Finite Temperature Phase Diagram of the Dipolar-Octupolar XYZ Model on the Pyrochlore Lattice

Dipolar-octupolar (DO) pyrochlore materials are an exciting platform for studying frustrated magnetism in three dimensions. The unique symmetry properties of these materials are well-captured through a pseudospin-1/2 description, whose different components transform as dipolar and octupolar moments under crystal symmetries. In particular, these materials are described by an alluringly simple XYZ Hamiltonian, whose zero-temperature phase diagram has been shown to host both long-range ordered and quantum spin liquid phases. Conversely, the finite-temperature properties of this quantum model have been less explored. Classical simulations and semiclassical calculations have primarily been used, with a few quantum studies focusing on the idealized XXZ limit. Motivated by this, we examine the finite-temperature phase diagram of sign-problem free regimes of the XYZ Hamiltonian using the quantum Monte Carlo stochastic series expansion with directed loops. In particular, we identify and precisely characterize thermally-driven phase transitions through various thermodynamic properties with a focus on regimes where successive transitions are observed. Furthermore, we compute spin-spin correlations in each thermally stabilized regime, revealing the nature of the magnetic phase. Where possible, we connect our study to recent experiments on real cerium- and neodymium-based DO materials.