  We report neutron scattering measurements on Er$_2$Pt$_2$O$_7$, a new
addition to the XY family of frustrated pyrochlore magnets. Symmetry analysis
of our elastic scattering data shows that Er$_2$Pt$_2$O$_7$ is the first XY
pyrochlore to order into the $k=0$, $\Gamma_7$ magnetic structure (the
Palmer-Chalker state), at $T_N = 0.38$ K. This contrasts with its sister XY
pyrochlore antiferromagnets Er$_2$Ti$_2$O$_7$ and Er$_2$Ge$_2$O$_7$, both of
which order into $\Gamma_5$ magnetic structures at much higher temperatures,
$T_N=1.2$ K and $1.4$ K, respectively. In this temperature range, the magnetic
heat capacity of Er$_2$Pt$_2$O$_7$ contains a broad anomaly centered at
$T^*=1.5$ K. Our inelastic neutron scattering measurements reveal that this
broad heat capacity anomaly sets the temperature scale for strong short-range
spin fluctuations. Below $T_N = 0.38$ K, Er$_2$Pt$_2$O$_7$ displays a gapped
spin wave spectrum with an intense, flat band of excitations at lower energy
and a weak, diffusive band of excitations at higher energy. The flat band is
well-described by classical spin wave calculations, but these calculations also
predict sharp dispersive branches at higher energy, a striking discrepancy with
the experimental data. This, in concert with the strong suppression of $T_N$,
is attributable to enhanced quantum fluctuations due to phase competition
between the $\Gamma_7$ and $\Gamma_5$ states that border each other within a
classically predicted phase diagram.
