Semi-classical simulation of spin-1 magnets

TL;DR

This paper introduces a novel semi-classical simulation method for spin-1 magnets that accounts for both dipole and quadrupole moments, enabling detailed analysis of thermodynamic and dynamical properties.

Contribution

The authors develop a $u(3)$ algebra-based simulation approach for spin-1 magnets, unifying classical and quantum calculations of their properties.

Findings

Successfully simulated thermodynamic properties of ferroquadrupolar order.

Demonstrated correction techniques to extrapolate classical simulations to quantum results.

Provided detailed analysis of spin-1 magnet dynamics on a triangular lattice.

Abstract

Theoretical studies of magnets have traditionally concentrated on either classical spins, or the extreme quantum limit of spin-1/2. However, magnets built of spin-1 moments are also intrinsically interesting, not least because they can support quadrupole, as well as dipole moments, on a single site. For this reason, spin-1 models have been extensively studied as prototypes for quadrupolar (spin-nematic) order in magnetic insulators, and Fe-based superconductors. At the same time, because of the presence of quadrupoles, the classical limit of a spin-1 moment is not an $O(3)$ vector, a fact which must be taken into account in describing their properties. In this Article we develop a method to simulate spin-1 magnets based on a $u(3)$ algebra which treats both dipole and quadrupole moments on equal footing. This approach is amenable to both classical and quantum calculations, and we develop the techniques needed to calculate thermodynamic properties through Monte Carlo simulations and classical low-temperature expansion, and dynamical properties, through "molecular dynamics" simulations and a multiple-boson expansion. As a case study, we present detailed analytic and numerical results for the thermodynamic properties of ferroquadrupolar order on the triangular lattice, and its associated dynamics. At low temperatures, we show that it is possible to "correct" for the effects of classical statistics in simulations, and extrapolate to the zero-temperature quantum results found in flavour-wave theory.