由第三代同步輻射光所衍生出來的能譜術，包含針對晶格結構的X射線繞射分析(XRD)，電子或軌域結構的X光吸收近邊結構能譜術(XANES)和X光線偏振二向性能譜術(XLD)，磁結構的X光磁圓偏振二向性能譜術(XMCD)，佔據態及其交互作用的X光發射能譜術(XES)和共振非彈性X光散射能譜術(RIXS)等各項技術被視為探究複雜耦合機制的有力工具。藉由其優異的對稱性及元素選擇性，在眾多錳系陶瓷薄膜及釓系化合物等強關聯系統研究中發揮關鍵的分析功能。
本文第一部分對釓基團簇富勒烯(metallofullerene)化合物 
Gd3-xScxN@C80進行XAS及RIXS相關研究。釓基團簇富勒烯作為核磁共振(MRI)高效顯影劑(CAs)的潛能被深入探討，然而其中關鍵的金屬釓離子在電子結構及交互作用上卻尚未被研究透徹。我們利用釓N4,5-edges RIXS對 Gd3-xScxN@C80進行釓4f電子結構以及帶自旋翻轉特性的激發。相較於標準樣品氧化釓以及商用顯影劑釓基螯合物，富勒烯包覆的釓離子在特徵峰能量上位移，且峰形表現出與激發能量無關的寬化現象。並結合理論與實驗，討論釓離子內部軌域各種能量參數如交換場(Jex)、4f-4f庫侖作用、自旋-軌道耦合(SOC)等在富勒烯碳離子環境下所產生的響應。
第二部份利用變溫XRD量測不同膜厚的C-type反鐵磁錳系陶瓷薄膜-釹鍶錳氧(NSMO)/鈦酸鍶(STO)其基板應力對釹鍶錳氧薄膜晶格結構的影響，並配合錳L3,2-edge XLD和理論計算判定此隨溫度變化之應力對於錳離子在室溫及低溫情況下3d eg軌域的有序度，佔據狀態以及分裂程度。並進一步討論由XMCD以及磁化強度對溫度(M-T)曲線所觀察到可隨膜厚調制的尼爾溫度(TN)及低溫鐵磁性與軌域狀態的關聯。
最後則介紹由淡江大學(TKU)，台灣同步輻射(NSRRC)以及美國勞倫茲國家實驗室-先進光源(ALS, LBNL)共同合作建造台灣光子源(TPS)-45A軟X光發射譜(SXE)實驗站XES/RIXS光譜儀的功能、光學設計以及直射X光測試。

The third-generation synchrotron radiation based spectroscopies such as X-ray diffraction (XRD) for lattice structure, X-ray absorption near edge structure (XANES) and X-ray linear dichroism (XLD) for electronic and orbital structures, X-ray magnetic circular dichroism (XMCD) for magnetic structure, X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS) for information of the occupied states and inherent elementary excitations, are considerable and powerful techniques for the study of various complex couplings in complex systems. Their excellent symmetry and element specific capabilities are certainly exhibited in many strongly correlated systems like manganite thin films and gadolinium (Gd)-based compounds.
In the first part of this thesis, XAS and RIXS study of 
Gd-based metallofullerene, Gd3-xScxN@C80, have been carried out. Because of the potentially efficient contrast agents (CAs) in magnetic resonance imaging (MRI), the Gd-based metallofullerene have particularly been well focused. However, the electronic structure and interaction of the key Gd ion remains unclear. Here, we have carried out RIXS experiments on GdxSc3-xN@C80 at Gd N4,5-edges to directly study the electronic structure and spin flip excitations of Gd 4f electrons. Compared with the reference Gd2O3 and contrast agent Gadodiamide, the features in the RIXS spectra of all metallofullerenes exhibit broader spectral lineshape and noticeable energy shift. Using atomic multiplet calculations, we have estimated the key energy scales such as the inter-site spin exchange field, intra-atom 4f-4f Coulomb interactions, and spin-orbit coupling. The implications of these parameters to the 4f states of encapsulated Gd atoms are discussed.
In the second part, temperature-dependent XRD has been used on the C-type antiferromagnetic Nd0.35Sr0.65MnO3 (NSMO)/SrTiO3 (STO) thin films of various thickness to study the response of the lattice structure under the strain of STO substrate. The combination of XRD, experimental and theoretical Mn L3,2-edges XLD is helpful to determine the degree of 3d eg orbital ordering, occupation and splitting with the strain in lattice structure as a function of temperature. Subsequently, the results of XMCD and magnetization vs temperature (M-T) curves, which show the thickness dependent Néel temperature (TN) and ferromagnetism at low temperature, have been discussed.
