Absence of Magnetic Order in Yb₃Ga₅O₁₂: Relation between Phase Transition and Entropy in Geometrically Frustrated Materials

From muon spin relaxation spectroscopy experiments, we show that the sharp peak (λ-type anomaly) detected by specific heat measurements at 54 mK for the ytterbium gallium garnet compound, Yb₃Ga₅O₁₂, does not correspond to the onset of a magnetic phase transition, but to a pronounced building up of dynamical magnetic pair correlations. Beside the λ anomaly, a broad hump is observed at higher temperature in the specific heat of this garnet and other geometrically frustrated compounds. Comparing with other frustrated magnetic systems we infer that a ground state with long-range order is reached only when at least 1/4-1/3 of the magnetic entropy is released at the λ transition.