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We describe a magnetic relation in analogy to the well-known dielectric Lyddane-Sachs-Teller relation [R. H. Lyddane , ]. This magnetic relation follows directly from the model equations for nuclear induction due to fast oscillating electromagnetic fields [F. Bloch, ] and relates the static permeability with the product over all ratios of antiresonance and resonance frequencies associated with all magnetic excitations within a given specimen. The magnetic relation differs significantly from its dielectric analog where the static properties are related to ratios of the squares of resonance frequencies. We demonstrate the validity of the magnetic Lyddane-Sachs-Teller relation using optical magnetization data from terahertz electron magnetic resonance spectroscopic ellipsometry measurements in the presence of an external magnetic field on an iron-doped semiconductor crystal of gallium nitride. 

Electron paramagnetic resonance of Cr3+ ions in β-Ga2O3 is investigated using terahertz spectroscopic ellipsometry under magnetic field sweeping, a technique that enables the polarization resolving capabilities of ellipsometry for magnetic resonance measurements. We employed a single-crystal chromium-doped β-Ga2O3 sample, grown by the Czochralski method, and performed ellipsometry measurements at magnetic field strengths ranging from 2 to 8 T, at frequencies from 82 to 125 and 190 to 230 GHz, and at a temperature of 15 K. Analysis of the frequency-field diagrams derived from all Mueller matrix elements allowed us to differentiate between the effects of electron spin Zeeman splitting and zero-field splitting and to accurately determine the anisotropic Zeeman splitting g-tensor and the zero-field splitting parameters. Our results confirm that Cr3+ ions predominantly substitute into octahedral gallium sites. Line shape analysis of Mueller matrix element spectra using the Bloch–Brillouin model provides the spin volume concentration of Cr3+ sites, showing very good agreement with results from chemical analysis by inductively coupled plasma-optical emission spectroscopy and suggesting minimal occupation of sites with inactive electron paramagnetic resonance. This study enhances our understanding of the magnetic and electronic properties of chromium-doped β-Ga2O3 and demonstrates the effectiveness of high-frequency/high-field electron paramagnetic resonance generalized spectroscopic ellipsometry for characterizing defects in ultrawide-bandgap semiconductors. 

The anisotropic optical absorption edge of β-Ga2O3 follows a modified Beer–Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in β-Ga2O3, which arises from the anisotropy and spectral splitting of the physical absorbers, i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of β-Ga2O3. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer–Lambert law arises from the interplay of both the dichroic and birefringent properties of β-Ga2O3. 

We experimentally demonstrate and theoretically verify a spectrally controllable, extremely large, broadband chiroptical response from three-dimensional all-dielectric broken L-shape nano-boomenrang metamaterial platforms. This innovative design holds great potential for seamless integration into on-chip photonic devices. 

A generalized approach derived from Bloch's 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 Mueller matrix element spectra measured. When augmented with thermodynamic considerations and suitable Hamiltonian description of the magnetic eigenvalue spectrum, important parameters such as density, spectral amplitude distribution, relaxation time constants, and geometrical orientation parameters of the magnetic moments 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 an oblique angle of incidence in the terahertz spectral range, across electron spin resonance quintuplet transitions observed in wurtzite-structure GaN doped with iron. 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 and will become useful for future analysis of frequency and magnetic field-dependent magnetic resonance measurements. Published by the American Physical Society2024 

We investigate the time evolution of ZnO thin film growth in oxygen plasma-enhanced atomic layer deposition using in situ spectroscopic ellipsometry. The recently proposed dynamic-dual-box-model approach [Kilic et al., Sci. Rep. 10, 10392 (2020)] is used to analyze the spectroscopic data post-growth. With the help of this model, we explore the in-cycle surface modifications and reveal the repetitive layer-by-layer growth and surface roughness modification mechanisms during the ZnO ultrathin film deposition. The in situ complex-valued dielectric function of the amorphous ZnO thin film is also determined from the model analysis for photon energies of 1.7–4 eV. The dielectric function is analyzed using a critical point model approach providing parameters for bandgap energy, amplitude, and broadening in addition to the index of refraction and extinction coefficient. The dynamic-dual-box-model analysis reveals the initial nucleation phase where the surface roughness changes due to nucleation and island growth prior to film coalescence, which then lead to the surface conformal layer-by-layer growth with constant surface roughness. The thickness evolution is resolved with Angstrom-scale resolution vs time. We propose this method for fast development of growth recipes from real-time in situ data analysis. We also present and discuss results from x-ray diffraction, x-ray photoelectron spectroscopy, and atomic force microscopy to examine crystallographic, chemical, and morphological characteristics of the ZnO film.