High-field/high-frequency electron spin resonances of Fe-doped β − Ga 2 O 3 by terahertz generalized ellipsometry: Monoclinic symmetry effects

Richter, Steffen; Knight, Sean; Bulancea-Lindvall, Oscar; Mu, Sai; Kühne, Philipp; Stokey, Megan; Ruder, Alexander; Rindert, Viktor; Ivády, Viktor; Abrikosov, Igor A.; Van de Walle, Chris G.; Schubert, Mathias; Darakchieva, Vanya

doi:10.1103/PhysRevB.109.214106

Title: High-field/high-frequency electron spin resonances of Fe-doped $β − {Ga}_{2} O_{3}$ by terahertz generalized ellipsometry: Monoclinic symmetry effects

Journal Article · 12 June 2024 · Physical Review. B

DOI: https://doi.org/10.1103/PhysRevB.109.214106 · OSTI ID:2372800

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We demonstrate detection and measurement of electron paramagnetic spin resonances (EPR) of iron defects in $β − {Ga}_{2} O_{3}$ utilizing generalized ellipsometry at frequencies between 110 and 170 GHz. The experiments are performed on an Fe-doped single crystal in a free-beam configuration in reflection at $45^{\circ}$ and magnetic fields between 3 and 7 T. In contrast with low-field, low-frequency EPR measurements, we observe all five transitions of the $s = 5 / 2$ high-spin state ${Fe}^{3 +}$ simultaneously. We confirm that ferric ${Fe}^{3 +}$ is predominantly found at octahedrally coordinated Ga sites. We obtain the full set of fourth-order monoclinic zero-field splitting parameters for both octahedrally and tetrahedrally coordinated sites by employing measurements at multiple sample azimuth rotations. The capability of high-field EPR allows us to demonstrate that simplified second-order orthorhombic spin Hamiltonians are insufficient, and fourth-order terms as well as consideration of the monoclinic symmetry are needed. These findings are supported by computational approaches based on density-functional theory for second-order and on ligand-field theory for fourth-order parameters of the spin Hamiltonian. Terahertz ellipsometry is a way to measure spin resonances in a cavity-free setup. Its possibility of varying the probe frequency arbitrarily without otherwise changing the experimental setup offers unique means of truly disentangling different components of highly anisotropic spin Hamiltonians. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0012704

OSTI ID:: 2372800

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 21 Vol. 109; ISSN 2469-9950; ISSN PRBMDO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (73)

Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)] Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias The Journal of Chemical Physics, Vol. 124, Issue 21 https://doi.org/10.1063/1.2204597	journal	June 2006
Electronic properties of the residual donor in unintentionally doped β-Ga2O3 Son, N. T.; Goto, K.; Nomura, K. Journal of Applied Physics, Vol. 120, Issue 23 https://doi.org/10.1063/1.4972040	journal	December 2016
Deep donor behavior of iron in β-Ga ₂ O ₃ crystals: Establishing the Fe ^4+/3+ level Gustafson, T. D.; Lenyk, C. A.; Halliburton, L. E. Journal of Applied Physics, Vol. 128, Issue 14 https://doi.org/10.1063/5.0021756	journal	October 2020
Electron paramagnetic resonance and theoretical study of gallium vacancy in β -Ga ₂ O ₃ Son, Nguyen Tien; Ho, Quoc Duy; Goto, Ken Applied Physics Letters, Vol. 117, Issue 3 https://doi.org/10.1063/5.0012579	journal	July 2020
Electrostatic interactions between charged defects in supercells Freysoldt, Christoph; Neugebauer, Jörg; Van de Walle, Chris G. physica status solidi (b), Vol. 248, Issue 5 https://doi.org/10.1002/pssb.201046289	journal	December 2010
β-Gallium oxide power electronics Green, Andrew J.; Speck, James; Xing, Grace APL Materials, Vol. 10, Issue 2 https://doi.org/10.1063/5.0060327	journal	February 2022
Integer-spin electron paramagnetic resonance of iron proteins Hendrich, M. P.; Debrunner, P. G. Biophysical Journal, Vol. 56, Issue 3 https://doi.org/10.1016/S0006-3495(89)82696-7	journal	September 1989
On standardization and algebraic symmetry of the ligand field Hamiltonian for rare earth ions at monoclinic symmetry sites Rudowicz, Czesl/aw The Journal of Chemical Physics, Vol. 84, Issue 9 https://doi.org/10.1063/1.450654	journal	May 1986
Importance of Fourth-Order Zero-Field Splitting Terms in Random-Orientation EPR Spectra of Eu(II)-Doped Strontium Aluminate Matsuoka, Hideto; Furukawa, Ko; Sato, Kazunobu The Journal of Physical Chemistry A, Vol. 107, Issue 51 https://doi.org/10.1021/jp030819+	journal	November 2003
Electron paramagnetic resonance signatures of Co²⁺ and Cu²⁺ in β-Ga₂O₃ Stehr, Jan E.; Hofmann, Detlev M.; Schörmann, Jörg Applied Physics Letters, Vol. 115, Issue 24 https://doi.org/10.1063/1.5127651	journal	December 2019
Singular optical axes in biaxial crystals and analysis of their spectral dispersion effects inβ−Ga2O3 Sturm, Chris; Grundmann, Marius Physical Review A, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevA.93.053839	journal	May 2016
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
First principles calculation of spin-related quantities for point defect qubit research Ivády, Viktor; Abrikosov, Igor A.; Gali, Adam npj Computational Materials, Vol. 4, Issue 1 https://doi.org/10.1038/s41524-018-0132-5	journal	December 2018
Ab initio molecular dynamics for open-shell transition metals Kresse, G.; Hafner, J. Physical Review B, Vol. 48, Issue 17 https://doi.org/10.1103/PhysRevB.48.13115	journal	November 1993
Wide Bandgap Oxide Semiconductors: from Materials Physics to Optoelectronic Devices Shi, Jueli; Zhang, Jiaye; Yang, Lu Advanced Materials, Vol. 33, Issue 50 https://doi.org/10.1002/adma.202006230	journal	April 2021
Non-Kramers iron S = 2 ions in β-Ga2O3 crystals: High-frequency low-temperature EPR study Babunts, R. A.; Gurin, A. S.; Edinach, E. V. Journal of Applied Physics, Vol. 132, Issue 15 https://doi.org/10.1063/5.0102147	journal	October 2022
Magnetic properties and energy-mapping analysis Xiang, Hongjun; Lee, Changhoon; Koo, Hyun-Joo Dalton Trans., Vol. 42, Issue 4 https://doi.org/10.1039/C2DT31662E	journal	January 2013
Longitudinal phonon plasmon mode coupling in β -Ga ₂ O ₃ Schubert, Mathias; Mock, Alyssa; Korlacki, Rafał Applied Physics Letters, Vol. 114, Issue 10 https://doi.org/10.1063/1.5089145	journal	March 2019
EasySpin, a comprehensive software package for spectral simulation and analysis in EPR Stoll, Stefan; Schweiger, Arthur Journal of Magnetic Resonance, Vol. 178, Issue 1, p. 42-55 https://doi.org/10.1016/j.jmr.2005.08.013	journal	January 2006
