Magnetic order, magnetic correlations, and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7

Abstract

Er${}_{2}$Ti${}_{2}$O${}_{7}$ is believed to be a realization of an $\mathit{XY}$ 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 Er${}_{2}$Ti${}_{2}$O${}_{7}$, which displays a second-order phase transition at ${T}_{\mathrm{N}}\ensuremath{\simeq}1.2$ 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 $\mathit{XY}$ 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 Tb${}_{2}$Sn${}_{2}$O${}_{7}$, 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.