Transition to long-range magnetic order in the highly frustrated insulating pyrochlore antiferromagnetGd2Ti2O7

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 $T\sim 1$ K. The Curie-Weiss temperature, ${\theta }_{\mathrm{CW}}=-9.6$ K, is largely due to exchange interactions. Deviations from the Curie-Weiss law occur below $\sim 10$ K while magnetic heat-capacity contributions are found at temperatures above 20 K. A sharp maximum in the heat capacity at $T_c=0.97\mathrm{}$ K signals a transition to a long-range-ordered state, with the magnetic specific accounting for only $\sim 50\%$ 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 ${\mathrm{ZnFe}}_2{\mathrm{O}}_4.$