Spin-orbit-induced Instability and Finite-Temperature Stabilization of a Triangular-lattice Supersolid

Geometrically frustrated triangular-lattice magnets provide fertile ground for realizing intriguing quantum phases such as spin supersolids. A common expectation is that spin-orbit coupling (SOC), which breaks continuous spin rotational symmetry, destabilizes these phases by gapping their low-energy modes. Revisiting this assumption, we map out the SOC-field phase diagram of a frustrated triangular-lattice magnet using spin-wave theory and infinite density-matrix renormalization group (iDMRG) simulations. We find that while infinitesimally weak SOC indeed drives a zero-temperature instability of the supersolid by opening a gap, certain supersolid states remain thermodynamically stable at non-zero temperatures. This reveals a previously unrecognized mechanism in which thermal fluctuations counteract SOC to stabilize supersolidity. The resulting finite-temperature supersolids retain key responses, including a giant magnetocaloric effect, highlighting their potential relevance to real materials. At larger SOC, the system transitions into distinct magnetic orders, including a skyrmion lattice, completing a unified phase diagram.