Exotic Spin Order due to Orbital Fluctuations

TL;DR

This paper explores how orbital fluctuations influence exotic spin orders in the spin-orbital $d^9$ Kugel-Khomskii model across different lattice dimensionalities, revealing complex entangled phases and temperature-dependent order stability.

Contribution

It provides a detailed analysis of the phase diagrams for varying system dimensionality, highlighting the role of orbital fluctuations in stabilizing exotic spin orders and their temperature evolution.

Findings

Entangled spin-orbital phases emerge at the crossover from antiferromagnetic to ferromagnetic regimes.

Orbital order is generally more robust than spin order, which melts at lower temperatures.

Long-range effective interactions stabilize the exotic spin orders.

Abstract

We investigate the phase diagrams of the spin-orbital $d^9$ Kugel-Khomskii model for increasing system dimensionality: from the square lattice monolayer, via the bilayer to the cubic lattice. In each case we find strong competition between different types of spin and orbital order, with entangled spin-orbital phases at the crossover from antiferromagnetic to ferromagnetic correlations in the intermediate regime of Hund's exchange. These phases have various types of exotic spin order and are stabilized by effective interactions of longer range which follow from enhanced spin-orbital fluctuations. We find that orbital order is in general more robust and spin order melts first under increasing temperature, as observed in several experiments for spin-orbital systems.