Neutron scattering, muon spin relaxation, and dc susceptibility studies have been carried out on polycrystalline Tb 2 Ti 2 O 7 , a pyrochlore antiferromagnet in which the Tb 31 moments reside on a network of corner-sharing tetrahedra. Unlike other geometrically frustrated systems, Tb 2 Ti 2 O 7 remains paramagnetic down to ϳ0.07 K, rather than ordering into a conventional Néel or spin-glass-like state, despite the fact that short-range antiferromagnetic correlations (AFC) develop at ϳ50 K. At the first AFC wave vector, its low-lying, relatively flat magnetic excitation spectrum softens partially below 30 K.
In a recent letter [Phys. Rev. Lett. 82, 1012(1999] it was found that the Tb 3+ magnetic moments in the Tb2Ti2O7 pyrochlore lattice of corner-sharing tetrahedra remain in a collective paramagnetic state down to 70mK. In this paper we present results from d.c. magnetic susceptibility, specific heat data, inelastic neutron scattering measurements, and crystal field calculations that strongly suggest that (1) the Tb 3+ ions in Tb2Ti2O7 possess a moment of approximatively 5µB, and (2) the ground state g−tensor is extremely anisotropic below a temperature of O(10 0 )K, with Ising-like Tb 3+ magnetic moments confined to point along a local cubic 111 diagonal (e.g. towards the middle of the tetrahedron). Such a very large easy-axis Ising like anisotropy along a 111 direction dramatically reduces the frustration otherwise present in a Heisenberg pyrochlore antiferromagnet. The results presented herein underpin the conceptual difficulty in understanding the microscopic mechanism(s) responsible for Tb2Ti2O7 failing to develop long-range order at a temperature of the order of the paramagnetic Curie-Weiss temperature θCW ≈ −10 1 K. We suggest that dipolar interactions and extra perturbative exchange coupling(s) beyond nearest-neighbors may be responsible for the lack of ordering of Tb2Ti2O7.
Experimental evidence from measurements of the a.c. and d.c. susceptibility, and heat capacity data show that the pyrochlore structure oxide, Gd2Ti2O7, exhibits short range order that starts developing at 30K, as well as long range magnetic order at T ∼ 1K. The Curie-Weiss temperature, θCW = -9.6K, is largely due to exchange interactions. Deviations from the Curie-Weiss law occur below ∼10K while magnetic heat capacity contributions are found at temperatures above 20K. A sharp maximum in the heat capacity at Tc = 0.97K signals a transition to a long range ordered state, with the magnetic specific accounting for only ∼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 Gd 3+ . There is no frequency dependence to the a.c. susceptibility in either the short range or long range ordered regimes, hence suggesting the absence of any spinglassy 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 Gd2Ti2O7 are compared with other geometrically frustrated antiferromagnets such as the Gd3Ga5O12 gadolinium gallium garnet, RE2Ti2O7 pyrochlores where RE = Tb, Ho and Tm, and Heisenberg-type pyrochlore such as Y2Mo2O7, Tb2Mo2O7, and spinels such as ZnFe2O4
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