本論文研究摻雜不同離子Cs2Nb4O11 塊材、不同厚度BiFeO3 薄膜、及 YBaCuFeO5 單晶的光譜性質，探討晶格、電子、及磁性結構的相關性。
首先，x光繞射能譜顯示未摻雜 Cs2Nb4O11 及摻雜 5 % 與 10 %的 Ta 離子和加上摻雜不同時間 (30、60、90 分鐘) S離子比例的樣品之晶格結構並未大幅改變，但隨著摻雜不同離子比例的增加，橢圓偏振光譜展現能隙值皆有變小的趨勢，由第一原理理論計算得知當S 原子取代單位晶胞內的O原子，導電帶能量下降，但價電帶能量不變， Ta 原子取代單位晶胞內的Nb原子，導電帶能量些微下降，但價電帶能量仍維持不變，造成能隙減小，我們的實驗結果與理論計算相符。
其次，橢圓偏振光譜顯示10 nm 與 70 nm 厚的四方晶系 BiFeO3 薄膜之能隙值分別約為 2.89 eV及 2.87 eV。x光繞射能譜呈現 70 nm 厚薄膜的 a 軸晶格常數較 10 nm 厚薄膜大，意味 YSZ 基板對70 nm 厚薄膜的壓縮應變減小，導致其能隙值較10 nm 厚薄膜為低。此外， 10 nm 厚 BiFeO3 薄膜的能隙在溫度約 670 K 附近，偏離波色-愛因斯坦模型理論預測值，此現象在 70 nm 厚 BiFeO3 薄膜並不明顯，推測與其複雜的自旋電荷間耦合交互作用有關。
最後，在外加磁場沿 YBaCuFeO5單晶 ab 平面的磁化率顯示 175 K 與455 K 的磁性相轉變。90 K 與 300 K 的 x 光繞射能譜顯示無繞射峰生成或消失，表示磁性相轉變溫度下，YBaCuFeO5 無結構相轉變。變溫拉曼散射光譜展現 576 cm-1 Eg 對稱性拉曼峰於第二尼爾溫度 175 K 附近有異常藍移現象，此與自旋聲子之交互作用有關，我們計算出自旋聲子耦合係數約為15.7 mRy/Å2 。分析橢圓偏振光譜得到YBaCuFeO5單晶的能隙約為 1.41 eV ，隨著溫度上升，能隙值在第一尼爾溫度 455 K附近偏離波色-愛因斯坦模型理論預測值，推測與其複雜的自旋電荷間耦合交互作用有關。

In this thesis, we study the optical properties of Cs2Nb4O11 bulk with doping different dopants, BiFeO3 thin films with different thickness, and YBaCuFeO5 single crystal. Our goal is to investigate the correlation among lattice dynamics, electronic and magnetic structures.
First, the x-ray powder diffraction spectra didn’t show significant changes with doping Ta and S ions. That indicates crystal structure of Cs2Nb4O11 remains robust after doping with doping Ta and S ions. With an increase of doping Ta and S elements, the analysis from spectroscopic ellipsometry indicate the band gap of Cs2Nb4O11 decreases. The first-principles calculations predicted, when the Ta atom substitutes the Nb atom or the S atom substitutes the O atom, the energy of conduction band decreases and the energy of valence band remains the same. Our experimental results are in good agreement with the predictions of first-principles calculations.
Second, the spectroscopic ellipsometry spectra of tetragonal phase of 10-nm- and 70-nm-thick BiFeO3 thin films show that their direct band gaps are approximately 2.89 eV and 2.87 eV. Furthermore, x-ray powder diffraction data show that the a-axis lattice constant of 70-nm-thick BiFeO3 thin film is bigger than that of 10-nm-thick BiFeO3 thin film. This indicates the release of compressive strain from YSZ substrate for a 70-nm-thick BiFeO3 thin film. With an increase of temperature, an anomaly in the band gap of the 10-nm-thick thin film is observed at approximately 670 K. This anomaly is weakening in the 70-nm-thick thin film. These results suggest a complex nature of charge-spin coupling in tetragonal phase BiFeO3 thin films.
Finally, YBaCuFeO5 single crystal shows two antiferromagnetic phase transition temperatures at approximately 455 K and 175 K. The x-ray powder diffraction spectra didn’t show significant changes at 90 K and 300 K. That indicates crystal structure of YBaCuFeO5 remains robust at the magnetic phase transition temperatures. The temperature dependent Raman scattering spectra exhibit the 576 cm-1 Eg symmetry phonon mode shows anomaly at the second Neel temperature of 175 K, indicating strong spin-phonon coupling. Based on analyzing the anomalies of the Eg mode at 175 K, the value of spin-phonon coupling constant is estimated to be 15.7 mRy/Å2. Additionally, the room temeperature band gap of YBaCuFeO5 is approximately 1.9 eV. With increasing temperature the band gap behaves anomalously at 455 K. These results suggest a complex nature of the lattice-spin-charge coupling in YBaCuFeO5.