The final part is associated with the performance, design and straight beam test of XES/RIXS spectrometer at Soft X-ray Emission (SXE) endstation in Taiwan Photon Source (TPS)-BL45A. This spectrometer was jointly built by groups in Tamkang University (TKU), National Synchrotron Radiation Research Center (NSRRC) and Advanced Light Source-Lawrence Berkeley National Laboratory (ALS, LBNL).

Table of Contents
Abstract ............................................... i
Table of Contents ...................................... iv
List of Figures ........................................ vi
List of Tables ......................................... xi
1. Introduction ......................................... 1
1-1. Strongly Correlated Electron System ................ 1
1-2. Necessity of Spectroscopic Studies ................. 3
2. Experimental Techniques .............................. 7
2-1. Synchrotron Radiation............................... 7
2-2. X-ray Diffraction (XRD) ............................ 9
2-3. X-ray Absorption Spectroscopy (XAS) ............... 11
2-4. X-ray Linear Dichroism (XLD) ...................... 15
2-5. X-ray Magnetic Circular Dichroism (XMCD) .......... 18
2-6. Normal/Resonant X-ray Emission Spectroscopy (N/RXES) ........................................................ 21
3. The Key Energy Scale of Gd-based Metallofullerene by RIXS ................................................... 27
3-1. Introduction ...................................... 27
3-2. Experimental ...................................... 31
3-3. Results and Discussion ............................ 35
3-4. Conclusion ........................................ 53
4. Epitaxial Nd0.35Sr0.65MnO3 Thin Films with Different Thicknesses ............................................ 55
4-1. Introduction ...................................... 55
4-2. Experimental ...................................... 59
4-3. Results and Discussion ............................ 62
4-4. Conclusion ........................................ 84
5. Modular Soft X-ray Spectrometer for Applications in Energy Sciences and Quantum Materials in TPS BL-45A ........................................................ 86
5-1. Introduction ...................................... 86
5-2. Optical and Mechanical Design ..................... 90
5-3. Straight Beam Test ............................... 104
6. Summary ............................................ 108
Reference ............................................. 111


List of Figures
Figure 1-1 
The scheme of the coupling between charge, orbit, lattice and spin in strongly correlated system. ................. 2
Figure 2-1 
Bragg’s law which shows the condition of diffraction. ... 9
Figure 2-2 
Q is the vectorial difference between the incoming wavevector kin and the outgoing wavevector kout. The magnitudes of kin and kout are equal to 2π/λ. .......... 11
Figure 2-3 
Left panel shows the process of XAS that X-ray beam promotes core-level electrons to unoccupied valence-state levels and thereby probes these upper states by varying the incident photon energy. Right panel exhibits the name of
the absorbing edges from core levels with variously principal quantum numbers. ............................. 12
Figure 2-4 
Regions of XAS data (Mn K-edge). ....................... 14
Figure 2-5 
The escape depth Λ (mean free path) of electrons in condensed matter.It depends strongly on the kinetic energy of electron. ........................................... 15
Figure 2-6 
XANES spectra of the formate radical absorbed on the Cu(110) surface change according to the orientation of the x-ray polarization vector (P) relative to the molecule. Strongly polarization-dependent π and σ features indicate the efficient absorption while the orientation is the same between polarization and orbits. ....................... 17
Figure 2-7 
A scheme of the L-edge XMCD. The efficiency of absorption at L3 and L2 edge are different by rcp and lcp, respectively. .......................................... 20
Figure 2-8 
The decay process after (a) XAS (ionization). The excited state can decay by (b) Auger electron and (b) emitted photon. ................................................ 21
Figure 2-9 
The decay process of RIXS after (a) XAS (resonant). The excited state can be unexcited by (b) elastic mode and (c) inelastic mode. ........................................ 24
Figure 2-10 
A typical 2-D map of the RIXS measurement of Cu L3 edge. ........ 26
Figure 2-11 
The general energy transfer range of these various interactions in
RIXS. ……........................................................................................................... 26
Figure 3-1 
Schematic illustration showing the key parameters affecting the MRI relaxivities: the electronic spin relaxation time of metal ions T1e,2e, the rotational correlation time τR and inner sphere water exchange reaction T1m+kex. ...... 30
Figure 3-2 
(a) From top to bottom: experimental XAS spectra of Gadodiamide (green), Gd1Sc2N@C80 (blue), Gd3N@C80 (red), and Gd2O3 (black) compared with simulated XAS spectrum using single Gd3+ ion (black dash line). Simulation parameters are listed in Table 3-1 (baseline).
