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

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(1)Department of Physics College of Science. National Taiwan Normal University Doctoral Dissertation. 以光譜實驗技術探究鈣鈦礦氧化物 SrFeO3-, 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-, Ba2CuTeO6, and Li2Ni(WO4)2. Yun-Chen Chung. Advisor: Prof. Hsiang-Lin Liu. August 2020.

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(3) Acknowledgements 博士論文能夠順利完成，真的是人生中最神奇的一件事情!完全沒想過自己寫得出英文的論文!一切都要多虧我有一位非常非常厲害的指導教授~劉祥麟老師。遙想八年前念博班的時候，其實就是瞬間的一個念頭，當時就想著大概英文這關就過不了了，不過再多念個幾年書也不錯!讀書是完全掌握在自己手上，要把握!於是繼續跟著十年前第一眼就確認的超級有耐心的超棒指導教授劉祥麟老師，學到了許多不一樣的做事方法，也看到老師非常厲害的開拓不一樣的學習環境讓我們學習，讓我從逃避英文，到現在能用英文去勇敢嘗試寫作與聊天，這樣的成長是我從未想過的! 在人生中遇到這麼棒的指導老師，真的非常幸運!另外，也要感謝臺大凝態中心周方正教授與淡江大學杜昭宏教授提供優質樣品，讓我進行研究。此外，也感謝實驗室的好夥伴們,在我的實驗撞牆期，給予我許多關鍵法子，讓我能一路的從摔倒中再次站起來!特別是橢偏專家孝文、還有提供非常非常厲害的論文文獻編輯軟體的 Rea 以及帥氣 Desman，讓我能夠在撰寫英文論文遇到問題的時候，有很厲害的夥伴可以詢問!還要感謝常常幫我下載論文的孟哲以及解答問題的松勳學長，雖然畢業卻還是很熱心的指點我所遇到的問題!. I.

(4) 還有我的摯友~秋蓉，非常感謝在我人生遇到問題，或是想要抱怨吐苦水的時候，都一直那，也在我的論文撞牆時期，或摸魚時期，給予鼓勵或是督促!非常期待之後有很多時間可以一起減重!回到正常體重!也要感謝工作上的好夥伴，真的是亦師亦友~世芳，在我的人生重要時期都會給予非常中肯的建議! 最重要的是感謝我在天上的老爸~鍾阿龍，我的爸爸雖然只有國小畢業，但他在待人處事各方面都是謙恭溫和，敦厚老實，對長輩真心孝順，做事也非常有毅力!他對我的決定全力支持!在台北、桃園兩邊跑的生活中，一通電話，他就會風雨無阻的接送我，從來沒有抱怨的話!人生一個小缺憾，莫過於當我博士畢業的時候，無法與之分享此喜悅與榮耀! 還有要感謝一個可愛的姪子~恩恩，從他還小的時候就聽到我說要寫論文，等到他會講話以後，就開始督促叫我”快去寫論文”! 最後要感謝辛苦的老媽~邱秀蘭，在我讀書的這段時間，陪伴著我台北、桃園兩邊跑，一邊還要帶著可愛的小姪子~恩恩，這幾年，辛苦的媽媽承受了許多人生巨變與壓力，但是在這樣的巨變與壓力下，最重要的是仍然保持善良的本性，陪著我完成博士班的學業!博班畢業這份榮耀!能夠與親愛的媽媽一同分享，真的非常高興!感謝爸媽從小的正向教導，讓我能夠有的堅忍的毅力，完成學業!也讓我在遇到問題能夠正向迅速的解決問題! II.

(5) Abstract We present the optical studies of electronic structure and lattice dynamics in SrFeO3Ba2CuTeO6,. and Li2Ni(WO4)2. SrFeO3-single crystals were grown using the floating. zone method;Ba2CuTeO6single 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-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 Ba 2CuTeO6 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- 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/Å 2). The stretching vibrations of WO6 octahedra located at 914 cm−1 in Li2Ni(WO4)2 exhibited the spin-phonon coupling constant (0.94 mRy/Å 2). 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- and III III.

(6) 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.. Keywords: Perovskite oxides, optical spectroscopy, spin-phonon coupling. IV.

(7) Contents Acknowledgements ..................................................................................... I Abstract .................................................................................................... III Contents...................................................................................................... V List of Figures ......................................................................................... VII List of Tables ........................................................................................... XV Chapter 1 Introduction ............................................................................... 1 Chapter 2 Overview of SrFeO3−, Ba2CuTeO6, and Li2Ni(WO4)2 ........... 12 2.1 SrFeO3− ............................................................................................................... 12 2.2 Ba2CuTeO6 ........................................................................................................... 16 2.3 Li2Ni(WO4)2 ......................................................................................................... 18. Chapter 3 Theory background and experimental techniques ................ 45 3.1 Spectroscopic ellipsometry .................................................................................. 45 3.2 Raman scattering measurement ........................................................................... 49. Chapter 4 Results and discussion ............................................................. 55 4.1 Optical properties of SrFeO3- single crystals ...................................................... 55 4.2 Optical studies of Ba2CuTeO6 single crystals ...................................................... 63 4.3 Electronic structure and lattice dynamics of Li2Ni(WO4)2 .................................. 67. Chapter 5 Summary ............................................................................... 110 References ............................................................................................... 112. V.

(8) VI.

(9) List of Figures Fig. 1-1: The crystal structure of ABO3 form [3]. ................................................................ 4 Fig. 1-2: The crystal structure of A2BBʹO6 form [7]. ........................................................... 5 Fig. 1-3: Crystal structure of SrFeO3 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28]. ......................................................... 6 Fig. 1-4: Crystal structure of Sr8Fe8O23 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28]............................................. 7 Fig. 1-5: Crystal structure of Sr4Fe4O11 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28]............................................. 8 Fig. 1-6: Crystal structure of Sr2Fe2O5 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28]............................................. 9 Fig. 1-7: Crystal structure of Ba2CuTeO6 at low temperatures. A schematic depicting its electric, structural, and magnetic properties (AFM: antiferromagnetic and PM: paramagnetic) [37]. ........................................................................................ 10 Fig. 1-8: Crystal structure of Li2Ni(WO4)2 at low temperatures. A schematic depicting its electric, structural, and magnetic properties (AFM: antiferromagnetic and PM: paramagnetic) [45]. ........................................................................................ 11 Fig. 2-1: Pseudobinary phase diagram showing the variation of composition with temperature at 1- and 350-atm oxygen pressure. The approximate lower oxygen limit of the perovskite phase is indicated with the dashed line [24]. 21 Fig. 2-2: Room-temperature Mössbauer spectra of ground SrFeO3−δ crystals. Subspectra: blue—Fe4+ (single line), red—Fe3.5+ (doublet with smaller splitting), and green—Fe3+ (doublet with larger splitting) [21]. ........................................... 22 Fig. 2-3: Temperature dependence of the lattice parameters of Sr8Fe8O23 [50]. ................ 23 Fig. 2-4: Linear scans along the longitudinal direction through the Bragg reflection (004) for the cooling and heating processes of Sr 8Fe8O23. (a) The evolution of the lattice parameter of the c-axis (unit, Å ) as a function of temperature. (b) The temperature dependence of the peak width (full width at half maximum, FWHM). Both graphs display the hysteresis behavior around the transition temperature of magnetic ordering [22]. ......................................................... 23 VII.

(10) Fig. 2-5: Neutron diffraction data from the single crystals of SrFeO 3.00 and SrFeO2.87 measured at various temperatures. The scans were performed along the [1,1,1] direction around the structural Bragg reflection (0, 0, 1) cub [50]. ............... 24 Fig. 2-6: Temperature dependence of the intensity, incommensurability, and magnetic correlation length of the helical magnetic Bragg reflections of the magnetic phase I in the single-crystal SrFeO3.00 (left) and the magnetic phases I and II in SrFeO2.87 (right) [50]. ................................................................................ 24 Fig. 2-7: Magnetic susceptibility of the single crystals of SrFeO3.00, SrFeO2.95, SrFeO2.85, SrFeO2.81, and SrFeO2.77 measured in field cooling and subsequent field heating runs at B = 1 T. Curves for the latter four samples were shifted by amounts indicated in the legend [21]. ............................................................ 25 Fig. 2-8: Magnetic ordering of iron moments in the system of SrFeO3−δ [50]. ................. 26 Fig. 2-9: (a) SrFeO3.00, (b) SrFeO2.95, (c) SrFeO2.85, (d) SrFeO2.81, and (e) SrFeO2.77 display the resistivity in zero-field cooling and heating runs (black) compared with field cooling and heating runs with a 9-T field (red) [21]. ............................ 27 Fig. 2-10: Temperature dependence of the resistivity of a single crystal of SrFeO 2.81, measured in the ab plane and along the c-axis. The top inset presents the temperature dependence of magnetic susceptibility (χ) measured along the caxis in ZFC and FC runs in a magnetic field of 1 T, and the bottom inset presents room-temperature X-ray diffraction profile showing (004) Bragg peak obtained in θ-scan [51]................................................................................... 28 Fig. 2-11: Susceptibility, resistivity, and magnetoresistance (MR) measurements of SrFeO2.875. (a) Susceptibility curves (MT), field cool (FC), and zero FC (ZFC) at an applied field of 1 T show a transition at T ≃120 K and a sharp antiferromagnetic transition at approximately 70 K. Resistivity curves (RT) for both cooling and heating measurements show two transitions at T ≃120 K and 50 K as indicated by green arrows, respectively. (b) MR data, both for the applied field perpendicular and parallel to c-axis, display a negative MR of approximately 45% at T ≃55 K. The inset shows that the transition temperature is reduced by the applied field [22]. .......................................... 28 Fig. 2-12: The temperature-dependent Fe K-edge XANES spectra of single-crystal SrFeO2.81 measured at two different angles of incidence θ = 0° (with electric field E parallel to the ab plane) and 70° (with electric field E nearly parallel to the c-axis) on heating and cooling processes. Corresponding spectra were obtained for FeO, Fe3O4, and Fe2O3 powder samples at room temperature, with VIII.

