Direct Observation of Collective Electronuclear Modes About a Quantum Critical Point

TL;DR

This study uses microwave spectroscopy to directly observe collective electronuclear modes in a quantum Ising magnet, revealing how these modes behave near a quantum critical point and under magnetic fields.

Contribution

It provides the first direct measurement of collective electronuclear modes in a quantum Ising system, showing their softening near the critical point and response to magnetic fields.

Findings

Electronuclear modes hybridize electronic and nuclear spins.

The lowest mode softens at the quantum critical point.

Magnetic field quenches the mode softening.

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.