Exchange interactions in itinerant magnets: the effects of local particle-hole irreducible vertex corrections and SU(2) symmetry of Hund interaction

We study exchange interactions in iron and nickel within the DFT+DMFT approach with density-density and SU(2) symmetric Coulomb interaction. In particular, we analyze the representation of exchange interactions through the non-local part of the particle-hole bubble, supplemented by the local particle-hole (ph) irreducible interaction vertices. The neglect of the local ph-irreducible vertex corrections, suggested previously within the dual fermion approach [E. A. Stepanov, et.al., Phys. Rev. Lett. 121, 037204 (2018)], yields the result, corresponding to generalization of the magnetic force theorem approach. While we argue that these vertex corrections are not important for strong localized magnets, such as iron, they become more essential for weak itinerant magnets, such as nickel. At the same time, the account of the full local vertex and self-energy corrections in the renormalized approach is essential for iron, and less important for nickel. The difference of the results of density-density and SU(2) symmetric Coulomb interaction is found relatively small, in contrast to the Curie temperature and the value of the local magnetic moment.