Microwave Spectroscopy for Probing Electronuclear Modes in Quantum Magnets

Crystals with rare earth ions present an opportunity to explore a range of model magnetic systems, allowing for an experimental realization of several important physical concepts. For example, the compound LiHoF₄ is a transparent, insulating crystal which implements the transverse field Ising model (TFIM) with the Ho³⁺ spins. The TFIM is a well-known model which is one of the simplest systems to display quantum behavior, such as quantum phase transitions (QPTs). This makes LiHoF₄ very useful for investigating these and other quantum effects. LiHoF₄ ~also has strong hyperfine coupling to the nuclear spins, which means the excitations must be considered as composite of electronic and nuclear states (i.e., 'electronuclear'). This introduces a nuclear spin bath which modifies behavior near the QPT. In this work, we investigate the behavior of this QPT by probing the electronuclear states in LiHoF₄ at microwave frequencies. To accomplish this, we develop the use of loop-gap resonators which enable sensitive microwave measurements in LiHoF₄. We also extend the techniques to related systems, such as the 2-dimensional XY antiferromagnet LiErF₄. We then investigate ways to observe new phenomena in the LiHoF₄ system, namely improving superconducting resonators as one possible way to observe the dynamics of quantum quenching through the QPT.