Orbital Isotropy of Magnetic Fluctuations in Correlated Electron Materials Induced by Hund’s Exchange Coupling

Abstract

Characterizing non-local magnetic fluctuations in materials with strong electronic Coulomb interactions remains one of the major outstanding challenges of modern condensed matter theory. Here, we address the spatial symmetry and orbital structure of magnetic fluctuations in perovskite materials, within an anisotropic threeorbital model of cubic t 2g symmetry. To this effect, we develop a consistent multi-orbital diagrammatic extension of dynamical mean field theory, which allows for a proper description of many-body effects. We find that the form of spatial spin fluctuations is governed by the local Hund's coupling. For small values of the coupling, magnetic fluctuations are anisotropic in orbital space, which reflects the symmetry of the considered t 2g model. Large Hund's coupling enhances collective spin excitations, which mixes orbital and spatial degrees of freedom, and magnetic fluctuations become orbitally isotropic. Remarkably, this effect can be seen only in two-particle quantities; single-particle observables remain anisotropic for any value of the Hund's coupling. Importantly, we find that the orbital isotropy can be induced in both half-filled and doped cases, where the magnetic instability is associated with different, antiferromagnetic and ferromagnetic modes, respectively.

Multi-band D-TRILEX approach to materials with strong electronic correlations

“…Compute the dressed Green's function G k,ll (20), the self-energy Σ k,ll (21), the susceptibility X ς q, l 1 l 2 , l 3 l 4 (25), and the polarization operator Π ς q, l 1 l 2 , l 3 l 4 (26) for the lattice problem (1). From these quantities determine the orbital-resolved average density 〈n l 〉 (98) and the average energy 〈E〉 of the system (99) and (100).…”

“…Additionally, vertex corrections in TRILEX are included in diagrams in an asymmetric way. This diagrammatic structure leads to inconsistent results in a strong-coupling limit [116] and does not have a correct symmetry in the orbital [20] space.…”

“…However, in most of the cases an accurate description of realistic materials with strong electronic correlations usually requires to take into account several bands that originate from different orbitals and/or atoms in the unit cell. Prominent examples of materials where the interplay of orbital degrees of freedom and strong correlations is believed to be of crucial importance are vanadates [10][11][12][13], ruthenates [14][15][16][17][18][19][20], nikelates [21][22][23][24][25][26][27], and iron-based superconductors [28][29][30][31][32][33][34][35][36][37]. Even in the case of cuprates the question whether an effective three-band model should be used instead of a single-band one is still under debate [38][39][40][41][42][43][44][45][46][47].…”

“…Particular examples of such theories are the GW +DMFT [63][64][65][66][67][68][69], the dual fermion (DF) [70][71][72][73][74][75], the dual boson (DB) [76][77][78][79][80][81][82], the dynamical vertex approximation (DΓ A) [83][84][85][86][87], the triply irreducible local expansion (TRILEX) [88][89][90], and the dual TRILEX (D-TRILEX) [20,[91][92][93][94][95] methods. Among them, DF, DB, and DΓ A have the most sophisticated diagrammatic structures that allow for a very accurate description of both local and non-local correlation effects [96].…”

“…However, among all non-local correlations this method considers only charge fluctuations and thus neglects important magnetic effects. Furthermore, GW +DMFT does not take into account vertex corrections that are crucial for an accurate description of magnetic, optical and transport properties [20,[103][104][105][106][107][108][109][110][111]. The TRILEX method partially cures these drawbacks by considering both the charge and magnetic fluctuations, and also by introducing vertex corrections in the form of the local Hedin's vertex [112] of the DMFT impurity problem.…”