[1] John David Jackson: Classical Electrodynamics (1st edition , 1998).
[2] H. Schmid, “Multi-ferroic magnetroelectrics”, Ferroelectrics 162, 317 (1994).
[3] N. A. Hill, “Why are there so few magnetic ferroelectrics?”, J. Phys. Chem. B 104, 6694 (2000).
[4] W. Eerenstein, N. D. Mathur, and J. F. Scott, “Multiferroic and magnetoelectric materials”, Nature (London) 442, 759 (2006).
[5] R. W. Smith, G. F. Luo, and W. N. Mei, “High-temperature crystal structure and electronic properties of cesium niobate Cs2Nb4O11”, Journal of Physics and Chemistry of Solids 71, 1357 (2010).
[6] Y. Miseki, H. Kato, and A. Kudo, “Water splitting into H2 and O2 over Cs2Nb4O11 photocatalyst”, Chem. Lett. 34, 54 (2005).
[7] J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare, N. A. Spaldin, K. M. Rabe, M. Wuttig, and R. Ramesh, “Epitaxial BiFeO3 multiferroic thin film heterostructures”, Science 299, 1719 (2003).
[8] Yen-Chung Lai , Guo-Jiun Shu , Wei-Tin Chen , Chao-Hung Du , and Fang-Cheng Chou, “Self-adjusted flux for the traveling solvent floating zone growth of YBaCuFeO5 crystal”, Journal of Crystal Growth. 413, 100 (2015).
[9] B. Kundys, A. Maignan, and Ch. Simon, “Multiferroicity with high-TC in ceramics of the YBaCuFeO5 ordered perovskite”, Appl. Phys. Lett 94, 072506 (2009).
[10] 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).
[11] 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).
[12] Hiromi Shima, Ken Nishida, Takashi Yamamoto, Toshiyasu Tadokoro, Koichi Tsutsumi, Michio Suzuki, and Hiroshi Naganuma, “Large refractive index in BiFeO3-BiCoO3 epitaxial films”, J. Appl. Phys. 113, 17A914 (2013).
[13] T. D. Kang, B. C. Jeon, and S. J. Moon, “Temperature dependence of the electronic transitions in BiFeO3 thin film studied by spectroscopic ellipsometry” , J. Appl. Phys. 117, 134107 (2015).
[14] Cameliu Himcinschi, Akash Bhatnagar, Andreas Talkenberger, Mykhailo Barchuk, Dietrich R. T. Zahn, David Rafaja, Jens Kortus, and Marin Alexe, “Optical properties of epitaxial BiFeO3 thin films grown on LaAlO3”, Appl. Phys. Lett 106, 012908 (2015).
[15] Daniel Schmidt, Lu You, Xiao Chi, Junling Wang, and Andrivo Rusydi, “Anisotropic optical properties of rhombohedral and tetragonal thin film BiFeO3 phases”, Phys. Rev. B 92, 075310 (2015).
[16] Mariona Coll, Jaume Gazquez, Ignasi Fina, Zakariya Khayat, Andy Quindeau, Marin Alexe, Maria Varela, Susan Trolier-McKinstry, Xavier Obradors, and Teresa Puig, “Nanocrystalline ferroelectric BiFeO3 thin films by low-temperature atomic layer deposition” Chem. Mater. 27 , 6322 (2015).
[17] Heng-Jui Liu, Yu-Hao Du, Peng Gao, Yen-Chin Huang, Hsiao-Wen Chen, Yi-Chun Chen, Hsiang-Lin Liu, Qing He, Yuichi Ikuhara, and Ying-Hao Chu, “Tetragonal BiFeO3 on yttria-stabilized zirconia” APL Mater. 3, 116104 (2015).
[18] L. Er-Rakho and C. Michel, “YBaCuFeO5+δ : A novel oxygen -deficient perovskite with a layer tructure” ,Journal of Solid State Chemsitry 73, 531 (1988)
[19] Y. K. Atanassova, V. N. Popov, G. G. Bogachev, and M. N. Iliev ”Raman- and infrared-active phonons in YBaCuFeO5: Experiment and lattice dynamics”, Phys. Rev. B 47, 15201 (1993).