(11) angle θ = 0° for reference [51]. ...................................................................... 29 Fig. 2-13: Temperature dependence of normalized Fe L3,2-edge XANES spectra of singlecrystal SrFeO2.81 at two angles of incidence θ = 0° and 70° during (a) heating and (b) cooling. The bottom panels show the corresponding XLD spectra [51]. ........................................................................................................................ 30 Fig. 2-14: (a) Conduction band and valence band positions for P25 and SrFeO (32d) [52]. (b) Band gap energy and redox enthalpy as a function of Fe content (x) in SrTi1−xFexO3−y solid solutions [53]. ............................................................... 30 Fig. 2-15: (a) Far-infrared ellipsometric and (b) Raman scattering spectra of SrFeO3.00 at 15, 160, and 300 K [21]. ................................................................................ 31 Fig. 2-16: Raman scattering and far-infrared ellipsometric spectra were compared for the charge-order composition of SrFeO2.85 at low temperature and room temperature. (a) Raman scattering spectra in parallel (ZZ) and cross (XZ) polarization and (b) far-infrared ellipsometric spectra: optical conductivity  and real part of the dielectric permittivity 1 [21]. ......................................... 32 Fig. 2-17: Temperature dependence of the Raman scattering spectra: (a) polarized Raman scattering spectra of SrFeO2.85 in ZZ direction and (b) unpolarized Raman scattering spectra of SrFeO2.69 [21]................................................................ 33 Fig. 2-18: (a) Room-temperature synchrotron X-ray powder diffraction pattern of Ba2CuTeO6. (b) A single-crystal diffraction pattern obtained using an X-ray (Cu-Kα) beam perpendicular to the ab plane. The inset is the optical image of grown single crystal [29]. .............................................................................. 34 Fig. 2-19: (a) The temperature dependence of magnetic susceptibility measured in an applied magnetic field of 10 kOe for H║ab and H⊥ab of single-crystal Ba2CuTeO6. (b) The dχ/dT vs T curves measured with a field of 10 kOe reveal an anisotropic cusp of TN ≃15 K [29]. .......................................................... 35 Fig. 2-20: The χ(T) for Ba2CuTeO6 single-crystal arrays with the magnetic field of μ0H = 1 T applied parallel (upper panel) and perpendicular (lower panel) to the ab plane. The dashed and solid lines indicate chain and ladder model fits, respectively. The inset in the upper panel displays the low temperature region for both orientations along with the high-field behavior for H⊥ab. The inset in the lower panel displays M(H) of Ba2CuTeO6 for H⊥ab [35]. ........................................ 36 Fig. 2-21: Temperature dependence of the magnetic susceptibility χ(T) for Ba 2CuTeO6 measured in an external field of µ 0H = 1 T applied parallel and perpendicular IX.

(12) to the ab plane. The red solid lines are fits using a two-leg ladder model. The inset shows the inverse susceptibility with a fitting to a Curie-Weiss law[57]. ........................................................................................................................ 36 Fig. 2-22: (a) Low-energy range of Raman spectra taken at T = 9 K in four different polarizations (aa, ab, bb, and cc). The gray shading denotes a two-magnon continuum. (b) Magnetic excitations in (bb) polarization for different temperatures. The spectra are vertically shifted by a constant amount [36]. . 37 Fig. 2-23: Raman spectra measured in (cc) and (bb) polarizations for different temperatures. The shadings emphasize scattering due to two-magnon excitations [36]. ..... 38 Fig. 2-24: Band structure (top panel) and density of states (bottom panel) of configuration AF1 in Ba2CuTeO6. The top of the valence band has been set to zero [29]. .. 39 Fig. 2-25: Rietveld refinement of powder synchrotron X-ray diffraction pattern for Li2Ni(WO4)2 at room temperature [39].......................................................... 40 Fig. 2-26: Partial Ni-3d and O-2p densities of states in Li2Ni(WO4)2 at 2 K. The Fermi energy is set to zero [39]. ............................................................................... 41 Fig. 2-27: UV-Vis diffuse reflectance spectra of (a) Li2Co(WO4)2, (b) Li2Ni(WO4)2, and (c) WO3, and the inset shows the optical absorption coefficient between 1.5 to 3.75 eV [43]. .................................................................................................. 41 Fig. 2-28: The temperature dependence of the dielectric constant (εr) under an applied frequency 100 kHz in Li2Ni(WO4)2. (a) The inset shows the first order derivative of the εr as a function of temperature. (b) The inset shows the temperature dependence of pyroelectric current [39]. ................................... 42 Fig. 2-29: Temperature dependence of the magnetic susceptibility of Li 2Co(WO4)2 measured in a 1-T magnetic field. The left axis of the inset highlights the lowtemperature regime, and the right axis highlights the derivative d(χT)/dT . The peaks of d(χT)d/dT reveal a minor reduction of (χ)T near T N1 ≃9 K and TN2 ≃7 K [37]. ............................................................................................................ 42 Fig. 2-30: (a) Magnetic susceptibility (black circles) as a function of temperature for Li2Ni(WO4)2 in a 1-T magnetic field. (b) The peaks of d(χT)d/dT reveal the minor reduction of (χ)T near TN1≃18 K and TN2 ≃13 K [39]. ...................... 43 Fig. 2-31: Raman scattering spectra of (a) Li2Co(WO4)2, (b) Li2Ni(WO4)2, and (c) Li2Cu(WO4)2 [55]. ......................................................................................... 44 Fig. 3-1: Spectroscopic ellipsometer with the focusing optics. ......................................... 52 X.

(13) Fig. 3-2: Schematic of Rayleigh, anti-Stokes, and Stokes scattering. ............................... 52 Fig. 3-3: Sketch map of the setup of the micro-Raman scattering spectroscopy. .............. 53 Fig. 3-4: The cross-sectional mechanical setup. ................................................................ 53 Fig. 3-5: Temperature-dependent Raman scattering experimental setup. .......................... 54 Fig. 4-1: Ellipsometric parameters  and  of (a) SrFeO2.86 and (b) SrFeO2.75 single crystals. ........................................................................................................................ 72 Fig. 4-2: Room-temperature refractive index n and extinction coefficient k of (a) SrFeO 2.86 and (b) SrFeO2.75 single crystals. ................................................................... 73 Fig. 4-3: Room-temperature optical absorption coefficient of (a) SrFeO2.86 and (b) SrFeO2.75 single crystals. The dashed lines represent the best fit obtained using the Lorentzian fit. ........................................................................................... 74 Fig. 4-4: (a). The direct band gap analysis of SrFeO2.86 (blue line) and SrFeO2.75 (red line) single crystals. (b). The indirect band gap analysis of SrFeO2.86. (c). The indirect band gap analysis of SrFeO2.75. ........................................................ 76 Fig. 4-5: Raman scattering spectra of SrFeO2.86 (blue line) and SrFeO2.75 (red line) single crystals measured at room temperature. The inset represents the range 0–1600 cm−1. ............................................................................................................... 77 Fig. 4-6: Polarized Raman scattering spectra of SrFeO2.86 single crystals in the frequency range of (a) 50–350 cm−1 and (b) 350–1500 cm−1. The notations used for the crystallographic directions are also presented. .............................................. 78 Fig. 4-7: The cross sectional polarized Raman scattering spectra of SrFeO2.86 single crystals. ........................................................................................................................ 79 Fig. 4-8: Polarized Raman scattering spectra and the optical image of SrFeO 2.75 single crystal. The notations used for the crystallographic directions are also presented. ....................................................................................................... 80 Fig. 4-9: Temperature dependence of the Raman scattering spectra of SrFeO2.86 single crystals. .......................................................................................................... 81 Fig. 4-10: Temperature dependence of the Raman scattering spectra of SrFeO 2.86 single crystals in the frequency range of 300~370 cm-1. . ........................................ 82 Fig. 4-11: Temperature dependence of frequency, linewidth, and normalized intensity of (a) 320, (b) 332, (c) 428, and (d) 626 cm−1 phonon modes of SrFeO2.86. The thin XI.