Terahertz electron paramagnetic resonance generalized spectroscopic ellipsometry: The magnetic response of the nitrogen defect in 4H-SiC Schubert, Mathias; Knight, Sean; Richter, Steffen Applied Physics Letters, Vol. 120, Issue 10 https://doi.org/10.1063/5.0082353	journal	March 2022
Proton irradiation induced defects in β-Ga ₂ O ₃ : A combined EPR and theory study von Bardeleben, Hans Jürgen; Zhou, Shengqiang; Gerstmann, Uwe APL Materials, Vol. 7, Issue 2 https://doi.org/10.1063/1.5053158	journal	February 2019
Zero-field splitting in metal complexes Boča, Roman Coordination Chemistry Reviews, Vol. 248, Issue 9-10 https://doi.org/10.1016/j.ccr.2004.03.001	journal	May 2004
Electrical properties of bulk semi-insulating β-Ga ₂ O ₃ (Fe) Polyakov, A. Y.; Smirnov, N. B.; Shchemerov, I. V. Applied Physics Letters, Vol. 113, Issue 14 https://doi.org/10.1063/1.5051986	journal	October 2018
Dielectric and conducting properties of unintentionally and Sn-doped β-Ga2O3 studied by terahertz spectroscopy Blumenschein, Nick; Kadlec, Christelle; Romanyuk, Oleksandr Journal of Applied Physics, Vol. 127, Issue 16 https://doi.org/10.1063/1.5143735	journal	April 2020
Correlation between blue luminescence intensity and resistivity in β -Ga ₂ O ₃ single crystals Onuma, T.; Fujioka, S.; Yamaguchi, T. Applied Physics Letters, Vol. 103, Issue 4 https://doi.org/10.1063/1.4816759	journal	July 2013
Lateral β -Ga ₂ O ₃ field effect transistors Chabak, Kelson D.; Leedy, Kevin D.; Green, Andrew J. Semiconductor Science and Technology, Vol. 35, Issue 1 https://doi.org/10.1088/1361-6641/ab55fe	journal	November 2019
Slow spin relaxation in single endohedral fullerene molecules Li, Jie; Gu, Lei; Wu, Ruqian Physical Review B, Vol. 104, Issue 22 https://doi.org/10.1103/PhysRevB.104.224431	journal	December 2021
PyCrystalField : software for calculation, analysis and fitting of crystal electric field Hamiltonians Scheie, A. Journal of Applied Crystallography, Vol. 54, Issue 1 https://doi.org/10.1107/S160057672001554X	journal	February 2021
Hybrid functionals based on a screened Coulomb potential Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias The Journal of Chemical Physics, Vol. 118, Issue 18 https://doi.org/10.1063/1.1564060	journal	May 2003
Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations Freysoldt, Christoph; Neugebauer, Jörg; Van de Walle, Chris G. Physical Review Letters, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevLett.102.016402	journal	January 2009
A 220 GHz–1.1 THz continuous frequency and polarization tunable quasi-optical electron paramagnetic resonance spectroscopic system Khatri, Gyan; Fritjofson, Gregory; Hanson-Flores, Jacob Review of Scientific Instruments, Vol. 94, Issue 3 https://doi.org/10.1063/5.0107237	journal	March 2023
A review of Ga ₂ O ₃ materials, processing, and devices Pearton, S. J.; Yang, Jiancheng; Cary, Patrick H. Applied Physics Reviews, Vol. 5, Issue 1 https://doi.org/10.1063/1.5006941	journal	March 2018
High-quality β-Ga ₂ O ₃ single crystals grown by edge-defined film-fed growth Kuramata, Akito; Koshi, Kimiyoshi; Watanabe, Shinya Japanese Journal of Applied Physics, Vol. 55, Issue 12 https://doi.org/10.7567/JJAP.55.1202A2	journal	November 2016
Ultra-broadband EPR spectroscopy in field and frequency domains Neugebauer, P.; Bloos, D.; Marx, R. Physical Chemistry Chemical Physics, Vol. 20, Issue 22 https://doi.org/10.1039/C7CP07443C	journal	January 2018
Advanced Terahertz Frequency-Domain Ellipsometry Instrumentation for In Situ and Ex Situ Applications Kuhne, Philipp; Armakavicius, Nerijus; Stanishev, Vallery IEEE Transactions on Terahertz Science and Technology, Vol. 8, Issue 3 https://doi.org/10.1109/TTHZ.2018.2814347	journal	May 2018
Band-to-band transitions, selection rules, effective mass, and excitonic contributions in monoclinic β − Ga 2 O 3 Mock, Alyssa; Korlacki, Rafał; Briley, Chad Physical Review B, Vol. 96, Issue 24 https://doi.org/10.1103/PhysRevB.96.245205	journal	December 2017
VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data Momma, Koichi; Izumi, Fujio Journal of Applied Crystallography, Vol. 44, Issue 6 https://doi.org/10.1107/S0021889811038970	journal	October 2011
Iron and intrinsic deep level states in Ga ₂ O ₃ Ingebrigtsen, M. E.; Varley, J. B.; Kuznetsov, A. Yu. Applied Physics Letters, Vol. 112, Issue 4 https://doi.org/10.1063/1.5020134	journal	January 2018
Anisotropic complex refractive index of β-Ga2O3 bulk and epilayer evaluated by terahertz time-domain spectroscopy Agulto, Verdad C.; Toya, Kazuhiro; Phan, Thanh Nhat Khoa Applied Physics Letters, Vol. 118, Issue 4 https://doi.org/10.1063/5.0031531	journal	January 2021
Experimental determination of the (0/−) level for Mg acceptors in β -Ga ₂ O ₃ crystals Lenyk, C. A.; Gustafson, T. D.; Basun, S. A. Applied Physics Letters, Vol. 116, Issue 14 https://doi.org/10.1063/5.0002763	journal	April 2020
Electrical Properties, Deep Levels and Luminescence Related to Fe in Bulk Semi-Insulating β-Ga ₂ O ₃ Doped with Fe Polyakov, A. Y.; Smirnov, N. B.; Schemerov, I. V. ECS Journal of Solid State Science and Technology, Vol. 8, Issue 7 https://doi.org/10.1149/2.0171907jss	journal	January 2019
Optical transitions for impurities in Ga ₂ O ₃ as determined by photo-induced electron paramagnetic resonance spectroscopy Bhandari, Suman; Zvanut, M. E. Journal of Applied Physics, Vol. 127, Issue 6 https://doi.org/10.1063/1.5140193	journal	February 2020
Deep donors and acceptors in β-Ga ₂ O ₃ crystals: Determination of the Fe ^2+/3+ level by a noncontact method Lenyk, C. A.; Gustafson, T. D.; Halliburton, L. E. Journal of Applied Physics, Vol. 126, Issue 24 https://doi.org/10.1063/1.5133051	journal	December 2019
Growth of β-Ga ₂ O ₃ Single Crystals by the Edge-Defined, Film Fed Growth Method Aida, Hideo; Nishiguchi, Kengo; Takeda, Hidetoshi Japanese Journal of Applied Physics, Vol. 47, Issue 11 https://doi.org/10.1143/JJAP.47.8506	journal	November 2008
Electron-spin resonance of transparent conductive oxide β-Ga2O3 Yamaga, Mitsuo; Tsuzuki, Hiromi; Takano, Sayumi Journal of Non-Crystalline Solids, Vol. 358, Issue 17 https://doi.org/10.1016/j.jnoncrysol.2011.11.033	journal	September 2012
Ir ⁴⁺ ions in β-Ga ₂ O ₃ crystals: An unintentional deep donor Lenyk, C. A.; Giles, N. C.; Scherrer, E. M. Journal of Applied Physics, Vol. 125, Issue 4 https://doi.org/10.1063/1.5081825	journal	January 2019
Dipole analysis of the dielectric function of color dispersive materials: Application to monoclinic Ga 2 O 3 Sturm, C.; Schmidt-Grund, R.; Kranert, C. Physical Review B, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevB.94.035148	journal	July 2016
Charge trapping at Fe due to midgap levels in Ga2O3 Bhandari, Suman; Zvanut, M. E. Journal of Applied Physics, Vol. 129, Issue 8 https://doi.org/10.1063/5.0042622	journal	February 2021
Perspective: Ga ₂ O ₃ for ultra-high power rectifiers and MOSFETS Pearton, S. J.; Ren, Fan; Tadjer, Marko Journal of Applied Physics, Vol. 124, Issue 22 https://doi.org/10.1063/1.5062841	journal	December 2018
Electron paramagnetic resonance study of neutral Mg acceptors in β-Ga ₂ O ₃ crystals Kananen, B. E.; Halliburton, L. E.; Scherrer, E. M. Applied Physics Letters, Vol. 111, Issue 7 https://doi.org/10.1063/1.4990454	journal	August 2017
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Electron paramagnetic resonance characterization of Cr3+ impurities in a β-Ga2O3 single crystal Yeom, T. H.; Kim, I. G.; Lee, S. H. Journal of Applied Physics, Vol. 93, Issue 6 https://doi.org/10.1063/1.1543648	journal	March 2003
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I. Physical Review Letters, Vol. 100, Issue 13 https://doi.org/10.1103/PhysRevLett.100.136406	journal	April 2008
Electrical properties of β -Ga ₂ O ₃ single crystals grown by the Czochralski method Irmscher, K.; Galazka, Z.; Pietsch, M. Journal of Applied Physics, Vol. 110, Issue 6 https://doi.org/10.1063/1.3642962	journal	September 2011
First principles method for the calculation of zero-field splitting tensors in periodic systems Rayson, M. J.; Briddon, P. R. Physical Review B, Vol. 77, Issue 3 https://doi.org/10.1103/PhysRevB.77.035119	journal	January 2008
