Rico Pohle

Shizuoka University, Japan
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From Spin Nematic Order to Nematic Spin Liquids

Our conventional classification of matter draws a sharp line between liquids and solids. Yet nematic liquid crystals challenge this distinction. As fluid phases with orientational — but not positional — order, nematics exhibit characteristics of both states. They have provided a rich platform for exploring phenomena such as topological defects, nonlinear optics, and soft-matter dynamics [1], while also revolutionizing everyday technology through their use in liquid crystal displays.

This raises a compelling question: could a similar type of nematic state exist in quantum materials?

The idea of spin nematic phases — magnetic analogues of nematic liquid crystals — was first proposed nearly 60 years ago  [2]. In particular, materials composed of
spin-1 magnetic moments have been predicted to host such phases, combining the orientational order of classical liquid crystals with the quantum properties of magnets. But the same features that make these states exciting also make them difficult to detect [3]. Spin nematics are invisible to conventional magnetic probes and require new theoretical and computational tools to understand their ground state and excitation properties.

In this talk, I will introduce the concept of spin nematics and present a new computational method designed to accurately capture their unique signatures [4]. This approach helps to bridge theory and experiment, offering concrete predictions for how such phases might be identified in future measurements — such as inelastic neutron scattering and resonant inelastic X-ray scattering (RIXS).

Using explicit examples, I will show how spin nematics open a new path into exotic quantum phases — ranging from spin liquids [5] and unconventional magnetic order [6] to analogues of gravitational wave-like excitations [7] — linking ideas across condensed matter, soft matter, and even high-energy physics.

[1] N. D. Mermin, Rev. Mod. Phys. 51, 591 (1979).
[2] M. Blume and Y. Hsieh, J. Appl. Phys. 40, 1249 (1969), V. M. Matveev, JETP, Vol. 38, No. 4, p. 813 (1974).
[3] K. Penc and A. Lauchli, Introduction to Frustrated Magnetism (Springer-Verlag, Berlin, Heidelberg, 2011), Chap. 13.
[4] K. Remund, R. Pohle, Y. Akagi, J. Romhányi, and N. Shannon, Phys. Rev. Research 4, 033106 (2022).
[5] R. Pohle and N. Shannon, arXiv:2503.12776v1
[6] R. Pohle, N. Shannon, and Y. Motome, Phys. Rev. B 107, L140403 (2023).
[7] L. Chojnacki, R. Pohle, H. Yan, Y. Akagi, N. Shannon, Phys. Rev. B 109, L220407 (2024).