New discoveries are often made on the border between different disciplines. One major discipline in solid state physics is dedicated to quantum spin liquids, an unconventional state of matter accompanied by emergent gauge fields, topological order, and fractionalized excitations. Another concept is that of spin nematics, a magnetically ordered state dominated by quadrupole moments, which breaks spin-rotation symmetry by selecting an axis, while not choosing a particular direction. Usually seen as two separate areas of study, we are interested in combining those two disciplines, by asking the question: “What happens, when a spin nematic and a spin liquid meet?”
To answer this question, we showed that the S=1 Kitaev model under the influence of bilinear-biquadratic interactions hosts many unconventional ordered and disordered phases. We obtain a comprehensive phase diagram including chiral ordered and quadrupolar ordered phases, in addition to already known ferro, antiferro, zigzag and stripy phases. Intriguingly, we find that the competition between Kitaev and positive biquadratic interactions also promotes a noncoplanar finite-temperature spin liquid state, with macroscopic degeneracy and finite scalar chirality.
Our results show that the competition between spin liquid and spin nematic phases is a promising way to explore new magnetic states of matter.

This work was published as “Spin nematics meet spin liquids: Exotic quantum phases in the spin-1 bilinear-biquadratic model with Kitaev interactions”, R. Pohle, N. Shannon, Y. Motome, Phys. Rev. B 107, L140403 (2023).