Momentum-dependent susceptibilities and magnetic exchange in bcc iron from supercell DMFT calculations

We analyze the momentum- and temperature dependences of the magnetic susceptibilities and magnetic exchange interaction in paramagnetic bcc iron by a combination of density functional theory and dynamical mean-field theory (DFT+DMFT). By considering a general derivation of the orbital-resolved effective model for spin degrees of freedom for Hund's metals, we relate momentum-dependent susceptibilities in the paramagnetic phase to the magnetic exchange. We then calculate non-uniform orbital-resolved susceptibilities at high-symmetry wave vectors by constructing appropriate supercells in the DMFT approach. Extracting the irreducible parts of susceptibilities with respect to Hund's exchange interaction, we determine the corresponding orbital-resolved exchange interactions, which are then interpolated to the whole Brillouin zone. Using the spherical model we estimate the temperature dependence of the resulting exchange between local moments.