental data. Finally, the strength of superexchange interaction mainly depends on 2b-4f1, 4f2-12k, 2a-4f1, and 4f1-12k interactions.