Transition to long-range magnetic order in the highly frustrated insulating pyrochlore antiferromagnet Gd 2 Ti 2 O 7

Experimental evidence from measurements of the ac and dc susceptibility, and heat-capacity data show that the pyrochlore structure oxide, ${\mathrm{Gd}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7},$ exhibits short-range order that starts developing at 30 K, as well as long-range magnetic order at $T\ensuremath{\sim}1$ K. The Curie-Weiss temperature, ${\ensuremath{\theta}}_{\mathrm{CW}}=\ensuremath{-}9.6$ K, is largely due to exchange interactions. Deviations from the Curie-Weiss law occur below $\ensuremath{\sim}10$ K while magnetic heat-capacity contributions are found at temperatures above 20 K. A sharp maximum in the heat capacity at ${T}_{c}=0.97$ K signals a transition to a long-range-ordered state, with the magnetic specific accounting for only $\ensuremath{\sim}50%$ of the magnetic entropy. The heat capacity above the phase transition can be modeled by assuming that a distribution of random fields acts on the ${}^{8}{S}_{7/2}$ ground state for ${\mathrm{Gd}}^{3+}.$ There is no frequency dependence to the ac susceptibility in either the short-range- or long-range-ordered regimes, hence suggesting the absence of any spin-glass behavior. Mean-field theoretical calculations show that no long-range-ordered ground state exists for the conditions of nearest-neighbor antiferromagnetic exchange and long-range dipolar couplings. At the mean-field level, long-range order at various commensurate or incommensurate wave vectors is found only upon inclusion of exchange interactions beyond nearest-neighbor exchange and dipolar coupling. The properties of ${\mathrm{Gd}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ are compared with other geometrically frustrated antiferromagnets such as the ${\mathrm{Gd}}_{3}{\mathrm{Ga}}_{5}{\mathrm{O}}_{12}$ gadolinium gallium garnet, ${R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ pyrochlores where $R=\mathrm{Tb},$ Ho, and Tm, and Heisenberg-type pyrochlore such as ${\mathrm{Y}}_{2}{\mathrm{Mo}}_{2}{\mathrm{O}}_{7},$ ${\mathrm{Tb}}_{2}{\mathrm{Mo}}_{2}{\mathrm{O}}_{7},$ and spinels such as ${\mathrm{ZnFe}}_{2}{\mathrm{O}}_{4}.$