(14) solid lines denote the fitting result obtained using the anharmonic model. ... 84 Fig. 4-12: Temperature dependence of the Raman scattering spectra of SrFeO 2.75 single crystals. .......................................................................................................... 85 Fig. 4-13: Temperature dependence of frequency, linewidth, and normalized intensity of (a) 319, (b) 333, and (c) 429 cm−1 phonon modes of SrFeO2.75 single crystals. The thin solid lines denote the magnetic phase transition temperatures. .............. 87 Fig. 4-14: Ellipsometric parameters  and  of Ba2CuTeO6 single crystals. ................... 88 Fig. 4-15: Dielectric function of Ba2CuTeO6 estimated at room temperature. .................. 88 Fig. 4-16: The optical absorption coefficient of Ba2CuTeO6 estimated at room temperature. The dashed lines show the optimal fit from the Lorentzian model. The inset illustrates the optical absorption coefficient in the low-energy region (0.0 ~ 4.0 eV) of Ba2CuTeO6. ........................................................................................ 89 Fig. 4-17: The direct band gap analysis of Ba2CuTeO6. .................................................... 89 Fig. 4-18: The indirect band gap analysis of Ba2CuTeO6. ................................................. 90 Fig. 4-19: Unpolarized Raman scattering spectrum of Ba2CuTeO6 measured at room temperature. The dashed line shows the fitting results of the spectrum obtained using the Lorentzian model. ........................................................................... 91 Fig. 4-20: The polarized Raman scattering spectra and the optical image of Ba2CuTeO6 single crystal. The notations used for the crystallographic directions are also given. .............................................................................................................. 91 Fig. 4-21: Temperature dependence of Raman scattering spectra of Ba 2CuTeO6. ............ 92 Fig. 4-22: Temperature dependence of Raman scattering spectra of Ba2CuTeO6 between 75 to 150 cm-1. .................................................................................................... 92 Fig. 4-23: Temperature dependence of frequency, linewidth, and normalized intensity of (a) 85, (b) 97, (c) 104, and (d) 119 cm−1 phonon modes. The vertical dashed lines indicate the magnetic phase transition temperatures at 15 K and 75 K and structure phase transition at 287 K. The thin solid line denotes the result of the fitting obtained using the anharmonic model................................................. 93 Fig. 4-24: Temperature dependence of frequency, linewidth, and normalized intensity of (a) 160, (b) 194, (c) 380, and (d) 396 cm−1 phonon modes. The vertical dashed lines indicate the magnetic phase transition temperatures at 15 K and 75 K and structure phase transition at 287 K. The thin solid line denotes the result of the XII.

(15) fitting obtained using the anharmonic model. ................................................ 94 Fig. 4-25: Temperature dependence of frequency, linewidth, and normalized intensity of (a) 404, (b) 409, (c) 492, and (d) 568 cm−1 phonon modes. The vertical dashed lines indicate the magnetic phase transition temperatures at 15 K and 75 K and structure phase transition at 287 K. The thin solid line denotes the result of the fitting obtained using the anharmonic model. ................................................ 95 Fig. 4-26: Temperature dependence of frequency, linewidth, and normalized intensity of (a) 574, (b) 606, (c) 678, and (d) 751 cm−1 phonon modes. The vertical dashed lines indicate the magnetic phase transition temperatures at 15 K and 75 K and structure phase transition at 287 K. The thin solid line denotes the result of the fitting obtained using the anharmonic model. ................................................ 96 Fig. 4-27: Temperature dependence of phonon frequency near 119, 124, and 128 cm -1. . 97 Fig. 4-28: Temperature dependence of frequency, linewidth, and normalized intensity of 152 and 606 cm−1 phonon modes. The vertical dashed lines indicate the magnetic phase transition temperatures at 15 K and 75 K and structure phase transition at 287 K. The thin solid line denotes the result of the fitting obtained using the anharmonic model. ......................................................................... 98 Fig. 4-29: Ellipsometric parameters  and  of Li2Ni(WO4)2. ......................................... 99 Fig. 4-30: Room-temperature dielectric function of Li2Ni(WO4)2. ................................... 99 Fig. 4-31: Optical absorption coefficient of Li2Ni(WO4)2 at 300 K. The black dashed lines are two fitted Lorentz oscillators. ................................................................ 100 Fig. 4-32: (a) The direct band gap analysis of Li2Ni(WO4)2. (b) The indirect band gap analysis of Li2Ni(WO4)2. ............................................................................. 101 Fig. 4-33: Room-temperature Raman scattering spectrum of Li2Ni(WO4)2. The inset shows the peak fit of fifteenth, sixteenth and seventeenth peak using the Lorentz model............................................................................................................ 102 Fig. 4-34: Temperature dependence of Raman scattering spectra of Li2Ni(WO4)2.The inset shows the strongest Raman phonon mode of Li2Ni(WO4)2. ........................ 103 Fig. 4-35: Temperature dependence of frequency, linewidth, and normalized intensity of 112 cm−1 phonon mode. The vertical dashed lines denote the magnetic phase transition temperatures. ................................................................................ 104 Fig. 4-36: Temperature dependence of frequency, linewidth, and normalized intensity of XIII.

(16) 143 cm−1 phonon mode. The vertical dashed lines denote the magnetic phase transition temperatures. ................................................................................ 105 Fig. 4-37: Temperature dependence of frequency, linewidth, and normalized intensity of 193 cm−1 phonon mode. The vertical dashed lines denote the magnetic phase transition temperatures. ................................................................................ 106 Fig. 4-38: Temperature dependence of frequency, linewidth, and normalized intensity of 754 cm−1 phonon mode. The vertical dashed lines denote the magnetic phase transition temperatures. The thin solid line indicates the result of the fitting obtained using the anharmonic model. ........................................................ 107 Fig. 4-39: Temperature dependence of frequency, linewidth, and normalized intensity of 792 cm−1 phonon mode. The vertical dashed lines denote the magnetic phase transition temperatures. The thin solid line indicates the result of the fitting obtained using the anharmonic model. ........................................................ 108 Fig. 4-40: Temperature dependence of frequency, linewidth, and normalized intensity of 914 cm−1 phonon mode. The vertical dashed lines denote the magnetic phase transition temperatures. The thin solid line indicates the result of the fitting obtained using the anharmonic model. ........................................................ 109. XIV.

(17) List of Tables Table 2-1: Structural parameters for Sr8Fe8O23 refined in space group I4/mmm [48]. ...... 13 Table 2-2: Structural parameters for Sr4Fe4O11 refined in the space group Cmmm [48]. .. 14 Table 2-3: Phonon frequencies in SrFeO2.85 at low temperatures with different polarizations [21]. ................................................................................................................ 16 Table 2-4: The lattice parameters of Ba2CuTeO6 [29]. ...................................................... 17 Table 2-5: Structural parameters of Li2Ni(WO4)2 obtained by refinement of synchrotron Xray diffraction data (λ = 0.619 Å) for T = 300 K (room temperature, RT) and high-resolution neutron powder diffraction data (λ = 1.6215 Å) for T = 2 K ̅ [39]. ....................... 18 (low temperature, LT) phases. The space group is 𝑃1 Table 2-6: Infrared and Raman phonon modes for Li2Ni(WO4)2, Li2Co(WO4)2, and Li2Cu(WO4)2 with assignment based on comparison with data reported for ZnWO4 [56]. ................................................................................................... 20 Table 4-1: Symmetry of Raman-active phonon modes observed in different scattering configurations for SrFeO2.86 single crystals. .................................................. 59 Table 4-2: Symmetry of Raman-active phonon modes observed in different scattering configurations for SrFeO2.75 single crystal. ................................................... 60 Table 4-3: The anharmonic parameters of SrFeO2.86 phonon modes. ................................ 61 Table 4-4: The anharmonic parameters of SrFeO2.75 phonon modes. ................................ 62 Table 4-5: The spin-phonon coupling constant for 14 phonon modes in Ba2CuTeO6. ...... 67. XV.

(18) XVI.

