Bloch equations in Terahertz magnetic-resonance ellipsometry

TL;DR

This paper develops a generalized Bloch equation-based model to analyze terahertz magnetic resonance ellipsometry data, enabling detailed characterization of magnetic materials' properties through polarization signatures.

Contribution

It introduces a comprehensive tensor model linking magnetic resonance parameters with polarization signatures, validated by experimental terahertz ellipsometry measurements on doped GaN.

Findings

Model accurately predicts polarization signatures in Mueller matrix spectra.

Extracts magnetic parameters like zero-frequency magnetization and relaxation times.

Demonstrates applicability to electron spin resonance in doped GaN.

Abstract

A generalized approach derived from Blochs equation of motion of nuclear magnetic moments is presented to model the frequency, magnetic field, spin density, and temperature dependencies in the electromagnetic permeability tensor for materials with magnetic resonances. The resulting tensor model predicts characteristic polarization signatures which can be observed, for example, in fully polarization-resolved Mueller matrix element spectra measured across magnetic resonances as a function of frequency, magnetic field, magnetic moment density, and temperature. When augmented with thermodynamic considerations and suitable Hamiltonian description of the magnetic eigenvalue spectrum, important parameters such as zero-frequency magnetization, spectral amplitude distribution, relaxation time constants, and geometrical orientation parameters of the magnetic moment density can be obtained from comparing the generalized model approach to experimental data. We demonstrate our approach by comparing model calculations with full Mueller matrix element spectra measured at oblique angle of incidence in the terahertz spectral range, across electron spin resonance quintuplet transitions observed in wurtzite-structure GaN doped with iron. Measurements were performed by ellipsometry, using a superconducting cryostat magnet at magnetic fields of 7.23 T and at temperatures of 20 K and 30 K. We detail the occurrence of linear and circular birefringence and dichroism associated with each of the zero-field split spin transitions in the S = 5/2 defect system. We derive the spectral dependence of the magnetic susceptibility function and obtain the temperature and magnetic field dependence of the spin Hamiltonian. Our model correctly predicts the complexity of the polarization signatures observed in the 15 independent elements of the normalized Mueller matrix for both positive and negative magnetic fields.