Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions

TL;DR

This paper explores a spin-1 honeycomb lattice model combining biquadratic and Kitaev interactions, revealing a rich variety of exotic quantum phases including spin liquids, nematic states, and chiral orders, with potential experimental relevance.

Contribution

It introduces a comprehensive study of the interplay between spin nematics and spin liquids in a spin-1 model with novel phase discoveries.

Findings

Identification of multiple exotic phases including nonzero scalar spin chirality states

Discovery of a chiral spin liquid at finite temperature

Revelation of complex phase diagram with competing dipole and quadrupole moments

Abstract

Spin liquid crystals are magnetic analogs of liquid crystals, possessing properties of both liquids and solids, a typical example of which are spin nematics. Spin nematics share many features with spin liquids, and the interplay between them is a promising, but little explored, route to uncovering new phases of matter. Here, we address this question in the context of a spin-$1$ magnet on the honeycomb lattice, by considering a model with both biquadratic interactions, favouring spin-nematic states, and Kitaev-like interactions, supporting spin liquids. Accompanying these, where dipole and quadrupole moments compete, we find a plethora of exotic phases, including multiple-$q$ states with nonzero scalar spin chirality; a quasi-one-dimensional coplanar phase; a twisted conical phase; and a noncoplanar order state which gives way to a chiral spin liquid at finite temperature. The implication of these results for experiment is discussed.