(19) Chapter 1 Introduction Perovskite oxide compounds have attracted enormous interest because of their outstanding optoelectronic [1,2], photocatalytic [3], ferroelectric [4], and magnetic properties [5]. Perovskites can be described by the common formula ABO3 [3]. Fig. 1-1 displays the crystal structure of ABO3: A is the large cation occupying the center of the cube, the oxide O lies in the corners of the octahedron, and B is the smaller cation placed in the octahedral center. The octahedron displays multiple structures of metal oxides [6], and different properties. They also can form a double-perovskite structure, denoted by the formula A2BBʹO6 [7]. Fig. 1-2 illustrates the crystal structure of A2BBʹO6： A is the cation occupying the center of cubic, B and Bʹ are the cations located in the center of octahedra, the oxide O occupies in the corners of the octahedral. Many of these functional characteristics represent the result of the subtle and complex interplay among spin, charge, orbital, and lattice degrees of freedom in perovskite oxide compounds [8-10]. The applications of perovskite oxides are described as follows. First, the optoelectronic properties of perovskite oxides can be applied as the chromogenic devices such as smart windows because of their unique physicochemical structures [2,11]. The band gap energy of perovskite oxides can be modulated by their different components, which is suitable for the application of photovoltaic devices such as solar cell [12]. Furthermore, the band gap of perovskite oxides near the visible-light absorption can be applied for photocatalytic applications. Photocatalytic reaction can break H2O down into H2 and O2 with no external bias potential and is used to harness solar energy for environmental purification and fuel production [2]. Second, the ferroelectric properties of perovskite 1.

(20) oxides show a strong inversion-symmetry breaking because of their spontaneous electric polarization, which can be built as ferroelectric memory devices [13]. Third, the high spin polarized properties of spin-up and spin-down density of states around the Fermi level in perovskite oxides can be used to establish spintronic devices [14,15]. Single-crystal SrFeO3− has four different phases: SrFeO3.00, SrFeO2.86, SrFeO2.75, and SrFeO2.50 [16-18]. SrFeO3−δ has generated considerable interest because of its colossal magnetoresistance [16] and catalytic activity [19], which can be used in next-generation magnetic read heads [20,21] and methane oxidation [19]. The crystal structure of SrFeO3.00 is cubic at all temperatures, and the prototype of Fe(IV) oxides displays a metallic state. SrFeO3.00 experiences a magnetic phase transition from paramagnetic to helicoidal magnetic state near 130 K [21]. The crystal structure of SrFeO2.86 is tetragonal at room temperature, and the valence Fe 4+ and Fe3.5+ oxides show semiconducting behavior. SrFeO2.86 reveals a tetragonal-to-monoclinic phase transition at 62 K. At this temperatures, it exhibits a hysteresis regime at approximately 11 K wide [22]. SrFeO2.86 undergoes the magnetic phase transition from paramagnetism to antiferromagnetic ordering near 75 K [22,23]. The crystal structure of SrFeO 2.75 is orthorhombic at room temperature and displays no obvious structural change with a decrease in the temperature. The mixedvalence (Fe4+ and Fe3.5) oxides exhibit semiconducting properties [24]. The magnetic properties of SrFeO2.75 transition from paramagnetism to antiferromagnetism with weak spin-glass at 232 K [25] and then saturate at < 70 K. The crystal structure of SrFeO 2.50 is brownmillerite-type at room temperature. The Fe3+ oxides show G-type antiferromagnetic ordering near 700 K and an insulating ground state [26,27]. The crystal structure and magnetic phase transitions of SrFeO3− are displayed from Fig. 1-3 to 1-6 [28]. The double-perovskite Ba2CuTeO6 has attracted considerable research interest because of its complex physical properties, such as structural phase transition [29,30], lowdimensional magnetism with S = ½ Cu2+ ions accompanied by magnetic phase transitions 2.

(21) [31], and quantum criticality [32]. Structurally, it comprises CuO6 octahedra that are linked with corner-shared and face-shared TeO6 [32-34]. The crystal structure of Ba2CuTeO6 is monoclinic at room temperature, undergoes a monoclinic-to-triclinic phase transition at approximately 287 K [35,36], and exhibits magnetic phase transition at approximately 75 and 15 K. When temperature decreases to 75 K, S = 1/2 Cu 2+ ions form complex-couple Cu–O–Te–O–Cu superexchange paths. Ba2CuTeO6 exhibits short-range antiferromagnetic correlations [29]. A long-range antiferromagnetic ordering is observed at 15–16 K. The two-leg ladders have strong interladder couplings, which stabilize the Néel-ordered ground state [32]. The crystal and magnetic phase transitions of Ba 2CuTeO6 are presented in Fig. 1-7 [37]. The double tungstates of Li2M(WO4)2 (M = Co, Ni, and Cu) have unique magnetic [38-43], photophysical [44], and photocatalytic properties [42]. Li2M(WO4)2 consists of MO6 octahedra that are linked with pairs of the corner-shared double WO4 group. The double WO4 group is also linked to pairs of edged-shared inverted WO5 pyramids. Li2Co(WO4)2 and Li2Cu(WO4)2 exhibit complex magnetic phase transitions [38,39]. Li2Ni(WO4)2 presents magnetic phase transitions at approximately 18 and 13 K. When temperature. decreases, short-range. ordering is presented that. later becomes. incommensurate magnetic ordering between 18 and 13 K. At temperatures < 13 K, longrange magnetic ordering is observed [40-42]. The crystal and magnetic phase transitions of Li2Ni(WO4)2 are presented in Fig. 1-8 [45]. The rest of this thesis is organized as follows. Chapter 2 surveys perovskite oxide compounds and a review of SrFeO2.86, SrFeO2.75, Ba2CuTeO6, and Li2Ni(WO4)2 . Chapter 3 presents the theory of general optical properties of solids and experimental spectroscopic ellipsometry and Raman scattering spectroscopy. Chapter 4 displays the optical properties of SrFeO2.86, SrFeO2.75, Ba2CuTeO6, and Li2Ni(WO4)2. Chapter 5 summarizes the thesis. 3.

(22) B A O. c b. Oʹ. a. Fig. 1-1: The crystal structure of ABO3 form [3].. 4.

(23) B. A Bʹ c O. b a. Fig. 1-2: The crystal structure of A2BBʹO6 form [7].. 5.

(24) Sr O c. Fe b a. Metallic Cubic PM. Helical magnetic ordering 130 K. 300 K. Fig. 1-3: Crystal structure of SrFeO3 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28].. 6.

(25) Sr O Fe c b a. Semiconductor Monoclinic. Tetragonal PM. Antiferromagnetic ordering 62 K. 75 K. 300 K. Fig. 1-4: Crystal structure of Sr8Fe8O23 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28].. 7.

(26) Sr O Fe c b a. Semiconductor Orthorhombic PM. Long-range AFM with weak spin-glass 232 K. 300 K. Fig. 1-5: Crystal structure of Sr4Fe4O11 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28].. 8.

(27) Sr O Fe c b c. Insulator Brownmillerite-type PM. G-type antiferromagnetism 700 K. Fig. 1-6: Crystal structure of Sr2Fe2O5 at room temperature. A schematic depicting its electric, structural, and magnetic properties [28].. 9.

(28) CuO6 Ba. Cu Te O c. a. TeO6. b. Semiconductor Triclinic P 1 Long-range Short-range AFM AFM 15 K 75 K. Monoclinic C2/m PM 287 K. Fig. 1-7: Crystal structure of Ba2CuTeO6 at low temperatures. A schematic depicting its electric, structural, and magnetic properties (AFM: antiferromagnetic and PM: paramagnetic) [37].. 10.

(29) a c. Semiconductor Triclinic 𝑷𝟏 Commensurate AFM 13 K. Incommensurate AFM 18 K. PM 300 K. Fig. 1-8: Crystal structure of Li2Ni(WO4)2 at low temperatures. A schematic depicting its electric, structural, and magnetic properties (AFM: antiferromagnetic and PM: paramagnetic) [45].. 11.

(30) Chapter 2 Overview of SrFeO3−, Ba2CuTeO6, and Li2Ni(WO4)2 2.1 SrFeO3− Single-crystal SrFeO3− compounds can be grown from polycrystalline rods by using the floating zone method. First, SrCO3 with 99.994% pure and Fe2O3 with 99.998% pure, powders are mixed in air to prepare the SrFeO3−δ powder, which is moderately ground. Next, the resulting powder is filled into latex sleeves and pressed into rods. The rods are sintered in flowing oxygen at 1300 °C for 24 h and then cooled down to room temperature [46]. Next, single crystals of SrFeO3−δ are grown from these polycrystalline rods by using the floating zone technique under ≃2.5 atm of oxygen pressure, flowing at 100 sccm. A slow growth rate of approximately 2 mm/h is used for low mosaicity [47]. The seed and feed rods are rotated counterclockwise at 12–14 rpm. The two single crystals, SrFeO2.75 and SrFeO2.81, with different oxide doping, are subjected to 0.002 atm O 2 at 449.2 °C and at 475.0 °C in 1 atm O2, respectively, for 7–10 days [46]. Fig. 2-1 shows an oversimplified relation of the variation of oxide doping with the temperature at 1- and 350-atm pressure of oxygen [24]. Fig. 2-2 displays the room-temperature Mössbauer spectra of ground SrFeO3− crystals showing the valence of iron ions. The blue line represents Fe4+, the red line represents Fe3.5+ and the green line represents Fe3+. SrFeO3.00 shows the single line of the Fe4+ signal. SrFeO2.95 consists of additional doublet line, indicating the appearance of the average charge of Fe3.5+. SrFeO2.87 reveals Fe3.5+ doublet in addition to an Fe4+ single 12.

