Quantum melting of magnetic long-range order near orbital degeneracy. Classical phases and Gaussian fluctuations

TL;DR

This paper investigates how orbital degeneracy in a spin-orbital model leads to quantum melting of magnetic order, resulting in a spin liquid state due to frustration, with implications for materials like LiNiO2.

Contribution

It introduces a detailed analysis of quantum fluctuations near orbital degeneracy, revealing a mechanism for spin liquid formation in three-dimensional perovskite systems.

Findings

Quantum fluctuations are enhanced near the orbital degeneracy point.

Classical magnetic order is suppressed in a crossover regime.

Orbital degeneracy can stabilize a spin liquid ground state.

Abstract

We study the effective spin-orbital model derived for the d9 ions in a three-dimensional perovskite lattice, as in KCuF_3, where at each site the doubly degenerate eg orbitals contain a single hole. The model describes the superexchange interactions that depend on the pattern of orbitals occupied. We present the ground state properties of this model, depending on the splitting between the eg orbitals E_z, and the Hund's rule coupling in the excited d8 states, J_H. The classical phase diagram consists of six magnetic phases which all have different orbital ordering: two antiferromagnetic (AF) phases with G-AF order and either x2-y2 or 3z2-r2 orbitals occupied, two phases with mixed orbital (MO) patterns and A-AF order, and two other MO phases with either C-AF or G-AF order. All of them become degenerate at the multicritical point M=(E_z,J_H)=(0,0). Using a generalization of linear spin-wave theory we study both the transverse excitations which are spin-waves and spin-and-orbital-waves, as well as the longitudinal (orbital) excitations. The transverse modes couple to each other, and the spin-and-orbital-wave turns into a soft mode near the M point. Therefore, quantum corrections to the long-range-order parameter are drastically increased near the orbital degeneracy, and classical order is suppressed in a crossover regime between the G-AF and A-AF phases in the (E_z,J_H) plane. This behavior is reminiscent of that found in frustrated spin models, and we conclude that orbital degeneracy provides a new and physically realizable mechanism which stabilizes a spin liquid ground state due to inherent frustration of magnetic interactions. We also point out that such a disordered magnetic phase is likely to be realized in LiNiO_2.