Enhanced-entropy phases in geometrically frustrated pyrochlore magnets

Frustrated magnets provide a platform for exploring exotic phases beyond conventional ordering, with potential relevance to functional materials and information technologies. In this work, we use Monte Carlo simulations to map the thermodynamic phase diagram of pyrochlore iridates ${R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ ($R$ = Dy, Ho) with three stable magnetic ground-state phases: frustrated spin-ice 2-in--2-out phase, frustrated fragmented 3-in--1-out/1-in--3-out phase, and antiferromagnetic all-in--all-out phase without frustration. We investigate the physical origin of two enhanced-entropy (EE) phases at finite temperatures, which emerge at the boundaries between stable phases. These EE phases exhibit high magnetic susceptibility and high entropy without long-range order. Their stabilization arises from entropic minimization of the free energy, where the entropy dominates energetic competition near phase boundaries at finite temperatures. Our results demonstrate a platform to engineer highly susceptible and degenerated states through frustration and thermal activation, offering a foundation for the design of entropy-based materials and phases in correlated systems.