Exotic spin orders driven by orbital fluctuations in the Kugel-Khomskii model

TL;DR

This paper explores the complex phase diagram of the 3D Kugel-Khomskii model, revealing exotic magnetic orders driven by orbital fluctuations and spin-orbital entanglement, including novel antiferromagnetic phases.

Contribution

It introduces new exotic magnetic phases stabilized by orbital fluctuations and provides a detailed mechanism involving extended spin interactions beyond simple Heisenberg models.

Findings

Identification of three exotic magnetic phases driven by orbital fluctuations

Derivation of effective spin models with extended interactions

Demonstration of spin-orbital entanglement effects on magnetic order

Abstract

We study zero temperature phase diagram of the three-dimensional Kugel-Khomskii model on a cubic lattice using the cluster mean field theory and different perturbative expansions in the orbital sector. The phase diagram is rich, goes beyond the single-site mean field theory due to spin-orbital entanglement. In addition to the antiferromagnetic (AF) and ferromagnetic (FM) phases, one finds also a plaquette valence-bond phase with singlets ordered either on horizontal or vertical bonds. More importantly, for increasing Hund's exchange we identify three phases with exotic magnetic order stabilized by orbital fluctuations in between the AF and FM order: (i) an AF phase with two mutually orthogonal antiferromagnets on two sublattices in each $ab$ plane and AF order along the c axis (ortho-$G$-type phase), (ii) a canted-$A$-type AF phase with a non-trivial canting angle between nearest neighbor FM layers along the c axis, and (iii) a striped-AF phase with anisotropic AF order in the $ab$ planes. We elucidate the mechanism responsible for each of the above phases by deriving effective spin models which involve second and third neighbor Heisenberg interactions as well as four-site spin interactions going beyond Heisenberg physics, and explain how the entangled nearest neighbor spin-orbital superexchange generates spin interactions between more distant spins.