Direct Observation of Collective Electronuclear Modes About a Quantum Critical Point

Abstract

We directly measure the low energy excitation modes of the quantum Ising magnet LiHoF${}_4$ using microwave spectroscopy. Instead of a single electronic mode, we find a set of collective electronuclear modes, in which the spin-$1/2$ Ising electronic spins hybridize with the bath of spin-$7/2$ Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point, even in the presence of disorder. This softening is rapidly quenched by a longitudinal magnetic field. Similar electronuclear structures should exist in other spin-based quantum Ising systems.

12 pages, 5 figures. Accepted for publication in Phys. Rev. Lett