[20] V. Caignaert, I. Mirebeau, F. Bouree, N. Nguyen, A. Ducouret, J-M. Greneche, and B.raveau “YBaCuFeO5+δ : Crystal and Magnetic Structure of YBaCuFeO5” ,Journal of Solid State Chemsitry 114, 24 (1995).
[21] M. Morin, A. Scaramucci, M. Bartkowiak, E. Pomjakushina, G. Deng, D. Sheptyakov, L. Keller, J. Rodriguez-Carvajal, N. A. Spaldin, M. Kenzelmann, K. Conder, and M. Medarde, “Incommensurate magnetic structure, Fe/Cu chemical disorder, and magnetic interactions in the high-temperature multiferroic YBaCuFeO5 ” Phys. Rev. B 91, 064408 (2015).
[22] 林宜霖，國立臺灣師範大學物理研究所碩士論文，101 年6月。
[23] 黃峻儒，國立臺灣師範大學物理研究所碩士論文，99年6月。
[24] R. W. Smith, C. H. Hu, J. J. Liu, W. N. Mei, and K. J. Lin, “Structure and antiferroelectric properties of cesium niobate, Cs2Nb4O11”, Journal of Solid State Chemistry 180, 1193 (2007).
[25] Yen-Chung Lai, Chao-Hung Du, Chun-Hao Lai, Yu-Hui Liang, Chin-Wei Wang, Kirrily C Rule, Hung-Cheng Wu, Hung-Duen Yang, Wei-Tin Chen, G J Shu, and Fang-Cheng Chou, “Magnetic ordering and dielectric relaxation in the double perovskite YBaCuFeO5”, Journal of Physics: Condensed Matter. 29, 145801 (2017).
[26] Jacques I. Pankove: Optical Processes in Semiconductors, Page 36 ~ 40 (1st edition , 1975).
[27] Robert W. Smith, Jianjun Liu, Charles A. May, Camille Nelson, Lu Wang, Wai-Ning Mei, Hsin-Yi Hsu, Hsiao-Wen Chen, Hsiang-Lin Liu, “Cesium Niobate Solid Solutions: Synthesis and Band Structure Modifications for Photocatalytic Application “ (unpublished).
[28] S. Heiroth, R. Ghisleni, T. Lippert, J. Michler, and A. Wokaun, “Optical and mechanical properties of amorphous and crystalline yttria-stabilized zirconia thin films prepared by pulsed laser deposition”, J. Acta. Materialia . 59, 2330 (2011).
[29] V. Železný, D. Chvostová, L. Pajasová, I. Vrejoiu, and M. Alexe, “Optical properties of epitaxial BiFeO3 thin films”, Appl. Phys. A 100, 1217 (2010).
[30] M. K. Singh, W. Prellier, M. P. Singh, R. S. Katiyar, and J. F. Scott, “Spin-glass transition in single-crystal BiFeO3”, Phys. Rev. B 77, 144403 (2008).
[31] R. C. Cai¸ A. Delmont, A. Sprow, B. Cai, and M. L. Nakarmi, “Spin-charge-orbital coupling in multiferroic LuFe2O4 thin films”, Appl. Phys. Lett. 100, 212904 (2012).
[32] Hans Kuzmany: Solid-state spectroscopy (1st edition , 1998).
[33] U. Fano, “Effect of configuration interaction on intensities and phase shifts”, Phys. Rev. 124, 1866 (1961).
[34] M. K. Singh and R. S. Katiyar, “Phonon anomalies near the magnetic phase transitions in BiFeO3 thin films with rhombohedral R3c symmetry”, J. Appl. Phys. 109, 07D916 (2011).
[35] W. Baltensperger and J. S. Helman, “Influence of magnetic order in insulators on the optical phonon frequency”, Helv. Phys. Acta. 41, 668 (1968).
[36] S. Issing, A. Pimenov, V. Yu. Ivanov, A. A. Mukhin, and J. Geurts, “Composition-dependent spin-phonon coupling in mixed crystals of the multiferroic maganite Eu1-xYxMnO3 (0 < x < 0.5) studied by Raman spectroscopy”, Phys. Rev. B 81, 024304 (2010).
[37] V. V. Eremenko, V. N. Samovarov, V. L. Vakula, M. Yu. Libin, and S. A. Uyutnov, “Optical evidence for compatibility of antiferromagnetism and superconductivity in YBa2Cu3O6+x”, Low Temperature Physics 26, 809 (2000).
[38] R. Vidya, P. Ravindran, A. Kjekshus, and H. Fjellvag, “Spin, charge, and orbital ordering in the ferromagnetic insulator YBaMn2O5” , Phys. Rev. B 65, 144422 (2002).