Thermally melted quadrupolar order and intrinsically quantum phases in 5$d^1$ double perovskites

Abstract

Spin-orbit-coupled $d^1$ double perovskites exhibit a rich interplay of spin, orbital, and quadrupolar degrees of freedom (DOF), giving rise to competing magnetic and multipolar phases. Although quantum mean-field theories predict many exotic phases, their stability against thermal fluctuations and reproducibility within a classical framework remain an open question. Here, we surpass the mean-field limitations by deploying large-scale classical Monte Carlo simulations on the projected $j=3/2$ manifold of the FCC lattice, allowing complex ordering patterns to emerge spontaneously without preassigned magnetic symmetries. Our thermodynamic mapping reveals that thermal fluctuations melt the intermediate-temperature quadrupolar phase over part of the phase diagram, while it survives intact elsewhere. Crucially, by systematically isolating the boundary between classical and quantum stability, we demonstrate that while the four-sublattice antiferromagnetic and ferromagnetic (FM) phases are robustly classical, the coplanar canted FM[110] state completely destabilizes. This identifies the FM[110] phase as an intrinsically quantum state born out of quantum fluctuations. Our results demonstrate that the dominant magnetic phases are robust within a classical description, where the essential physics of the system is captured by weakly entangled, short-range correlated DOF and highlight the role of thermal fluctuations in determining the stability of different types of magnetic and quadrupolar order.