Bloch equations in Terahertz magnetic-resonance ellipsometry
arxiv(2024)
摘要
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.
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