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Systems based on spin-1 moments exhibit many fascinating properties, as demonstrated by recent work on spin-nematics, Fe-based superconductors, and cold atom systems.  However, because spin-1 moments support quadrupoles, they cannot be described using O(3) vectors, even in the classical limit.  For this reason, conventional Monte Carlo and molecular-dynamics simulations fail to describe many of the most interesting phenomena.

In this talk, we introduce a new method of simulating spin-1 magnets at a (semi-)classical level [1].  Our approach is based on a representation of spin-1 moments within the group U(3), and allows us to explore the thermodynamics and dynamics of spin liquid and spin nematic phases, as well as conventional magnetic order.

As an applications, we explore the dynamics of the ferroquadrupolar (FQ) phase in the spin-1 bilinear biquadratic (BBQ) model on a triangular lattice, previously discussed as a prototype for unconventional magnetism in NiGaAs, and the spin-1 Kitaev model with competing biquadratic exchange [2].

[1] Kimberly Remund, Rico Pohle, Yutaka Akagi, Judit Romhanyi and Nic Shannon, Phys. Rev. Research 4, 033106 (2022)

[2] Rico Pohle, Nic Shannon and Yukitoshi Motome, https://arxiv.org/abs/2212.10040

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