研究生: |
鍾沄蓁 Chung, Yun-Chen |
---|---|
論文名稱: |
以光譜實驗技術探究鈣鈦礦氧化物SrFeO3-δ, Ba2CuTeO6, 及 Li2Ni(WO4)2的電子結構與晶格動力學 Optical studies of electronic structure and lattice dynamics in perovskite oxides: SrFeO3-δ, Ba2CuTeO6, and Li2Ni(WO4)2 |
指導教授: |
劉祥麟
Liu, Hsiang-Lin |
學位類別: |
博士 Doctor |
系所名稱: |
物理學系 Department of Physics |
論文出版年: | 2020 |
畢業學年度: | 108 |
語文別: | 英文 |
論文頁數: | 119 |
英文關鍵詞: | Perovskite oxides, optical spectroscopy |
DOI URL: | http://doi.org/10.6345/NTNU202001198 |
論文種類: | 學術論文 |
相關次數: | 點閱:155 下載:5 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
We present the optical studies of electronic structure and lattice dynamics in SrFeO3-d, Ba2CuTeO6, and Li2Ni(WO4)2. SrFeO3-d single crystals were grown using the floating zone method;Ba2CuTeO6single crystals were grown using the flux method; and polycrystalline Li2Ni(WO4)2 was grown using the solid-state reaction method. These materials are unusual given their complex magnetic phase transitions.
At room temperature, the optical absorption spectra of SrFeO3-d displayed three maxima in the spectral range of 1.8–5.1 eV and exhibited the direct band gap at approximately 1.98–2.08 eV. SrFeO2.86 exhibited 14 Raman-active phonon modes, and the phonon frequencies of SrFeO2.75 were close to those of SrFeO2.86 with the disappearance of one feature at approximately 226 cm−1. The optical absorption spectrum of Ba2CuTeO6 showed a direct optical band gap at approximately 1.04 eV and exhibited four bands at higher photon energies. The room-temperature Raman scattering spectrum of Ba2CuTeO6 displayed 16 phonon modes. The optical absorption spectrum of Li2Ni(WO4)2 presented a direct optical band gap at 2.25 eV and displayed one band at approximately 5.6 eV. The Raman scattering spectrum of Li2Ni(WO4)2 measured at room temperature presented 17 phonon modes.
With decreasing temperature, the onset of magnetic ordering of SrFeO3-d did not influence the phonon parameters. By contrast, the stretching vibrations of CuO6 octahedra located at 679 cm−1 in Ba2CuTeO6 had the largest spin-phonon coupling constant (1.67 mRy/Å2). The stretching vibrations of WO6 octahedra located at 914 cm−1 in Li2Ni(WO4)2 exhibited the spin-phonon coupling constant (0.94 mRy/Å2).
In this study, we demonstrated the direct optical band gap at low photon energy and charge-transfer bands at higher photon energy in the perovskite oxides of SrFeO3-d and double perovskite oxides of Ba2CuTeO6 and Li2Ni(WO4)2. Their room-temperature Raman scattering spectra showed rich phonon modes. The symmetric stretching vibrations of CuO6 and WO6 octahedra connected the magnetic ordering and the spin-phonon coupling constants were estimated.
[1] D. Zhou, T. Zhou, Y. Tian, X. Zhu, and Y.Tu, “Perovskite-based solar cells: materials, methods, and future perspectives”, J. Nanomater. 2018, 15 (2018).
[2] S. Cong, F. Geng, and Z. Zhao, “Tungsten Oxide Materials for Optoelectronic Applications”, Adv. Mater. 28, 10518 (2016).
[3] M. A. Peña and J. L. G. Fierro, “Chemical structures and performance of perovskite oxides”, Chem. Rev. 101, 1981 (2001).
[4] R. E. Cohen, “Origin of ferroelectricity in perovskite oxides”, Nature 28, 136 (1992).
[5] N. C. Bristowe, J. Varignon, D. Fontaine, E. Bousquet, and P. Ghosez, “Ferromagnetism induced by entangled charge and orbital orderings in ferroelectric titanate perovskites”, Nat. Commun. 6, 6677 (2015).
[6] B. Raveau, “Oxides with a tunnel structure characterized by a mixed framework of octahedra and tetrahedra”, J. Chem. Sci. 96, 419 (1986).
[7] S. Vasala and M. Karppinen, “A2B′B″O6 perovskites: A review”, Prog. Solid State Chem. 43, 1 (2015).
