Spin-1 magnets allow for dipolar and quadrupolar moments on a single site, leading to rich physical properties as seen in spin nematic phases, Fe-based superconductors and cold atom systems. However, experimental probing of these unconventional phases remains challenging, and therefore requires new theoretical tools to describe and interpret their ground state and excitation properties.
In this work, we introduce a new Monte Carlo and Molecular Dynamics method designed to study thermodynamic and dynamic properties of spin-1 magnets. We benchmark our numerical implementation by on the ferroquadrupolar phase of the spin-1 bilinear-biquadratic (BBQ) Hamiltonian on the triangular lattice, and show excellent agreement with analytical flavour-wave theory and low-temperature expansion results.
These results open the door to efficiently study realistic spin-1 magnets, and spin-1 models in the context of cold atoms, and Fe-based superconductors.

This work was published as “Semi-classical simulation of spin-1 magnets”, Kimberly Remund, Rico Pohle, Yutaka Akagi, Judit Romhànyi and Nic Shannon, Phys. Rev. Research 4, 033106 (2022)