Doubly degenerate orbital system in honeycomb lattice: implication of orbital state in layered iron oxide

TL;DR

This paper investigates a doubly-degenerate orbital model on a honeycomb lattice relevant to layered iron oxides, revealing macroscopic degeneracy, thermal and quantum fluctuation effects, and a unique low-temperature orbital structure.

Contribution

It introduces a detailed analysis of orbital degeneracy and fluctuation effects in a honeycomb lattice model for layered iron oxides, combining classical and quantum approaches.

Findings

Macroscopic degeneracy in classical ground state.

Low-temperature peak in specific heat unrelated to conventional order.

Quantum zero-point fluctuations partially lift degeneracy, leading to a specific orbital configuration.

Abstract

We study a doubly-degenerate orbital model on a honeycomb attice. This is a model for orbital states in multiferroic layered iron oxides. The classical and quantum models are analyzed by spin-wave approximation, Monte-Carlo simulation and Lanczos method. A macroscopic number of degeneracy exists in the classical ground state. In the classical model, a peak in the specific heat appears at a temperature which is much lower than the mean-field ordering one. Below this temperature, angle of orbital pseudo-spin is fixed, but conventional orbital orders are not suggested. The degeneracy in the ground state is partially lifted by thermal fluctuation. We suggest a role of zero-dimensional fluctuation in hexagons on a low-temperature orbital structure. Lifting of the degeneracy also occurs at zero temperature due to the quantum zero-point fluctuation. We show that the ground-state wave function is well represented by a linear combination of the states where a honeycomb lattice is covered by nearest-neighboring pairs of orbitals with the minimum bond energy.