[8] F. Denis Romero and Y. Shimakawa, “Charge transitions in perovskite oxides containing unusually high-valent Fe”, Chem. Commun. 55, 3690 (2019).
[9] A. Cammarata and J. M. Rondinelli, “Spin-assisted covalent bond mechanism in “charge-ordering” perovskite oxides”, Phys. Rev. B - Condens. Matter Mater. Phys. 86, 195144 (2012).
[10] Z. Liao, N. Gauquelin, R. J. Green, K. Müller-Caspary, I. Lobato, L. Li, S. VanAert, J. Verbeeck, M. Huijben, M. N. Grisolia, V. Rouco, R. ElHage, J. E. Villegas, A. Mercy, M. Bibes, P. Ghosez, G. A. Sawatzky, G. Rijnders, and G. Koster, “Metal–insulator-transition engineering by modulation tilt-control in perovskite nickelates for room temperature optical switching”, Proc. Natl. Acad. Sci. U. S. A. 115, 9515 (2018).
[11] H. Zheng, J. Z. Ou, M. S. Strano, R. B. Kaner, A. Mitchell, and K. Kalantar-Zadeh, “Nanostructured tungsten oxide - properties, synthesis, and applications”, Adv. Funct. Mater. 21, 2175 (2011).
[12] I. Grinberg, D. V. West, M. Torres, G. Gou, D. M. Stein, L. Wu, G. Chen, E. M. Gallo, A. R. Akbashev, P. K. avies, J. E. Spanier, and A. M. Rappe, “Perovskite oxides for visible-light-absorbing ferroelectric and photovoltaic materials”, Nature. 503, 509 (2013).
[13] W. Gao, Y. Zhu, Y. Wang, G. Yuan, and J. M. Liu, “A review of flexible perovskite oxide ferroelectric films and their application”, J. Mater. 6,1 (2020).
[14] M. P. Ghimire, L. H. Wu, and X. Hu, “Possible half-metallic antiferromagnetism in an iridium double-perovskite material”, Phys. Rev. B. 93, 134421 (2016).
[15] M. Saad HE, “Half-metallic double perovskites Sr2CrWO6 and Sr2FeReO6 materials for spintronics applications”, Adv. Tissue Eng. Regen. Med. Open Access. 4, 27 (2018).
[16] Y. Takeda, K. Kanno, T. Takada, O. Yamamoto, M. Takano, N. Nakayama, and Y. Bando, “Phase relation in the oxygen nonstoichiometric system, SrFeOx (2.5 ≤ x ≤ 3.0) ”, J. Solid State Chem. 63, 237 (1986).
[17] S. Diodati, L. Nodari, M. M. Natile, U. Russo, E. Tondello, L. Lutterottic, and S. Gross, “Highly crystalline strontium ferrites SrFeO3−δ an easy and effective wet-chemistry synthesis”, Dalton Trans., 41, 5517 (2012).
[18] S. Stølen, E. Bakken, and C. E. Mohn, “Oxygen-deficient perovskites: Linking structure, energetics and ion transport”, Phys. Chem. Chem. Phys. 8, 429 (2006).
[19] H. Falcón, J. A. Barbero, J. A. Alonso, M. J. Martínez-Lope, and J. L. G. Fierro, “SrFeO3-δ perovskite oxides: Chemical features and performance for methane combustion”, Chem. Mater. 14 2325 (2002).
[20] A. Lebon, P. Adler, C. Bernhard, A. V.Boris, A. V.Pimenov, A. Maljuk, C. T. Lin, C. Ulrich, and B. Keimer, “Magnetism, charge order, and giant magnetoresistance in SrFeO3-δ single crystals”, Phys. Rev. Lett. 92, 4 (2004).
[21] P. Adler, A. Lebon, V. Damljanović, C. Ulrich, C. Bernhard, A. V. Boris, A. Maljuk, C. T. Lin, and B. Keimer, “Magnetoresistance effects in SrFeO3-δ: Dependence on phase composition and relation to magnetic and charge order”, Phys. Rev. B - Condens. Matter Mater. Phys. 73, 1 (2006).
[22] S. H. Lee, T. W. Frawley, C. H. Yao, Y. C. Lai, C. H. Du, P. D. Hatton, M. J. Wang, F. C. Chou, and D. J. Huang, “Charge and spin coupling in magnetoresistive oxygen-vacancy strontium ferrate SrFeO3-δ”, New J. Phys. 18, 093033 (2016).
