Spin liquids meet spin nematics in the S=1 Kitaev model with bilinear-biquadratic interactions

New discoveries are often made at the intersection of different disciplines. One major area of research focuses on quantum spin liquids--an unconventional state of matter characterized by emergent gauge fields, topological order, and fractionalized excitations [1]. Another intriguing concept is that of spin nematics, a magnetically ordered state dominated by quadrupole moments, which breaks spin-rotation symmetry by selecting an axis without choosing a specific direction [2]. Usually seen as two separate areas of study, we are interested in connecting those disciplines by asking: “What happens when a spin liquid and a spin nematic meet?”

To address this question, we adopt the recently developed U(3) formalism [3] to investigate the S=1 Kitaev model with bilinear-biquadratic interactions. Our study reveals a comprehensive phase diagram featuring triple-q chiral and quadrupolar ordered phases, alongside already known ferro, antiferro, zigzag, and stripy phases [4,5]. Intriguingly, the competition between Kitaev and positive biquadratic interactions stabilizes a novel Z2 chiral spin liquid state, which is transparently understood through an effective eight-color model and its associated lattice gauge theory [6].

[1] L. Balents, Nature 464, 199 (2010).

[2] K. Penc, A. M. Läuchli (2011). Spin Nematic Phases in Quantum Spin Systems. In: C. Lacroix, P. Mendels, F. Mila, (eds) Introduction to Frustrated Magnetism. (Springer Series in Solid-State Sciences, vol 164. Springer, Berlin, Heidelberg).

[3] K. Remund, R. Pohle, Y. Akagi, J. Romhányi, and N. Shannon, Phys. Rev. Research 4, 033106 (2022).

[4] R. Pohle, N. Shannon, and Y. Motome, Phys. Rev. B 107, L140403 (2023).

[5] R. Pohle, N. Shannon, and Y. Motome, Phys. Rev. Research 6, 033077 (2024).

[6] H. Yan, R. Pohle, arXiv:2409.04061.