Spin Waves and Quantum Criticality in the Frustrated XY Pyrochlore Antiferromagnet Er$_2$Ti$_2$O$_7$

We report recent single crystal neutron scattering measurements of the XY pyrochlore antiferromaget Er$_2$Ti$_2$O$_7$, in zero and non-zero magnetic field applied along the (110) direction. Previous results show a magnetically-ordered ground state which is suggested to be stabilized by an unusual order-by-disorder mechanism driven by quantum fluctuations [1]. We present measurements of the low-lying spin excitations of this system, revealing Goldstone modes previously thought to be absent [1]. Also, we explore the response of the ground state to applied magnetic fields, which are shown to induce a quantum phase transition separating the low-field antiferromagnetically ordered phase from the high-field polarized phase. \newline [1] J.D.M. Champion et al. ``Er$_2$Ti$_2$O$_7$: Evidence of quantum order by disorder in a frustrated antiferromagnet'' PRB 68 (2003)