Low-energy physics of three-orbital impurity model with Kanamori interaction

Abstract

We discuss the low-energy physics of the three-orbital Anderson impurity model with the Coulomb interaction term of the Kanamori form which has orbital SO(3) and spin SU(2) symmetry and describes systems with partially occupied t2g shells. We focus on the case with two electrons in the impurity that is relevant to Hund's metals. Using the Schrieffer-Wolff transformation we derive an effective Kondo model with couplings between the bulk and impurity electrons expressed in terms of spin, orbital, and orbital quadrupole operators. The bare spin-spin Kondo interaction is much smaller than the orbit-orbit and spin-orbital couplings or is even ferromagnetic. Furthermore, the perturbative scaling equations indicate faster renormalization of the couplings related to orbital degrees of freedom compared to spin degrees of freedom. Both mechanisms lead to a slow screening of the local spin moment. The model thus behaves similarly to the related quantum impurity problem with a larger SU(3) orbital symmetry (Dworin-Narath interaction) where this was first observed. We find that the two problems actually describe the same low-energy physics since the SU(3) symmetry is dynamically established through the renormalization of the splittings of coupling constants to zero. The perturbative renormalization group results are corroborated with the numerical-renormalization group (NRG) calculations. The dependence of spin Kondo temperatures and orbital Kondo temperatures as a function of interaction parameters, the hybridization, and the impurity occupancy is calculated and discussed.

Spin-orbit coupling in three-orbital Kanamori impurity model and its relevance for transition-metal oxides

“…1 separately displays for the λ = 0 case the local spin moment χ S T and the orbital angular moment χ L T evaluated respectively from spin and orbital susceptibilities. As discussed in earlier work [29][30][31] the screening of the spin moment occurs at a lower temperature T spin K than the one for the orbital moment T orb K (the two Kondo temperatures are indicated by the two vertical lines and differ by about an order of magnitude). The initial drop of χ J T and the associated suppression of the impurity contribution to entropy, seen in Fig.…”

Spin-orbit coupling and correlations in three-orbital systems

“…This criterion failed for an occupancy of N = 2, where the additional suppression of the coherence scale is important [25][26][27]. This suppression coincides with the slowing down of the spin fluctuations [28] and was explained from the perspective of the impurity model that is influenced by a reduction of the spin-spin Kondo cou-pling due to virtual fluctuations to a high-spin multiplet at half filling [29][30][31][32]. The occurrence of strong correlations at N = 2 for moderate interactions was also interpreted (in the context of iron-based superconductors) as a consequence of the proximity to a half-filled (in our case N = 3) Mott insulating state [33][34][35][36], for which the critical interaction is very small due to the Hund's rule coupling.…”

Fork Tensor-Product States: Efficient Multiorbital Real-Time DMFT Solver

“…in the number of bath sites. Quite recently, NRG was shown to be a * daniel.bauernfeind@tugraz.at viable three-band solver by exploiting non-abelian quantum number conservation [15][16][17]. NRG works on the real axis and captures the low-energy physics well, but it has by construction a poor resolution at higher energies.…”