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Using a simple scaling law, a unique set of crystal-field parameters for the rare-earth ions R in the R(2)Ti(2)O(7) pyrochlore series is shown to provide a proper description of the crystal-field excitations previously observed by neutron scattering. The two spectroscopic g factors are given for the compounds with doublet ground states, as well as the ground-state wavefunctions for all the compounds.

Er2Ti2O7 is believed to be a realization of an XY antiferromagnet on a frustrated lattice of corner-sharing regular tetrahedra. It is presented as an example of the order-by-disorder mechanism in which fluctuations lift the degeneracy of the ground state, leading to an ordered state. Here we report detailed measurements of the low temperature magnetic properties of Er2Ti2O7, which displays a second-order phase transition at TN ≃ 1.2 K with coexisting short-and long-range orders. Magnetic-susceptibility studies show that there is no spin-glass-like irreversible effect. Heatcapacity measurements reveal that the paramagnetic critical exponent is typical of a 3-dimensional XY magnet while the low-temperature specific heat sets an upper limit on the possible spin-gap value and provides an estimate for the spin-wave velocity. Muon spin relaxation measurements show the presence of spin dynamics in the nanosecond time scale down to 21 mK. This time range is intermediate between the shorter time characterizing the spin dynamics in Tb2Sn2O7, which also displays long-and short-range magnetic order, and the time scale typical of conventional magnets. Hence the ground state is characterized by exotic spin dynamics. We determine the parameters of a symmetry-dictated Hamiltonian restricted to the spins in a tetrahedron, by fitting the paramagnetic diffuse neutron scattering intensity for two reciprocal lattice planes. These data are recorded in a temperature region where the assumption that the correlations are limited to nearest neighbors is fair.