Cavity-Magnon-Polariton spectroscopy of strongly hybridized electro-nuclear spin excitations in LiHoF4

TL;DR

This paper develops a formalism combining input-output and linear response theories to use cavity-magnon-polariton coupling as a spectroscopic tool for probing hybridized electro-nuclear spin excitations, demonstrated on LiHoF4.

Contribution

It introduces a microscopic relation between susceptibility and scattering parameter in strongly hybridized systems, enabling detailed analysis and simulation of complex magnetic materials.

Findings

Quantitative analysis of electro-nuclear spin states in LiHoF4.

Reproduction of experimental data across various magnetic fields.

Potential to study quantum phase transitions in complex magnetic systems.

Abstract

We first present a formalism that incorporates the input-output formalism and the linear response theory to employ cavity-magnon-polariton coupling as a spectroscopic tool for investigating strongly hybridized electro-nuclear spin excitations. A microscopic relation between the generalized susceptibility and the scattering parameter |S11| in strongly hybridized cavity-magnon-polariton systems has been derived without resorting to semi-classical approximations. The formalism is then applied to both analyze and simulate a specific systems comprising a model quantum Ising magnet (LiHoF4) and a high-finesse 3D re-entrant cavity resonator. Quantitative information on the electro-nuclear spin states in LiHoF4 is extracted, and the experimental observations across a broad parameter range were numerically reproduced, including an external magnetic field titraversing a quantum critical point. The method potentially opens a new avenue not only for further studies on the quantum phase transition in LiHoF4 but also for a wide range of complex magnetic systems.