Maximum energy product at elevated temperatures for hexagonal strontium ferrite (SrFe12O19) magnet

• We have calculated exchange integrals for SrFe12O19.
• The Brillouin functions for the five magnetic sublattices were derived.
• Temperature dependences of the five magnetic sublattices were calculated.
• The calculated magnetization agrees well with experimental values with temperature.
• Temperature dependence of maximum energy product from 0 to 750 K was calculated.

The electronic structure of hexagonal strontium ferrite (SrFe12O19) was calculated based on the density functional theory (DFT) and generalized gradient approximation (GGA). The GGA+U method was used to improve the description of localized Fe 3d electrons. Three different effective U (Ueff) values of 3.7, 7.0, and 10.3 eV were used to calculate three sets of exchange integrals for 21 excited states. We then calculated the temperature dependence of magnetic moments m(T) for the five sublattices (2a, 2b, 12k, 4f1, and 4f2) using the exchange integrals. The m(T) of the five sublattices are inter-related to the nearest neighbors, where the spins are mostly anti-ferromagnetically coupled. The five sublattice m(T) were used to obtain the saturation magnetization Ms(T) of SrFe12O19, which is in good agreement with the experimental values. The temperature dependence of maximum energy product ((BH)max(T)) was calculated using the calculated Ms(T).