  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 T_N \simeq 1.2 K with
coexisting short- and long-range orders. Magnetic-susceptibility studies show
that there is no spin-glass-like irreversible effect. Heat-capacity
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.
