Spin Waves and Quantum Criticality in the Frustrated XY Pyrochlore Antiferromagnet Er2Ti2O7

We report detailed measurements of the low temperature magnetic phase diagram of Er$_2$Ti$_2$O$_7$. Heat capacity and time-of-flight neutron scattering studies of single crystals, subject to magnetic fields applied along the crystallographic [110] direction, reveal unconventional low energy states. Er$^{3+}$ magnetic ions reside on a pyrochlore lattice in Er$_2$Ti$_2$O$_7$, where local XY anisotropy and antiferromagnetic interactions give rise to a unique frustrated system. In zero field, the ground state exhibits coexisting short and long range order, accompanied by soft collective spin excitations previously believed to be absent. The application of finite magnetic fields tunes the ground state continuously through a landscape of non-collinear phases, divided by a zero temperature phase transition at $\mu_0 H_c \sim$ 1.5 T. The characteristic energy scale for spin fluctuations is seen to vanish at the critical point, as expected for a second order quantum phase transition driven by quantum fluctuations.