Octupolar Ordering in the b>0 Bilinear-Biquadratic Heisenberg Pyrochlore

Abstract

We investigate the bilinear-biquadratic Heisenberg model on the pyrochlore lattice. While negative biquadratic couplings result in a first-order transition into a nematic ordered state with spins aligned mutually collinearly, it is found that positive biquadratic interactions lead to spins orienting in mutually perpendicular directions, described as octupolar or tetrahedral ordering. This transition is probed using classical Monte Carlo and it is found that the system undergoes a first-order transition into a octupolar ordered state with no long-range order. Unfortunately, we find that single spin-flip Monte Carlo simulations freeze completely at the transition with exceptionally slow dynamics and an extreme lack of ergodicity. The application of parallel tempering does not improve simulation results, which, due to the poor ergodicity of the simulation, cannot be reweighted using histogram techniques. We also present and discuss a potential loop algorithm which may allow simulations to overcome local energy barriers and regain ergodicity.

Upon warming Monte Carlo simulations initialized in potential octupolar long-range ordered states, we observe the dynamics of weathervane modes; zero energy rotational excitations in the lattice. Taking the form of 2D membranes in the lattice, these weathervane modes may rotate at no energy cost, allowing for the successful use of the single spin-flip Monte Carlo algorithm. We note that these weathervane modes exist at rotational angles of 0 and corresponding to alternating layers of spins, in agreement with previous work. Depending on the long-range ordered state that the simulation is initialized in, weathervane modes may be stabilized by the periodic boundary conditions or, if free to rotate at will, may enter a weathervane manifold state where fast dynamics permit the simulation to rapidly sample various weathervane ordered states.