Intertwined nematic orders in a frustrated ferromagnet

TL;DR

This paper explores the quantum phases of a frustrated square-lattice Heisenberg model, revealing an intermediate paramagnetic phase with complex nematic orders arising from quantum fluctuations and symmetry-breaking interactions.

Contribution

It demonstrates the emergence of intertwined nematic orders in a frustrated ferromagnetic model, highlighting the role of quantum fluctuations and symmetry-breaking perturbations.

Findings

Identification of an intermediate paramagnetic phase

Quantum fluctuations shift spiral pitch angles

Coexistence of different nematic orders

Abstract

We investigate the quantum phases of the frustrated spin-$\frac{1}{2}$ $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice with ferromagnetic $J_1$ and antiferromagnetic $J_2$ and $J_3$ interactions. Using the pseudo-fermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry-breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time-reversal invariance, these phases either break spin-rotation symmetry, lattice-rotation symmetry, or a combination of both. We therefore propose the $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematic orders emerge in the same model.