Absence of Magnetic Order inYb3Ga5O12: Relation between Phase Transition and Entropy in Geometrically Frustrated Materials

From muon spin relaxation spectroscopy experiments, we show that the sharp peak ($\lambda$-type anomaly) detected by specific heat measurements at 54 mK for the ytterbium gallium garnet compound, ${\mathrm{Y}\mathrm{b}}_3{\mathrm{G}\mathrm{a}}_5{\mathrm{O}}_{12}$, does not correspond to the onset of a magnetic phase transition, but to a pronounced building up of dynamical magnetic pair correlations. Beside the $\lambda$ 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 $\lambda$ transition.