Three-state Potts nematic order in stacked frustrated spin models with SO(3) symmetry

TL;DR

This paper introduces stacked frustrated spin models with SO(3) symmetry that exhibit emergent Z3 Potts nematic order, revealing new phases and mechanisms for experimental realization.

Contribution

It proposes novel lattice designs with SO(3) symmetry that realize emergent Potts nematic order and demonstrates how biquadratic interactions are induced by fluctuations.

Findings

Discovery of a Potts nematic phase above the ferrimagnetic ground state.

Mapping of phase diagrams using Monte Carlo simulations and analytical methods.

Biquadratic exchange is induced by fluctuations, facilitating experimental realization.

Abstract

We propose stacked two-dimensional lattice designs of frustrated and SO(3) symmetric spin models consisting of antiferromagnetic (AFM) triangular and ferromagnetic (FM) sixfold symmetric sublattices that realize emergent Z3 Potts nematic order. Considering bilinear-biquadratic spin interactions, our models describe an SO(3)-symmetric triangular lattice AFM subject to a fluctuating magnetization arising from the FM coupled sublattice. We focus on the classical AFM-FM windmill model and map out the zero- and finite-temperature phase diagram using Monte Carlo simulations and analytical calculations. We discover a state with composite Potts nematic order above the ferrimagnetic three-sublattice up-up-down ground state and relate it to Potts phases in SO(3)-broken Heisenberg and Ising AFMs in external magnetic fields. Finally, we show that the biquadratic exchange in our model is automatically induced by thermal and quantum fluctuations in the purely bilinear Heisenberg model, easing the requirements for realizing these lattice designs experimentally.