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

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