(31) line. SrFeO2.81 shows a larger splitting, indicating the appearance of Fe3+. SrFeO2.69 shows Fe3+ as its main consistence but the splitting of blue line indicates the Fe4+ come from the square pyramidal. SrFeO2.86 is tetragonal with space group I4/mmm at room temperature with lattice constants of a = 10.929 Å and c =7.698 Å . All lattice constants are summarized in Table 2-1. Fig. 2-3 and 2-4 show the temperature dependence of the lattice parameters of Sr8Fe8O23, those proposed that when the temperature decreases below room temperature, lattice parameters in the c-axis change because of the structure change from tetragonal to monoclinic at approximately 62 K [22].. Table 2-1: Structural parameters for Sr8Fe8O23 refined in space group I4/mmm [48].. SrFeO2.75 is orthorhombic with the space group Cmmm with the lattice constants of a = 10.974 Å , b = 7.702 Å , and c = 5.473 Å [49]. The structural parameters are listed in Table 2-2.. 13.

(32) Table 2-2: Structural parameters for Sr4Fe4O11 refined in the space group Cmmm [48].. Reehuis et al. [50] measured the neutron diffraction data of SrFeO3.00 and SrFeO2.87, shown in Fig. 2-5, revealing an interesting result—the phase I appeared in SrFeO3.00 and SrFeO2.87 and phase II appeared in SrFeO2.87. Fig. 2-6 shows the temperature dependence of the intensity, incommensurability, and magnetic correlation length of the helical magnetic Bragg reflections. The magnetic reflections of Phase I emerged in both samples below TN = 133 K. The magnetic reflection of phase II appears in SrFeO2.87 below TN = 75 K [50]. Fig. 2-7 illustrates the magnetic susceptibility of single-crystal SrFeO3.00, SrFeO2.95, SrFeO2.85, SrFeO2.81, and SrFeO2.77 measured in field cooling and subsequent field heating runs at B = 1 T. Adler et al. [21] illustrated that at 130 K, SrFeO3.00 exhibits the maximum susceptibility for the helical order, and above 60 K, it exhibits wide thermal hysteresis of 10 K. SrFeO2.95 exhibits the maximum susceptibility at 130 K and, at 75 K, it exhibits a shoulder because of the antiferromagnetic order with thermal hysteresis. SrFeO 2.85 displays a sharp maximum result from the antiferromagnetic order at 70 K with a hysteresis of ≃3 K. The shape of SrFeO2.81 broadened at 70 K and shifted toward a lower temperature for SrFeO2.77 [21]. The susceptibility of SrFeO2.875 exhibits a similar behavior as reported by Lee et al [22]. Reehuis et al. [42] illustrated the magnetic ordering structures of SrFeO3.00, 14.

(33) Sr8Fe8O23, and Sr4Fe4O11 (Fig. 2-8). SrFeO3.00 exhibits helical magnetic ordering with a propagation vector K parallel to the direction [1,1,1] of the cubic unit cell. Sr8Fe8O23 displays similar helical behavior with SrFeO3.00. Sr4Fe4O11 shows a commensurate collinear antiferromagnetic state. Fig. 2-9 (a)-(e) displays the dc resistivity in zero-field cooling and heating processes of SrFeO3.00, SrFeO2.95, SrFeO2.85, SrFeO2.81, and SrFeO2.77, respectively. The SrFeO3.00-C phase (Cubic perovskite phase) exhibits metallic behavior with hysteresis near 60 K. Below 70 K, the SrFeO2.95-C and SrFeO2.85-T phase (Tetragonal phase) mixed also displays a resistivity anomaly, revealing as metallic behavior. The SrFeO2.85-T phase exhibits a semiconductor behavior above 70 K. At 70 K, the resistivity suddenly increases, indicating magnetic ordering, and both SrFeO2.85 and SrFeO2.81 display similarly weak semiconductor behavior. Below 50 K, resistivity increases by a large value, indicating that SrFeO2.81 exhibits an insulating behavior at low temperatures. The resistivity of SrFeO 2.77 follows a similar pattern as SrFeO2.81, but the shift in resistivity increases at lower temperatures, and a decreased thermal hysteresis appears, indicating the increased volume fraction of the orthorhombic phase [21]. The susceptibilities of SrFeO 2.81 and SrFeO2.875 (Fig. 2-10 and 2-11) display similar magnetic transition behavior [22,51]. Lee et al. [51] demonstrated the temperature-dependent Fe K-edge XANES spectra and the temperature-dependent XANES spectra of the normalized Fe L3,2-edge of singlecrystal SrFeO2.81 (Fig. 2-12 and 2-13). The average valence of Fe in SrFeO2.81 was between Fe3+ and Fe4+, closer to Fe4+. Two valence states of Fe display as Fe3.5+ and Fe4+, and the 3d electrons of Fe occupy out-of-plane Fe 3d3z2−r2 orbits during cooling and in-plane Fe 3d3x2−y2 orbits during heating. Fig. 2-14 (a) shows the conduction band and valence band positions SrFeO3-with range between 0 to 1.8 eV. Fig. 2-14 (b) shows the band gap energy as a function of Fe content (x) in SrTi1-xFexO3-y solid solutions. The band gap energy of SrTi1−xFexO3− y family changes from 3.17 eV (x = 0) to 1.80 eV (x = 1). The band gap absorption energy range 15.

(34) changes from UV light to visible light. The band gap of SrFeO3− at above 1.8 eV is shown in both literatures [52,53]. Adler et al. [21] demonstrated far-infrared ellipsometric and Raman scattering spectra of SrFeO3.00 at selected temperatures. They didn’t observe any Raman-active phonon modes but three infrared-active phonon modes, shown in Fig. 2-15. Below room temperature, no structural phase transitions occur [54]. Far-infrared ellipsometric and polarized Raman scattering spectra of SrFeO2.85 single crystal display complementary phonon modes at low temperatures (Fig. 2-16 and 2-17 and Table 2-3). The unpolarized Raman scattering spectra of SrFeO2.69 (Fig. 2-17) did not display any new phonon modes at low temperatures, suggesting no T phases.. Table 2-3: Phonon frequencies in SrFeO2.85 at low temperatures with different polarizations [21].. 2.2 Ba2CuTeO6 Ba2CuTeO6 single crystals were grown by two steps. First, the polycrystalline Ba2CuTeO6 was prepared by the solid-state reaction method. BaCO3, CuO, and TeO2 powders were mixed and fired in the air at 1000 ℃ for 12 h with heating and then cooling. And then the flux of BaCl2 was used. Dark green crystals were separated from the crucible mechanically. Hot water was used to wash the separated part [29]. Rao et al. [29] measured the synchrotron X-ray diffraction of Ba2CuTeO6 powders 16.

(35) and single-crystal diffraction pattern, shown in Fig. 2-18. The Ba2CuTeO6 powders display a space group in triclinic symmetry. The fitted lattice parameters were listed in Table 2-4. Table 2-4: The lattice parameters of Ba2CuTeO6 [29].. 5.7288(1) 5.8677(1) 12.2237(2). The temperature-dependent magnetic susceptibility of Ba2CuTeO6 (Fig. 2-19) displays the antiferromagnetic-like short-range exchange correlations at 75 K. This was commonly found in the Cu-O chain or plane systems with the superexchange spin coupling. The antiferromagnetic-like long-range ordering appears at approximately 15 K. The spins were oriented perpendicular to the ab plane [21]. The magnetic susceptibility behavior was similar to those shown by Gibbs et al. (Fig. 2-19) [35]. Fig. 2-20 displays a broad peak near 75 K, which is characteristic of low-dimensional systems [35]. These results confirmed the quasi-1D ladder system of Ba2CuTeO6. The similar magnetic susceptibility behavior was also shown by Glamazda et al. (Fig. 2-21) [36]. They found a broaden maximum near 75 K, indicating a low-dimensional antiferromagnets—short-range spin correlations. Glamazda et al. [36] examined the temperature-dependent polarized Raman scattering spectra of Ba2CuTeO6 (Fig. 2-22 and 2-23). They found that the two-magnon Raman response of Ba2CuTeO6 exhibits linear temperature dependence in its peak energy, linewidth, and intensity over a wide range of temperatures. This scaling behavior suggests that Ba2CuTeO6 is close to a quantum-critical point from an ordered side [28]. The firstprinciples calculations predicted the direct band gap energy of 1.0 eV for Ba2CuTeO6, shown in Fig. 2-24 [29]. 17.