[23] E. K. Hemery, G. V. M. Williams, and H. J. Trodahl, “Anomalous thermoelectric power in SrFeO3-δ from charge ordering and phase separation”, Phys. Rev. B 75, 092403 (2007).
[24] J. B. MacChesney, R. C. Sherwood, and J. F. Potter, “Electric and magnetic properties of the strontium ferrates”, J. Chem. Phys. 43, 1907 (1965).
[25] M. Schmidt, M. Hofmann, and S. J. Campbell, “Magnetic structure of strontium ferrite Sr4Fe4O11”, J. Phys. Condens. Matter. 15, 8691 (2003).
[26] K. B. Suchita and S. Singh, “Synthesis and characterization of brownmillerite SrFeO2.5 in nanostructured form”, AIP Conf. Proc. 1665, 050005 (2015).
[27] A. Khare, J. Lee, J. Park, G. Y. Kim, S. Y. Choi, T. Katase, S. Roh, T. S. Yoo, J. Hwang, H. Ohta, J. Son, and W. S. Choi, “Directing oxygen vacancy channels in SrFeO2.5 epitaxial thin films”, ACS Appl. Mater. Interfaces. 10, 4831 (2018).
[28] E. Heifets, E. A. Kotomin, A. A. Bagaturyants, and J. Maier, “Thermodynamic stability of non-stoichiometric SrFeO3-δ : a hybrid DFT study”, Phys. Chem. Chem. Phys. 21, 3918 (2019).
[29] G. N. Rao, R. Sankar, A. Singh, I. P. Muthuselvam, W. T. Chen, V. N. Singh, G. Y. Guo, and F. C. Chou, “Tellurium-bridged two-leg spin ladder in Ba2CuTeO6”, Phys. Rev. B. 93, 104401 (2016).
[30] V. P. Köhl and D. Reinen, “Strukturelle und spektroskopische Untersuchungen am Ba2CuTeO6”, Z. Anorg. Allg. Chem. 409, 257 (1974).
[31] V. P. Köhl, U. Müller, and D. Reinen, “Ba2NiTeO6 – eine neue Verbindung in der Reihe der hexagonalen Perowskite”, Z. Anorg. Allg. Chem. 392, 124 (1972).
[32] D. Macdougal, A. S. Gibbs, T. Ying, S. Wessel, H. C. Walker, D. Voneshen, F. Mila, H. Takagi, and R. Coldea, “Spin dynamics of coupled spin ladders near quantum criticality in Ba2CuTeO6”, Phys. Rev. B. 98,1 (2018).
[33] R. L. Moreira, R. P. S. M.Lobo, S.L.L.M. Ramos, M.T. Sebastian, F.M. Matinaga, A. Righi, and A. Dias, “Raman and infrared spectroscopic investigations of a ferroelastic phase transition in Ba2ZnTeO6 double perovskite”, Phys. Rev. Mater. 2, 054406 (2018).
[34] D. Iwanaga, Y. Inaguma, and M. Itoh, “Crystal structure and magnetic properties of B-site ordered perovskite-type oxides A2CuB′O6 (A=Ba, Sr; B′=W, Te) ”, J. Solid State Chem. 147, 291 (1999).
[35] A. S. Gibbs, A. Yamamoto, A. N. Yaresko, K. S. Knight, H. Yasuoka, M. Majumder, M. Baenitz, P. J. Saines, J. R. Hester, D. Hashizume, A. Kondo, K. Kindo, and H. Takagi, “S = 1/2 quantum critical spin ladders produced by orbital ordering in Ba2CuTeO6”, Phys. Rev. B. 95, 2 (2017).
[36] A. Glamazda, Y. S. Choi, S. H. Do, S. Lee, P. Lemmens, A. N. Ponomaryov, S. A. Zvyagin, J. Wosnitza, D. P. Sari, I. Watanabe, and K. Y. Choi, “Quantum criticality in the coupled two-leg spin ladder Ba2CuTeO6”, Phys. Rev. B. 95, 184430 (2017).
[37] Y. C. Chung, S. K. Karna, F. C. Chou, and H. L. Liu, “Electronic structure and lattice dynamics of Ba2CuTeO6 single crystals”, RSC Adv. 10, 20067 (2020).
[38] I. P. Muthuselvam, R. Sankar, A. V. Ushakov, G. N. Rao, S. V. Streltsov, and F. C. Chou, “Two-step antiferromagnetic transition and moderate triangular frustration in Li2Co(WO4)2”, Phys. Rev. B - Condens. Matter Mater. Phys. 90, 1 (2014).
