The classical-quantum disproportionation transition and magnetic ordering in RNiO$_3$ nickelates

TL;DR

Nickelates $RNiO_3$ display an insulator-to-bad-metal transition that cannot be explained by conventional bandwidth-controlled Hubbard physics. The authors develop a purely electronic $U$–$V$–$t_b$ framework based on a charge-triplet pseudospin $\Sigma=1$ formalism, where inter-site correlations and two-particle transfer generate composite spin-triplet bosons with transfer $t_b$ and yield a minimal effective-field description of the competing charge-ordered (CO) and charge-disproportionated quantum (CDq) phases. The theory identifies a high-temperature disordered no-phase and a low-temperature CO or CDq phase, with a CO–NO transition controlled by $V$ and a rich $T$–$t_b$ phase diagram that reproduces key trends across the $RNiO_3$ series, including mixed-valence $[NiO_6]^{(9\pm\delta)-}$ states and valence fluctuations. The work highlights the crucial role of two-particle boson transfer and boson exchange in setting magnetic and electronic order, and it points to necessary extensions to include lattice breathing modes and explicit spin-exchange interactions to capture the full AFM structure, especially in LaNiO$_3$ and related compounds.

Abstract

The insulator-quasi-metal (bad metal) transition observed in Jahn-Teller (JT) magnets orthonickelates RNiO$_3$ (R = rare earth, or yttrium Y) is considered a canonical example of the Mott transition, traditionally described in the framework of Hubbard's $U-t$ model. However, in reality, the insulating phase of nickelates is the result of charge disproportionation (CD) with the formation of a system of spin-triplet ($S = 1$) electron [NiO$_6$]$^{10-}$ and spinless ($S = 0$) hole [NiO$_6$]$^{8-}$ centers, equivalent to a system of effective spin-triplet composite bosons moving in a nonmagnetic lattice. The effective CD-phase Hamiltonian takes into account local ($U$) and nonlocal ($V$) correlations, and the transfer of composite bosons ($t_b$). Within the framework of the effective field approximation, we have shown the existence of two types of CD phases: the high-temperature classical paramagnetic CO-phase of charge ordering of electron and hole centers, and the low-temperature magnetic quantum CDq phase with charge and spin density transfer between electron and hole centers, with ''uncertain valence'' [NiO$_{6}$]$^{(9\pmδ)-}$ ($0 \le δ\le 1$) and spin density $(1 \pm δ)/2$ NiO$_6$-centers. In the classical CO phase, spin-triplet electron centers are surrounded by the nearest nonmagnetic hole centers, which ''turns off'' the strong superexchange interaction of the nearest neighbors. The magnetic ordering in the quantum CDq phase is determined by a strong traditional superexchange and an unusual bosonic double exchange mechanism.

Figures (6)

• Figure 1: Energy spectrum scheme of the NiO6 cluster octets in two model orthonickelate sublattices in the ground state: upper panel $V<V_{cr}$, , lower panel $V>V_{cr}$.
• Figure 2: Dependence of the free energy of the model nickelate (per site) on the order parameter $l$ at various temperatures and relations between the local and nonlocal correlation parameters.
• Figure 3: Dependence of the CO-NO transition temperature on non-local correlation parameter in the atomic limit of the model ($T-V$-phase diagram).
• Figure 4: Energy spectrum scheme of the NiO$_6$ cluster octets in two model orthonickelate sublattices in the ground state taking into account the two-particle transfer effect with $V<V_{cr}$.
• Figure 5: Dependence of the free energy of the model nickelate on $l$ with various temperatures with $V$ = 0.25 $U$, $t_b$ = 0.17 $U$ (left) and $t_b$ = 0.18 $U$ (right). CDq-CO and CO-NO transition temperatures, respectively, are shown in bold.