(36) 2.3 Li2Ni(WO4)2 Polycrystalline Li2Ni(WO4)2 samples were prepared using a conventional solid-state reaction method. The high-purity (> 99.5%) powder mixtures of NiO, Li2CO3, and WO3 were heated to 550 and 650 ℃ for 24 h and ground intermittently to pelletize. The samples were then annealed at 700 ℃ for 160 h, followed by furnace cooling to room temperature at a rate of approximately 150 ℃/h [39,40]. Muthuselvam et al. [39] described the Rietveld refinement of synchrotron X-ray powder diffraction pattern of Li2Ni(WO4)2 (Fig. 2-25), suggesting the triclinic symmetry ̅ . The lattice parameters of Li2Ni(WO4)2 at room temperature and low with space group P1 temperatures are shown in Table 2-5.. Table 2-5: Structural parameters of Li2Ni(WO4)2 obtained by refinement of synchrotron Xray diffraction data (λ = 0.619 Å) for T = 300 K (room temperature, RT) and high-resolution neutron powder diffraction data (λ = 1.6215 Å) for T = 2 K (low temperature, LT) phases. ̅ [39]. The space group is P1. Fig. 2-26 displays the densities of states of Ni-3d and O2p for Li2Ni(WO4)2. The theoretical band structure calculations [39] predicted that Li2Ni(WO4)2 has band gap energy of 2.7 eV. Lv et al. [43] examined the ultraviolet–visible diffuse reflectance and Raman scattering spectra of Li2Co(WO4)2 and Li2Ni(WO4)2 (Fig. 2-27). They discovered the primary absorption bands at approximately 2.6 and 2.9 eV, respectively, which can be 18.

(37) attributed to charge-transfer excitations from the 2p orbitals of O ions to the 5d orbitals of W ions. The other absorption bands observed in the visible frequency region can be attributed to the d–d transitions of Ni and Co ions. Fig. 2-28 demonstrates the temperaturedependent dielectric constant of Li2Ni(WO4)2. The anomalies near TN1 = 18 K and TN2 = 13 K connect the long range 3D antiferromagnetism ordering [37]. Fig. 2-29 exhibits the magnetic susceptibility of Li2Co(WO4)2, with two magnetic phase transitions at approximately 9 K and 7 K [37]. Fig. 2-30 illustrates the magnetic susceptibility of Li2Ni(WO4)2, with two magnetic phase transitions at approximately 18 K and 13 K. Li2Ni(WO4)2 exhibited strong Raman-active phonon modes (Fig. 2-31) at approximately 899 and 902 cm−1, respectively, due to the symmetric stretching vibrations of WO6 octahedra. Maczka et al. [55] studied the infrared and Raman scattering spectra of Li2M(WO4)2 (M = Co, Ni, and Cu). The observed phonon modes were appropriately assigned, as shown in Table 2-6. The vibrational properties of Li2Co(WO4)2 and Li2Ni(WO4)2 were well correlated with their crystal structures.. 19.

(38) Table 2-6: Infrared and Raman phonon modes for Li2Ni(WO4)2, Li2Co(WO4)2, and Li2Cu(WO4)2 with assignment based on comparison with data reported for ZnWO4 [56].. 20.

(39) Fig. 2-1: Pseudobinary phase diagram showing the variation of composition with temperature at 1- and 350-atm oxygen pressure. The approximate lower oxygen limit of the perovskite phase is indicated with the dashed line [24].. 21.

(40) Fig. 2-2: Room-temperature Mössbauer spectra of ground SrFeO3−δ crystals. Subspectra: blue—Fe4+ (single line), red—Fe3.5+ (doublet with smaller splitting), and green—Fe3+ (doublet with larger splitting) [21].. 22.

(41) Fig. 2-3: Temperature dependence of the lattice parameters of Sr8Fe8O23 [50].. Fig. 2-4: Linear scans along the longitudinal direction through the Bragg reflection (004) for the cooling and heating processes of Sr8Fe8O23. (a) The evolution of the lattice parameter of the c-axis (unit, Å ) as a function of temperature. (b) The temperature dependence of the peak width (full width at half maximum, FWHM). Both graphs display the hysteresis behavior around the transition temperature of magnetic ordering [22].. 23.

(42) Fig. 2-5: Neutron diffraction data from the single crystals of SrFeO3.00 and SrFeO2.87 measured at various temperatures. The scans were performed along the [1,1,1] direction around the structural Bragg reflection (0, 0, 1) cub [50].. Fig. 2-6: Temperature dependence of the intensity, incommensurability, and magnetic correlation length of the helical magnetic Bragg reflections of the magnetic phase I in the single-crystal SrFeO3.00 (left) and the magnetic phases I and II in SrFeO2.87 (right) [50]. 24.

(43) Fig. 2-7: Magnetic susceptibility of the single crystals of SrFeO 3.00, SrFeO2.95, SrFeO2.85, SrFeO2.81, and SrFeO2.77 measured in field cooling and subsequent field heating runs at B = 1 T. Curves for the latter four samples were shifted by amounts indicated in the legend [21].. 25.

(44) Fig. 2-8: Magnetic ordering of iron moments in the system of SrFeO3−δ [50].. 26.

(45) Fig. 2-9: (a) SrFeO3.00, (b) SrFeO2.95, (c) SrFeO2.85, (d) SrFeO2.81, and (e) SrFeO2.77 display the resistivity in zero-field cooling and heating runs (black) compared with field cooling and heating runs with a 9-T field (red) [21].. 27.

(46) Fig. 2-10: Temperature dependence of the resistivity of a single crystal of SrFeO 2.81, measured in the ab plane and along the c-axis. The top inset presents the temperature dependence of magnetic susceptibility (χ) measured along the c-axis in ZFC and FC runs in a magnetic field of 1 T, and the bottom inset presents room-temperature X-ray diffraction profile showing (004) Bragg peak obtained in θ-scan [51].. Fig. 2-11: Susceptibility, resistivity, and magnetoresistance (MR) measurements of SrFeO2.875. (a) Susceptibility curves (MT), field cool (FC), and zero FC (ZFC) at an applied field of 1 T show a transition at T ≃120 K and a sharp antiferromagnetic transition at approximately 70 K. Resistivity curves (RT) for both cooling and heating measurements show two transitions at T ≃120 K and 50 K as indicated by green arrows, respectively. (b) MR data, both for the applied field perpendicular and parallel to c-axis, display a negative MR of approximately 45% at T ≃55 K. The inset shows that the transition temperature is reduced by the applied field [22].. 28.

(47) Fig. 2-12: The temperature-dependent Fe K-edge XANES spectra of single-crystal SrFeO2.81 measured at two different angles of incidence θ = 0° (with electric field E parallel to the ab plane) and 70° (with electric field E nearly parallel to the c-axis) on heating and cooling processes. Corresponding spectra were obtained for FeO, Fe3O4, and Fe2O3 powder samples at room temperature, with angle θ = 0° for reference [51].. 29.

(48) Fig. 2-13: Temperature dependence of normalized Fe L3,2-edge XANES spectra of singlecrystal SrFeO2.81 at two angles of incidence θ = 0° and 70° during (a) heating and (b) cooling. The bottom panels show the corresponding XLD spectra [51]. (a). (b).. Fig. 2-14: (a) Conduction band and valence band positions for P25 and SrFeO (32d) [52]. (b) Band gap energy and redox enthalpy as a function of Fe content (x) in SrTi 1−xFexO3−y solid solutions [53].. 30.

(49) Fig. 2-15: (a) Far-infrared ellipsometric and (b) Raman scattering spectra of SrFeO3.00 at 15, 160, and 300 K [21].. 31.

(50) Fig. 2-16: Raman scattering and far-infrared ellipsometric spectra were compared for the charge-order composition of SrFeO2.85 at low temperature and room temperature. (a) Raman scattering spectra in parallel (ZZ) and cross (XZ) polarization and (b) far-infrared ellipsometric spectra: optical conductivity  and real part of the dielectric permittivity 1 [21].. 32.

(51) Fig. 2-17: Temperature dependence of the Raman scattering spectra: (a) polarized Raman scattering spectra of SrFeO2.85 in ZZ direction and (b) unpolarized Raman scattering spectra of SrFeO2.69 [21].. 33.

(52) Fig. 2-18: (a) Room-temperature synchrotron X-ray powder diffraction pattern of Ba2CuTeO6. (b) A single-crystal diffraction pattern obtained using an X-ray (Cu-Kα) beam perpendicular to the ab plane. The inset is the optical image of grown single crystal [29].. 34.