[39] I. P. Muthuselvam, R. Sankar, V. N. Singh, G. N. Rao, W. L. Lee, G. Y. Guo, and F. C. Chou, “Magnetic orderings in Li2Cu(WO4)2 with tungstate-bridged quasi-1D spin-1/2 chains”, Inorg. Chem. 54, 4303 (2015).
[40] I. Panneer Muthuselvam, R. Sankar, A. V. Ushakov, W. T. Chen, G. Narsinga Rao, S. V. Streltsov, S. K. Karna, L. Zhao, M. K. Wu, and F. C. Chou, “Successive spin orderings of tungstate-bridged Li2Ni(WO4)2 of spin 1”, J. Phys. Condens. Matter. 27, 456001 (2015).
[41] S. K. Karna, C. W. Wang, R. Sankar, M. Avdeev, A. Singh, I. Panneer Muthuselvam, V. N. Singh, G. Y. Guo, and F. C. Chou, “Antiferromagnetic spin structure and negative thermal expansion of Li2Ni(WO4)2”, Phys. Rev. B 92, 1 (2015).
[42] K. M. Ranjith, R. Nath, M. Majumder, D. Kasinathan, M. Skoulatos, L. Keller, Y. Skourski, M. Baenitz, and A. A. Tsirlin, “Commensurate and incommensurate magnetic order in spin-1 chains stacked on the triangular lattice in Li2NiW2O8”, Phys. Rev. B. 94, 1 (2016).
[43] I. Panneer Muthuselvam, R. Sankar, G. Narsinga Rao, S. K. Karna, and F. C. Chou, “Ferromagnetic nature in low-dimensional S = 1 antiferromagnetic Li2Ni(WO4)2 nanoparticles”, J. Magn. Magn. Mater. 449, 83 (2018).
[44] J. Lv, Y. Yuan, X. Huang, H. Shi, H. Tian, Z. Li, T. Yu, J. Ye, and Z. Zou, “Photophysical and photocatalytic properties of Li2M (WO4)2 (M = Co and Ni) ”, J. Mater. Res. 23, 3309 (2008).
[45] Y. C. Chung, S. K. Karna, F. C. Chou, and H. L. Liu, “Electronic structure and lattice dynamics of Li2Ni(WO4)2”, Chinese J. Phys. 60, 473 (2019).
[46] D. C. Peets, J. H. Kim, M. Reehuis, P. Dosanjh, and B. Keimer, “Floating zone growth of large single crystals of SrFeO3-δ”, J. Cryst. Growth. 361, 201 (2012).
[47] A. Maljuk, J. Strempfer, C. Ulrich, A. Lebon, and C. T. Lin, “Growth and characterization of high-quality SrFeOx single crystals”, J. Cryst. Growth. 257, 427 (2003).
[48] J. P. Hodges, S. Short, J .D. Jorgensen, X. Xiong, B. Dabrowski, S. M. Mini, and C. W. Kimball, “Evolution of oxygen-vacancy ordered crystal structures in the perovskite series Sr(n)Fe(n)O(3n-1) (n = 2, 4, 8, and ∞), and the relationship to electronic and magnetic properties”, J. Solid State Chem. 151,190 (2000).
[49] Vladimir Damljanovi, Der Fakultät Mathematik und Physik der Universität Stuttgart, “Raman scattering, magnetization and magnetotransport study of SrFeO3-, Sr3Fe2O7-” (2008).
[50] M. Reehuis, C. Ulrich, A. Maljuk, C. Niedermayer, B. Ouladdiaf, A. Hoser, T. Hofmann, and B. Keimer, “Neutron diffraction study of spin and charge ordering in SrFeO 3-δ”, Phys. Rev. B 85, 18410 (2012).
[51] S. H. Hsieh, R. S. Solanki, Y. F. Wang, Y. C. Shao, S. H. Lee, C. H. Yao, C. H. Du, H. T. Wang, J. W. Chiou, Y. Y. Chin, H. M. Tsai, J. L. Chen, C. W. Pao, C. M. Cheng, W. C. Chen, H. J. Lin, J. F. Lee, and F. C. Chou, W.F. Pong, “Anisotropy in the thermal hysteresis of resistivity and charge density wave nature of single crystal SrFeO3-δ: X-ray absorption and photoemission studies”, Sci. Rep. 7, 161 (2017).
