Absence of Magnetic Order in ${\mathrm{Y}\mathrm{b}}_3{\mathrm{G}\mathrm{a}}_5{\mathrm{O}}_{12}$: 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.

Figure 1

Zero-field $\mu \mathrm{S}\mathrm{R}$ spectra recorded for ${\mathrm{Y}\mathrm{b}}_3{\mathrm{G}\mathrm{a}}_5{\mathrm{O}}_{12}$, both above and below $T_{\lambda }$. The solid lines in the $\mu \mathrm{S}\mathrm{R}$ spectra are the results of fits to exponential relaxation functions as explained in the text. In the inset, ${}^{170}\mathrm{Y}\mathrm{b}$ Mössbauer reproduced from Ref. 25. These data show the absence of long- or short-range correlations below $T_{\lambda }$.

Figure 2

Zero-field muon spin-lattice relaxation rate, ${\lambda }_Z$, versus temperature measured for ${\mathrm{Y}\mathrm{b}}_3{\mathrm{G}\mathrm{a}}_5{\mathrm{O}}_{12}$. The solid line is the result of a fit to a model explained in the main text. The two straight dashed lines for $T\le 0.4\mathrm{K}$ down to 21 mK are guides to the eye. The specific heat (from Ref. 20) of ${\mathrm{Y}\mathrm{b}}_3{\mathrm{G}\mathrm{a}}_5{\mathrm{O}}_{12}$ is also reproduced. A marked change of slope in ${\lambda }_Z(T)$ occurs at $T_{\lambda }=54\mathrm{m}\mathrm{K}$.