(53) Fig. 2-19: (a) The temperature dependence of magnetic susceptibility measured in an applied magnetic field of 10 kOe for H║ab and H⊥ab of single-crystal Ba2CuTeO6. (b) The dχ/dT vs T curves measured with a field of 10 kOe reveal an anisotropic cusp of T N ≃15 K [29].. 35.

(54) Fig. 2-20: The χ(T) for Ba2CuTeO6 single-crystal arrays with the magnetic field of μ0H = 1 T applied parallel (upper panel) and perpendicular (lower panel) to the ab plane. The dashed and solid lines indicate chain and ladder model fits, respectively. The inset in the upper panel displays the low temperature region for both orientations along with the high-field behavior for H⊥ab. The inset in the lower panel displays M(H) of Ba2CuTeO6 for H⊥ab [35].. Fig. 2-21: Temperature dependence of the magnetic susceptibility χ(T) for Ba2CuTeO6 measured in an external field of µ 0H = 1 T applied parallel and perpendicular to the ab plane. The red solid lines are fits using a two-leg ladder model. The inset shows the inverse susceptibility with a fitting to a Curie-Weiss law [57]. 36.

(55) Fig. 2-22: (a) Low-energy range of Raman spectra taken at T = 9 K in four different polarizations (aa, ab, bb, and cc). The gray shading denotes a two-magnon continuum. (b) Magnetic excitations in (bb) polarization for different temperatures. The spectra are vertically shifted by a constant amount [36].. 37.

(56) Fig. 2-23: Raman spectra measured in (cc) and (bb) polarizations for different temperatures. The shadings emphasize scattering due to two-magnon excitations [36].. 38.

(57) Fig. 2-24: Band structure (top panel) and density of states (bottom panel) of configuration AF1 in Ba2CuTeO6. The top of the valence band has been set to zero [29].. 39.

(58) Fig. 2-25: Rietveld refinement of powder synchrotron X-ray diffraction pattern for Li2Ni(WO4)2 at room temperature [39].. 40.

(59) Fig. 2-26: Partial Ni-3d and O-2p densities of states in Li2Ni(WO4)2 at 2 K. The Fermi energy is set to zero [39].. Fig. 2-27: UV-Vis diffuse reflectance spectra of (a) Li2Co(WO4)2, (b) Li2Ni(WO4)2, and (c) WO3, and the inset shows the optical absorption coefficient between 1.5 to 3.75 eV [43]. 41.

(60) Fig. 2-28: The temperature dependence of the dielectric constant (εr) under an applied frequency 100 kHz in Li2Ni(WO4)2. (a) The inset shows the first order derivative of the εr as a function of temperature. (b) The inset shows the temperature dependence of pyroelectric current [39].. Fig. 2-29: Temperature dependence of the magnetic susceptibility of Li 2Co(WO4)2 measured in a 1-T magnetic field. The left axis of the inset highlights the low-temperature regime, and the right axis highlights the derivative d(χT)/dT . The peaks of d(χT)d/dT reveal a minor reduction of (χ)T near TN1 ≃9 K and TN2 ≃7 K [37]. 42.

(61) Fig. 2-30: (a) Magnetic susceptibility (black circles) as a function of temperature for Li2Ni(WO4)2 in a 1-T magnetic field. (b) The peaks of d(χT)d/dT reveal the minor reduction of (χ)T near TN1≃18 K and TN2 ≃13 K [39]. .. 43.

(62) Fig. 2-31: Raman scattering spectra of (a) Li2Co(WO4)2, (b) Li2Ni(WO4)2, and (c) Li2Cu(WO4)2 [55].. 44.

(63) Chapter 3 Theory background and experimental techniques 3.1 Spectroscopic ellipsometry Ellipsometry is commonly used to characterize both thin films and bulk materials. Its most common application is the determination of thin film thickness and its optical constants (n, k, or ε1 and ε2). Ellipsometry has also been used to study doping concentration, surface and interfacial roughness, alloy ratio, crystallinity, optical anisotropy, and depth profile of material properties [58]. The measured values are expressed as psi (  ) and delta (  ). These values are related to the ratio of Fresnel reflection coefficients Rp and Rs for p- and s-polarized light, respectively. The ellipsometric parameter ρ is commonly expressed in terms of the two real-valued ellipsometric parameters psi (  ) and delta (  ) as follows:.   tan()ei. where tan( ) =. ，. Rp Rs.    p  s. ，. (3.1.1). (3.1.2). (3.1.3). where tan( ) is the magnitude of the ratio of the p- to s-direction complex reflection coefficients for the sample, and.  is the phase difference between the p- and s-reflection 45.

(64) coefficients. When a beam of light is directed to an interface at an angle a1, and the reflectance beam from the substrate surface has a reflectance index N2, from classical electrodynamics, the Fresnel reflection coefficients Rp and Rs are derived as follows:. RR12pp . RR12Ss . N 2 cos a1  N 1 cos a2 N 2 cos a1  N 1 cos a2. ，. N 1 cos a1  N 2 cos a2 N 1 cos a1  N 2 cos a2. ∙. (3.1.4). (3.1.5). From Snell’s law, we know that ，. N1sina1=N2sina2 and substituting it into Eqs. (3.1.4) and (3.1.5) . p R 12 R p . cos a1 sin a1  cos a2 sin a2 cos a1 sin a1  cos a2 sin a2. . (sin2 a2  cos2 a2 )(cos a1 sin a1)  (sin 2 a1  cos2 a1)(cos a2 sin a2) (sin2 a2  cos2 a2 )(cos a1 sin a1)  (sin 2 a1  cos2 a1)(cos a2 sin a2). . (cos a2 sin a1  cos a1 sin a2)(cos a1 cos a2  sin a1 sin a2 ) (cos a2 sin a1  cos a1 sin a2)(cos a1 cos a2  sin a1 sin a2). . R 12p. sin(a1  a2 ) cos(a1  a2 ) cos a1 acos sin( a1 a1 sin a2 ) cos( 1  a2 )sin a2  cos a1 sin a1  cos a2 sin a2. . (sin2 a2  cos2 a2 )(cos a1 sin a1)  (sin 2 a1  cos2 a1)(cos a2 sin a2) (sin2 a2  cos2 a2 )(cos a1 sin a1)  (sin 2 a1  cos2 a1)(cos a2 sin a2). . (cos a2 sin a1  cos a1 sin a2)(cos a1 cos a2  sin a1 sin a2 ) (cos a2 sin a1  cos a1 sin a2)(cos a1 cos a2  sin a1 sin a2). . sin(a1  a2 ) cos(a1  a2 ) sin(a1  a2 ) cos(a1  a2 ). 46. (3.1.6).

(65) . tan(a1  a2 ) tan(a1  a2 ). ∙. (3.1.7). We can also obtain a similar result for Rs. RR12Ss . cos a1 sin a2  sin a1 cos a2 cos a1 sin a2  sin a1 cos a2. .. (3.1.8). Thus, we can obtain the ellipsometric parameter ρ:.   tan()ei   tan  e i  cos(a1  a2 ) tan a1 tan a2  1    cos(a1  a2 ) tan a1 tan a2  1. . 1 1 1－tan()e  tan  e i i = tan a1 tan a2 1 1＋tan()e  tan  e i i. (3.1.9). . (3.1.10). From Eq. (3.1.10),   tan()ei i  1  tan()e tan  e ii (1  tan()e tan  e ii )(1  tan()e tan  ei )  ii  ii  i  i tan()e tan()e 1  tan e (1  tan  e )(1  tan()e tan  e ). 1  tan2   i2 tan  sin  1  tan2   2 tan  cos  1  tan2  2 tan  i sin  2 1  tan2   1  tan  2 tan  1 cos  1  tan2  . . cos 2  i2 sin  cos  sin  1  2 sin  cos  cos  . cos 2  i sin 2 sin  1  sin 2 cos . ，. (3.1.11). .. (3.1.12). and from Eq. (3.1.10),. 1 1  tan a1 tan a2 tan a1. N 22  N 12 sin2 a1 N 1 sin a1 47.