[52] M. Ghaffari, H. Huang, O. K. Tan, and M. Shannon, “Band gap measurement of SrFeO3-δ by ultraviolet photoelectron spectroscopy and photovoltage method”, CrystEngComm. 14, 7487 (2012).
[53] A. Rothschild, W. Menesklou, H. L. Tuller, and E. Ivers-Tiffée, “Electronic structure, defect chemistry, and transport properties of SrTi1-xFexO3-y solid solutions”, Chem. Mater. (2006).
[54] D. D. Sarma, E. V. Sampathkumaran, S. Ray, R.Nagarajan, S. Majumdar, A. Kumar, G. Nalini, and T. N. Guru Row, “Magnetoresistance in ordered and disordered double perovskite oxide, Sr2FeMoO6”, Solid State Commun. 16, 3151 (2000).
[55] M. Mczka, J. Hanuza, A. F. Fuentes, and U. Amador, “Vibrational characteristics of new double tungstates Li2MII(WO4)2 (M = Co, Ni and Cu) ”, J. Raman Spectrosc. 33, 56 (2002).
[56] R. L. Moreira, R. P. S. M. Lobo, S. L. L. M. Ramos, M. T. Sebastian, F. M. Matinaga, A. Righi, and A. Dias, “Raman and infrared spectroscopic investigations of a ferroelastic phase transition in Ba2ZnTeO6 double perovskite”, Phys. Rev. Mater. 2, 054406 (2018).
[57] A. Glamazda, Y. S. Choi, S. H. Do, S. Lee, P. Lemmens, A. N. Ponomaryov, S. A. Zvyagin, J. Wosnitza, D. P. Sari, I. Watanabe, and K. Y. Choi, “Quantum criticality in the coupled two-leg spin ladder Ba2CuTeO6”, Phys. Rev. B. 95, 1 (2017).
[58] John A. Woollam, James N. Hilfiker, Corey L. Bungay, Ron A. Synowicki, Thomas E. Tiwald, and Daniel W. Thompson. “Spectroscopic ellipsometry from the vacuum ultraviolet to the far infrared”, AIP Conference Proceedings 550, 511 (2001).
[59] C. V. Raman, “A new radiation”, Indian J. Phys. 2, 387 (1928).
[60] A. Smekal, “Zur Quantentheorie der Dispersion”, Die Naturwissenschaften. 11, 873 (1923).
[61] H. Kuzmany, Solid-State Spectroscopy:An Introduction, Springer Verlag, Berlin. Heidelberg (1998).
[62] F. Wooten, Optical Properties of Solids, Academic. New York (1972).
[63] V. R. Galakhov, E. Z. Kurmaev, K. Kuepper, M. Neumann, J. A. McLeod, A. Moewes, I. A. Leonidov, and V. L. Kozhevnikov, “Valence band structure and X-ray spectra of oxygen-deficient ferrites SrFeOx”, J. Phys. Chem. C. 114, 5154 (2010).
[64] P. G. Manning, “Absorption spectra of iron(III) in octahedral sites in sphalerite”, Can Miner. 9, 57 (1967).
[65] J. I. Pankove, “Optical processes in semiconductors”, Dover. New York (1971).
[66] H. L. Liu, C. R. Huang, G. F. Luo, and W. N. Mei, Optical properties of antiferroelectric Cs2Nb4O11: Absorption spectra and first-principles calculations, J. Appl. Phys. 110, 103515 (2011).
[67] L. Wang, Z. Yang, M. E. Bowden, and Y. Du, “Brownmillerite phase formation and evolution in epitaxial strontium ferrite heterostructures”, Appl. Phys. Lett. 114, 631202 (2019).
[68] R. K. Mishra, D. K. Pradhan, R. N. P. Choudhary, and A. Banerjee, “Effect of yttrium on improvement of dielectric properties and magnetic switching behavior in BiFeO3”, J. Phys. Condens. Matter. 20, 045218 (2008).
[69] X. Ren, H. Yang, S. Gen, J. Zhou, T. Yang, X. Zhang, Z. Cheng, and S. Sun, “Controlled growth of LaFeO3 nanoparticles on reduced graphene oxide for highly efficient photocatalysis”, Nanoscale. 8, 752 (2016).
