Direct Observation of Collective Electronuclear Modes About a Quantum Critical Point

The quantum Ising magnet LiHoF₄ provides an ideal platform for exploring excitations near a quantum phase transition. We use microwave spectroscopy to probe the dynamics near the critical point, finding that instead of a single electronic mode we observe a sequence of low energy modes in which the spin-1/2 Ising electronic spins hybridize with the spin-7/2 ¹⁶⁵Ho nuclei. The lowest-lying electronuclear mode softens at the approach to the quantum critical point, showing that quantum criticality persists in the presence of disorder. As expected, a magnetic field applied parallel to the Ising axis rapidly quenches the mode softening. We also observe spectroscopic features that provide insight into the domain formation and dynamics, as well as the physics of strong coupling between the electronuclear excitations and microwave resonator photons. The electronuclear modes observed here and in related solid-state materials, and their coupling to the environment, should be of interest in microwave-optical transduction.