(66) Now, assuming N = 1 (in air). 1 1  tan a1 tan a2 tan a1. N 22  sin2 a1 ， sin a1. (3.1.13). and substituting Eqs. (3.1.11) and (3.1.13) into Eq. (3.1.10). . 1 tan a1. N 22  sin2 a1 cos 2  i sin 2 sin   ， sin a1 1  sin 2 cos . (3.1.14). and squaring each side of Eq. (3.1.14), we get. N 22  tan2 a1 sin2 a1. cos2 2  i2 sin 2 cos 2 sin   sin 2 2 sin 2  (1  sin 2 cos )2.  sin2 a1. ∙. (3.1.15). Moreover, we can define a complex dielectric function (  ) as. N 22    1  i 2 where. ，. (3.1.16). 1 and 2 are the real and imaginary parts of the dielectric function. Comparing. with Eqs. (3.1.15) and (3.1.16), we obtain. 1  sin2 a1 (tan 2 a1  2  tan 2 a1 sin 2 a1. cos 2 2  sin 2 2 sin 2   1) (1  sin 2 cos ) 2. ，. (3.1.17). 2sin 2 cos 2 sin  (1  sin 2 cos ) 2. ，. (3.1.18). ，. (3.1.19). and N2  n  ik. where n and k are the refractive index and extinction coefficient, respectively. Combining Eqs. (3.1.17), (3.1.18), and (3.1.19), n and k are as follows:. 48.

(67) n  4 12   22 cos k  4 12   22 sin.  2.  2. where   tan 1. 2 1. Using these results, we measure psi (  ) and delta (  ), and. ，. (3.1.20). ，. (3.1.21). ∙. (3.1.22). 1 ,  2 , n, and k can then be. calculated. Ellipsometry is a very sensitive technique that measures the changes in the polarization state of light reflected from the surface of a sample. The ellipsometer arrangements start with a light source and end with a detector. Fig. 3-1 shows the spectroscopic ellipsometer with the focusing optics used in this investigation. Spectroscopic ellipsometry measurements were conducted under angles of incidence between 60° and 75° by using a J. A. Woollam Co. M-2000U ellipsometer over a spectral range of 0.73–6.42 eV. The experimental data were reproducibly observed at three spots on the sample surfaces using a specially designed focusing optics coupled with an ellipsometer for spot (100 × 100 µm2) measurements.. 3.2 Raman scattering measurement Raman scattering was first observed by Raman and Krishnan in 1928 [59], although the Raman effect had been predicted by Smekal in 1923 [60]. Raman spectra are established by analyzing inelastically scattered light. Raman scattering originates from a change in the polarizability of molecules or susceptibility of crystals by quasi-particles [61]. Fig. 3-2 shows the schematic of Rayleigh and Raman scattering processes. The frequency of the incident light is i, and the frequency of the scattered light is s. The energy of incident and scattered light is given by Eqs. (3.2.1) and (3.2.2): 49.

(68) Ei = hi. ，. (3.2.1). Ei = hs. ，. (3.2.2). The scattered photon has an energy that is less than the incident photon called Stokes Raman scattering, and the energy that is greater than the incident photon called anti-Stokes Raman scattering. The difference between the inverse of these two wavelengths is known as the Raman shift, a value that is directly related to the energy. The Raman shift depends on the scattering media, demonstrating that the Raman spectrum is strongly related to the properties of the scattering materials. Raman scattering measurements yield information on lattice vibration and the excitations of the charge, spin, and orbital degrees of freedom [61]. Fig. 3-3 shows the sketch map of micro-Raman spectroscopy. The first laser light wavelength is 785 nm with the input power of 0, 1, 10, 25, 50, and 100 mW. The second laser light wavelength is 532 nm with the output power of 0, 0.2, 2, 5, 10, and 20 mW. The third laser light wavelength is 488 nm with the output power of 0, 0.4, 4, 10, 20, and 40 mW. The laser is in conjunction with the grating density of 400 grooves/mm or 1200 grooves/mm. The laser light is focused by the 50× microscope objective with NA = 0.5 and directed perpendicular to the surface of the sample, with the spatial resolution of 4 μm. Then, the scattering light is collected at 180° and compared with the incident light. Alternatively, the laser light is focused on the 100× microscope objective with NA = 0.9 and directed perpendicular to the surface of the sample, with the spatial resolution of 1 μm. The charge-coupled detector with the model DU 420A-OE-152 can reduce lower the temperature to −60 ℃ to −65 ℃ with a 1024 × 256 resolution. The spectral resolution of these instruments is typically less than 0.5 cm−1. Fig. 3-4 shows a mechanical crosssectional device. The sample was clamped on the gap for cross-sectional measurement. A cryostat is used for temperature-dependent measurements. The continuous liquid helium flow into the cryostat allows measurements to be conducted in the temperature range of 50.

(69) 10–300 K. Fig. 3-5 illustrates the setup for temperature-dependent Raman scattering measurements. The sample was mounted inside the cryostat. Coaxial shield flow liquid helium transfer line, flow meter panel for helium gas flow control, silicon diode sensor, and temperature controller were used to monitor the sample’s temperature.. 51.

(70) Focusing optics coupled tube. Sample. Fig. 3-1: Spectroscopic ellipsometer with the focusing optics.. Fig. 3-2: Schematic of Rayleigh, anti-Stokes, and Stokes scattering.. 52.

(71) Fig. 3-3: Sketch map of the setup of the micro-Raman scattering spectroscopy.. Sample position. Fig. 3-4: The cross-sectional mechanical setup. 53.

(72) Cryostat on the stage of optical microscopy. LHe transfer line. Flow meter. Vacuum pump LHe dewar. Temperature controller. Fig. 3-5: Temperature-dependent Raman scattering experimental setup.. 54.

(73) Chapter 4 Results and discussion 4.1 Optical properties of SrFeO3- single crystals In this section, we present the spectroscopic ellipsometry and Raman scattering measurements of SrFeO2.86 and SrFeO2.75 single crystals. These samples were acquired from Prof. C. H. Du’s research group at the Department of Physics, Tamkang University. We used spectroscopic ellipsometry to investigate the dielectric function and optical constants. Fig. 4-1 displays the ellipsometric parameters  and  of SrFeO2.86 and SrFeO2.75 single crystal at 70° angles of incidence. Optical constants can be derived from these ellipsometric parameters using Eqs. 3.1.17 and 3.1.18. Fig. 4-2 reveals the refractive index n and extinction coefficient k of SrFeO2.86 and SrFeO2.75 single crystals. We observed that the shapes of the refraction index dispersion of SrFeO 2.86 and SrFeO2.75 single crystal were similar despite the different oxygen contents. As displayed in Fig. 4-2(a), when the photon energy increased from 2.1 to 3.8 eV and from 4.7 to 5.4 eV, the refractive index decreased, which indicates anomalous dispersion. As illustrated in Fig. 4-2(b), when the photon energy increased from 2.3 to 3.9 eV and from 4.6 to 5.3 eV, the refractive index decreased, which displays anomalous dispersion. Fig. 4-3 illustrates the optical absorption coefficient spectra of SrFeO2.86 and SrFeO2.75 single crystals measured at room temperature. We fitted these absorption spectra by using a standard Lorentzian model [62]. The background was fitted using the Lorentzian functions [62]. The absorption was resolved into two peaks. An increase in the photon energy resulted in a progressive increase in the absorption. Two absorption bands were observed at approximately 2.98, and 5.05 eV for 55.

(74) the SrFeO2.86 single crystal. Galakhov et al. [63] presented the valence band region of the XPS spectra, showing the similar absorption bands. Similar absorption bands were also observed for the SrFeO2.75 single crystal. The first-principles calculations [31,33,64] indicated that 2.98 and 5.05 eV peaks were associated with the charge transfer transitions between oxygen 2p states to the iron 3d states. The absorption coefficient included contributions from the direct and indirect bandgap transitions in the typical solid state and is expressed as follows [65,66]: (5.1) where Eg,dir is the magnitude of the direct bandgap, Eg,ind is the magnitude of the indirect bandgap, Eph means the absorbed (emitted) phonon energy, and A and B are constants. The model described above, which supposes a simple band shape, causes the extraction of the direct energy gap when (·E)2 is plotted as a function of photon energy. Fig. 4-4 (a) displays the direct bandgap analysis of SrFeO2.86 and SrFeO2.75 single crystals. Plotting (α．E)0.5 as a function of photon energy led to an indirect band gap shown in Fig. 4-4(b) and (c). The values of band gap of both samples are 2.00 ± 0.01 and 1.98 ± 0.01 eV at 300 K, respectively. Rothschild et al. [52] performed the four-point probe conductivity measurements and demonstrated the band gap of SrFeO3- at approximately 1.9 ± 0.1 eV. Ghaffari et al. [53] employed the ultraviolet photoelectron spectroscopy and determined the band gap of SrFeO3- at approximately 1.8 eV. L. Wang et al. [67] measured the spectroscopic ellipsometry spectra of SrFeO2.5, SrFeO2.5+ and SrFeO3 thin films. The decrease in band gap from 2.05 to 0 eV indicated that thin films transitioned from semiconductor to metal. Our experimental results are comparable to these previous studies [52,53,67]. Fig. 4-5 demonstrates the room-temperature Raman scattering spectra of SrFeO2.86 and SrFeO2.75 single crystals. We fitted these Raman scattering spectra using the standard Lorentzian functions [62]. The factor group analysis indicated that SrFeO2.86 has a 56.