[70] S. Ghosh, N. Kamaraju, M. Seto, A. Fujimori, Y. Takeda, S. Ishiwata, S. Kawasaki, M. Azuma, M. Takano, and A. K. Sood, “Raman scattering in CaFeO3 and La0.33Sr0.67FeO3 across the charge-disproportionation phase transition”, Phys. Rev. B - Condens. Matter Mater. Phys. 71, 254110 (2005).
[71] M. I. Aroyo, J. M. Perez-Mato, D. Orobengoa, E. Tasci, G. DeLa Flor, and A. Kirov, “Crystallography online: Bilbao crystallographic server”, Bulg. Chem. Commun. 43, 183 (2011).
[72] M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G.Madariaga, A. Kirov, and H. Wondratschek “Bilbao Crystallographic Server I: Databases and crystallographic computing programs”, Z. Krist. 221, 15 (2006).
[73] M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato, and H. Wondratschek “Bilbao Crystallographic Server II: Representations of crystallographic point groups and space groups”, Acta Cryst.A62, 115 (2006).
[74] S. Ivantchev, E. Kroumova, G. Madariaga, J. M. Perez-Mato and M. I. Aroyo “SUBGROUPGRAPH - a computer program for analysis of group-subgroup relations between space groups”, J. Appl. Cryst.33, 1190-1191 (2000).
[75] S. Ivantchev, E. Kroumova, M. I. Aroyo, J. M. Perez-Mato, J. M. Igartua, G. Madariaga, and H. Wondratschek “SUPERGROUPS: a computer program for the determination of the supergroups of the space groups”, J. Appl. Cryst. 35, 511-512 (2002).
[76] E. Kroumova, J. M. Perez-Mato, and M. I. Aroyo “WYCKSPLIT: a computer program for determination of the relations of Wyckoff positions for a group-subgroup pair”, J. Appl. Cryst. 31, 646 (1998).
[77] J. Menéndez and M. Cardona, “Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and -Sn: Anharmonic effects”, Phys. Rev. B 29, 2051 (1984).
[78] G. N. Rao, R. Sankar, A. Singh, I. P. Muthuselvam, W. T. Chen, V. N. Singh, G. Y. Guo, and F. C. Chou, “Tellurium-bridged two-leg spin ladder in Ba2CuTeO6”, Phys. Rev. B. 93.1 (2016).
[79] J. Xu, J. H. Park, and H. M. Jang, “Orbital-spin-phonon coupling in Jahn-Teller-distorted LaMnO3: Softening of the 490 and 610 cm−1 Raman-active modes”, Phys. Rev. B 75, 012409 (2007).
[80] W. Baltensperger and J. S. Helman, “Influence of magnetic order in insulators on the optical phonon frequency”, Helv. Phys. Acta. 41, 668 (1968).
[81] J. Vermette, S. Jandl, and M. M. Gospodinov, “Raman study of spin–phonon coupling in ErMnO3”, J. Phys.: Condens. Matter 20, 425219 (2008).
[82] E. Granado, A. García, J. A. Sanjurjo, C. Rettori, I. Torriani, F. Prado, R. D. Sánchez, A. Caneiro, and S. B. Oseroff, “Magnetic ordering effects in the Raman spectra of La1-xMn1-xO3, Phys. Rev. B 60, 11879 (1999).
[83] S. Issing, A. Pimenov, Y. V. Ivanov, A. A. Mukhin, and J. Geurts, “Spin-phonon coupling in multiferroic manganites RMnO3: Comparison of pure (R = Eu, Gd, Tb) and substituted (R = Eu1-xYx) compounds”, Eur. Phys. J. B. 78, 367 (2010).
[84] S. Issing, A. Pimenov, V. Yu. Ivanov, A. A. Mukhin, and J. Geurts, “Composition-dependent spin-phonon coupling in mixed crystals of the multiferric manganite Eu1-xYxMnO3 (0 ≤ x ≤ 0.5) studied by Raman spectroscopy”, Phys. Rev. B 81, 024304 (2010).
[85] H. W. Chen, Y.-W. Chen, J.-L. Kuo, Y. C. Lai, F. C. Chou, C. H. Du, and H. L. Liu, “Spin-charge-lattice coupling in YBaCuFeO5: Optical properties and first-principles calculations”, Science Reports 9, 3223 (2019).
[86] D D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen”, Ann. Phys. 24, 636 (1935).
[87] H. L. Liu, M. K. Lin, Y. R. Cai, C. K. Tung, and Y. H. Chu, “Strain modulated optical properties in BiFeO3 thin films”, Appl. Phys. Lett. 103, 181907 (2013).