Simplified approach to the magnetic blue shift of Mott gaps

The antiferromagnetic ordering in Mott insulators upon lowering the temperature is accompanied by a transfer of the single-particle spectral weight to lower energies and a shift of the Mott gap to higher energies (magnetic blue shift, MBS). The MBS is governed by the double exchange and the exchange mechanisms. Both mechanisms enhance the MBS upon increasing the number of orbitals. By performing a polynomial fit to numerical dynamical mean-field theory data we provide an expansion for the MBS in terms of hopping and exchange coupling of a prototype Hubbard-Kondo-Heisenberg model and discuss how the results can be generalized for application to realistic Mott or charge-transfer insulator materials. This allows estimating the MBS of the charge gap in real materials in an extremely simple way avoiding extensive theoretical calculations. The approach is exemplarily applied to $\alpha$-MnTe, NiO, and BiFeO$_3$ and an MBS of about $130$ meV, $360$ meV, and $157$ meV is found, respectively. The values are compared with the previous theoretical calculations and the available experimental data. Our ready-to-use formula for the MBS simplifies the future studies searching for materials with a strong coupling between the antiferromagnetic ordering and the charge excitations, which is paramount to realize a coupled spin-charge coherent dynamics at a femtosecond time scale.