Quantum 120-degree model on pyrochlore lattice: orbital ordering in MnV2O4

TL;DR

This paper develops an analytical model for orbital ordering in MnV2O4, revealing a quantum 120-degree antiferromagnetic interaction on a pyrochlore lattice that explains observed magnetic and orbital structures.

Contribution

It introduces a novel quantum antiferromagnetic 120-degree model for orbital interactions in MnV2O4 based on first-principles calculations.

Findings

Orbital order involves two inequivalent orbital chains.

The model's orbital order matches experimental tetragonal symmetry.

Spin anisotropy stabilizes the observed magnetic structure.

Abstract

We present an analytical model of orbital ordering in vanadium spinel MnV2O4. The model is based on recent first-principles calculation indicating a strong trigonal distortion at the vanadium sites of this compound [Phys. Rev. Lett. 102, 216405 (2009)]. At the single-ion level, the trigonal crystal field leaves a doubly degenerate atomic ground state and breaks the approximate rotational symmetry of t2g orbitals. We find that the effective interaction between the low-energy doublets is described by a quantum antiferromagnetic 120-degree model on the pyrochlore lattice. We obtain the classical ground state and show its stability against quantum fluctuations. The corresponding orbital order consisting of two inequivalent orbital chains is consistent with the experimentally observed tetragonal symmetry. A periodic modulation of electron density function along orbital chains is shown to arise from the staggering of local trigonal axes. In the presence of orbital order, single-ion spin anisotropy arising from relativistic spin-orbit interaction stabilizes the experimentally observed orthogonal magnetic structure.