An official website of the United States government
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.
more »
« less
One-loop electron mass and QED trace anomaly
Abstract Electron mass is considered as a matrix element of the energy–momentum trace in the rest frame. The one-loop diagrams for this matrix element are different from the textbook diagrams for the electron mass renormalization. We clarify connection between the two sets of diagrams and explain analytically and diagrammatically why the results of both calculations coincide.
more »
« less
- Award ID(s):
- 2011161
- PAR ID:
- 10411065
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- The European Physical Journal C
- Volume:
- 83
- Issue:
- 5
- ISSN:
- 1434-6052
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract This paper proposes and investigates the two-grid stabilized lowest equal-order finite element method for the time-independent dual-permeability-Stokes model with the Beavers-Joseph-Saffman-Jones interface conditions. This method is mainly based on the idea of combining the two-grid and the two local Gauss integrals for the dual-permeability-Stokes system. In this technique, we use a difference between a consistent mass matrix and an under-integrated mass matrix for the pressure variable of the dual-permeability-Stokes model using the lowest equal-order finite element quadruples. In the two-grid scheme, the global problem is solved using the standard$$ P_1-P_1-P_1-P_1 $$ finite element approximations only on a coarse grid with grid sizeH. Then, a coarse grid solution is applied on a fine grid of sizehto decouple the interface terms and the mass exchange terms for solving the three independent subproblems such as the Stokes equations, microfracture equations, and the matrix equations on the fine grid. On the other hand, microfracture and matrix equations are decoupled through the mass exchange terms. The weak formulation is reported, and the optimal error estimate is derived for the two-grid schemes. Furthermore, the numerical results validate that the two-grid stabilized lowest equal-order finite element method is effective and has the same accuracy as the coupling scheme when we choose$$ h=H^2 $$ .more » « less
-
We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 ° . Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.more » « less
-
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 Society2024more » « less
-
Summary In this paper, we propose and analyze two stabilized mixed finite element methods for the dual‐porosity‐Stokes model, which couples the free flow region and microfracture‐matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea of partitioned time stepping, the four interface conditions, and the mass exchange terms in the dual‐porosity model, the second stabilized mixed finite element method is decoupled in two levels and allows a noniterative splitting of the coupled problem into three subproblems. Due to their superior conservation properties and convenience of the computation of flux, mixed finite element methods have been widely developed for different types of subsurface flow problems in porous media. For the mixed finite element methods developed in this article, no Lagrange multiplier is used, but an interface stabilization term with a penalty parameter is added in the temporal discretization. This stabilization term ensures the numerical stability of both the coupled and decoupled schemes. The stability and the convergence analysis are carried out for both the coupled and decoupled schemes. Three numerical experiments are provided to demonstrate the accuracy, efficiency, and applicability of the proposed methods.more » « less
