Charge and spin degrees of freedom in strongly correlated systems: Mott states opposite Hund’s metals

A correlated metallic state can arise as a result of the presence either strong charge or strong spin fluctuations. In the first case, as was shown first in (2004 Phys. Today 57 53) for the Hubbard model on the Bethe lattice, the system is a correlated metallic state close to the Mott-insulator state if the ratio of the value of the Coulomb interaction parameter U and the band width W is [Formula: see text]. The later case exist if [Formula: see text] and Hund's exchange parameter [Formula: see text]. In both cases narrowing of the bands near the Fermi level and renormalization of the effective electron mass is observed, although the mechanism for realizing this state will be fundamentally different. We performed the electronic structure calculations of the paramagnetic phase [Formula: see text]-iron which is a typical Hund's metal. We showed that the statistical distribution of charge between possible electronic d-configurations has a very weak dependence on the exchange interaction and is specific for metals. At the same time, the distribution of statistical weights between different spin configurations fundamentally changes with the inclusion of J. If we neglect Hund's interaction by setting J = 0, the contributions from the low-spin configurations for all possible charge states dominate. The exchange interaction causes a redistribution of probability in favor of high-spin multiplets, leading to the formation of a larger local moment. We also performed calculations for the two-bands half-filled model. By varying the values of the Coulomb and Hund's exchange interaction parameters, we reproduced the region of the phase diagram of the model in which the system undergoes a transition from the Mott-insulator state to the Hund's metal. This transition is accompanied by a change in the statistical probability distribution of possible multiple configurations. In the region corresponding to the Hund's metal state, a change of J leads to the effect of weights redistribution similar that we observe in [Formula: see text]-iron.