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We report detailed measurements of the low temperature magnetic phase diagramof Er$_2$Ti$_2$O$_7$. Heat capacity and time-of-flight neutron scatteringstudies of single crystals, subject to magnetic fields applied along thecrystallographic [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 aunique frustrated system. In zero field, the ground state exhibits coexistingshort and long range order, accompanied by soft collective spin excitationspreviously believed to be absent. The application of finite magnetic fieldstunes the ground state continuously through a landscape of non-collinearphases, divided by a zero temperature phase transition at $\mu_0 H_c \sim$ 1.5T. The characteristic energy scale for spin fluctuations is seen to vanish atthe critical point, as expected for a second order quantum phase transitiondriven by quantum fluctuations.

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