β -Ga ₂ O ₃ for wide-bandgap electronics and optoelectronics Galazka, Zbigniew Semiconductor Science and Technology, Vol. 33, Issue 11 https://doi.org/10.1088/1361-6641/aadf78	journal	October 2018
Influence of strain and chemical substitution on the magnetic anisotropy of antiferromagnetic Cr 2 O 3 : An ab-initio study Mu, Sai; Belashchenko, K. D. Physical Review Materials, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevMaterials.3.034405	journal	March 2019
On standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry Rudowicz, C.; Bramley, Richard The Journal of Chemical Physics, Vol. 83, Issue 10 https://doi.org/10.1063/1.449731	journal	November 1985
The anisotropic quasi-static permittivity of single-crystal β-Ga₂O₃ measured by terahertz spectroscopy Gopalan, Prashanth; Knight, Sean; Chanana, Ashish Applied Physics Letters, Vol. 117, Issue 25 https://doi.org/10.1063/5.0031464	journal	December 2020
Point-Charge Calculations of Energy Levels of Magnetic Ions in Crystalline Electric Fields Hutchings, Michael T. Solid State Physics https://doi.org/10.1016/S0081-1947(08)60517-2	book	January 1964
A New Q-Band EPR Probe for Quantitative Studies of Even Electron Metalloproteins Petasis, D. T.; Hendrich, M. P. Journal of Magnetic Resonance, Vol. 136, Issue 2 https://doi.org/10.1006/jmre.1998.1657	journal	February 1999
Optical absorption of Fe in doped Ga ₂ O ₃ Bhandari, Suman; Zvanut, M. E.; Varley, J. B. Journal of Applied Physics, Vol. 126, Issue 16 https://doi.org/10.1063/1.5124825	journal	October 2019
On the bulk β-Ga2O3 single crystals grown by the Czochralski method Galazka, Zbigniew; Irmscher, Klaus; Uecker, Reinhard Journal of Crystal Growth, Vol. 404 https://doi.org/10.1016/j.jcrysgro.2014.07.021	journal	October 2014
Identification of different iron sites in β-Ga2O3 nanoparticles by spectroscopic methods Toloman, D.; Popa, A.; Stan, M. AIP Conference Proceedings https://doi.org/10.1063/1.4938455	conference	January 2015
β‐Gallium Oxide Devices: Progress and Outlook Higashiwaki, Masataka physica status solidi (RRL) – Rapid Research Letters, Vol. 15, Issue 11 https://doi.org/10.1002/pssr.202100357	journal	October 2021
Correlation of Zero-Field Splittings and Site Distortions. IX. Fe3+ and Cr3+ in β -Ga2O3 Büscher, R.; Lehmann, G. Zeitschrift für Naturforschung A, Vol. 42, Issue 1 https://doi.org/10.1515/zna-1987-0111	journal	January 1987
Anisotropy, phonon modes, and free charge carrier parameters in monoclinic β -gallium oxide single crystals Schubert, M.; Korlacki, R.; Knight, S. Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevB.93.125209	journal	March 2016
Determination of the correlation between the crystal field axis system and the crystallographic axes in chromium‐doped β‐Ga₂O₃ by EPR Gunsser, W.; Rohwer, K. physica status solidi (b), Vol. 116, Issue 1 https://doi.org/10.1002/pssb.2221160132	journal	March 1983
Structural and electronic characteristics of Fe-doped β-Ga2O3 single crystals and the annealing effects Zhang, Naiji; Liu, Haoyue; Sai, Qinglin Journal of Materials Science https://doi.org/10.1007/s10853-021-06027-5	journal	May 2021
Dielectric tensor of monoclinic Ga ₂ O ₃ single crystals in the spectral range 0.5–8.5 eV Sturm, C.; Furthmüller, J.; Bechstedt, F. APL Materials, Vol. 3, Issue 10 https://doi.org/10.1063/1.4934705	journal	October 2015
Theoretical unification of hybrid-DFT and DFT + U methods for the treatment of localized orbitals Ivády, Viktor; Armiento, Rickard; Szász, Krisztián Physical Review B, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevB.90.035146	journal	July 2014
Role of screening in the density functional applied to transition-metal defects in semiconductors Ivády, Viktor; Abrikosov, I. A.; Janzén, E. Physical Review B, Vol. 87, Issue 20 https://doi.org/10.1103/PhysRevB.87.205201	journal	May 2013
Spectroscopic Ellipsometry Fujiwara, Hiroyuki https://doi.org/10.1002/9780470060193	book	January 2007