(b) Zoom-in pre-edge region of XAS spectra. The simulated spectra with Gd3+ and Gd2+ ions are denoted by dash black and grey line, respectively. The blue vertical lines mark the main peak positions and are guides for eyes. ....... 38
Figure 3-3 
(a) Schematic illustration of RIXS process producing the inelastic features with term symbols 6PJ, 6DJ, and 6GJ (in [3.5 eV, 8 eV] energy loss window). (b)-(d) RIXS maps of (b) Gd2O3, (c) Gd3N@C80, and (d) simulated Gd3+ single ion. The experimental RIXS maps in panels (b) and (c) are produced by interpolating the RIXS spectra recorded at 141, 141.5, 142, 142.4, 142.7, 143.1, 143.5, 144.5, and 145.5 eV excitation photon energies. The intensity of the elastic peak (zero energy loss) is scaled to 1 with color bars shown on the right. .................................... 39
Figure 3-4 
(a) The RIXS spectra of (from top to bottom) Gd3N@C80, Gd2Sc1N@C80, Gd1Sc2N@C80, Gd2O3, and Gadodiamide recorded at excitation energy of (a) 142.4 eV (at 6D9/2 in XAS) and (b) 143.1 eV (at 6D7/2 in XAS). (c) Relative peak positions
(relative to the peaks in Gd2O3) plotted against the energies of the peaks in Gd2O3 and (d) full width at half maximum (FWHM) from Lorentzian fitting of RIXS spectra in
panels (a) and (b). .................................... 43
Figure 3-5 
Comparison of Gd2O3 (black line) and simulated Gd3+(baseline; dash black line) RIXS spectra at 142.4 eV excitation photon energy. The simulation parameters for baseline spectrum are listed in Table 3-1. For 142.4 (143.1) eV excitation energy, the simulation is scaled up by a factor of 6 (15) in [3.4 eV, 4.0 eV] window; in [4.0 eV, 4.4 eV] window, the simulation and experiment are scaled up by a factor of 150 (200) and 5 (5), respectively; in [4.4 eV, 5.4 eV] window, the simulation is scaled up by a factor of 20 (20). This scaling is also applied to Fig.
3-7. ................................................... 45
Figure 3-6 
(a) Simulated RIXS spectra with varying 4f-4f Coulomb interactions. (b) Relative peak positions plotted against the ones with 0% variation (dash black line) in 4f-4f Coulomb interactions. (c) Simulated RIXS spectra with varying spin exchange field Jex. The inverted triangles mark the peak position and are guides for eyes. (d)
Simulated RIXS spectra with varying spin-orbit coupling (SOC). ................................................. 49
Figure 3-7 
Comparison of Gd3N@C80 and simulated RIXS spectra (yellow line) with optimized energy parameters (1% reduction in 4f-4f Coulomb interactions, 10% reduction in SOC, and Jex=40 meV; parameters are listed in Table 3-1) at excitation
photon energy of (b) 142.4 eV and (c) 143.1 eV. The experimental Gd2O3 RIXS spectra and baseline simulations plus Jex=30 meV (red line) are also shown in the bottom part of the same figures. The scaling mode in each energy window is the same as Fig. 3-5. The scaling factors (red for simulations and black for experiments) are also listed in the figures. ........................................ 51
Figure 4-1 
(a) The XRD (112) and (004) Bragg peaks of both the S20 and S72 samples at 300 K and 30 K. Inset shows the (002) and (022) Bragg peaks of STO substrate. It shows that the behavior in lattice parameter ab and c of both thin films is similar to STO in cooling process. (b) Schematics of the Nd0.35Sr0.65MnO3 unit cellthat is rotated by 45° around c-axis and depositing on the STO substrate. .............. 64
Figure 4-2 
The magnetization versus temperature (M-T) graph for S20 and S72. The inset is the resistivity versus temperature (ρ-T) plot for S20 and S72 samples. .................... 68
Figure 4-3 
(a) The plot of lattice parameter ‘ab’ with respect to the temperature of S20 and S72 thin film along with lattice parameter ‘ab’ of the STO substrate for comparison. (b) The plot of lattice parameter ‘c’ with respect to the temperature of S20 and S72 thin film along with lattice parameter ‘c’ of the STO substrate for comparison. (c) The plot of the lattice mismatch f (T) with respect to temperature for S20 and S72 thin film samples. ......... 71
Figure 4-4 
(a) The Polarization-dependent Mn K-edge X-ray absorption near-edge structures (XANES) of both thin films compared to powder sample and standards (i.e., MnO, MnO2 and Mn2O3) at 300 K. (b) The Polarization-dependent Mn K-edge XANES of both thin films compared to powder sample at 30 K. (a) and (b) demonstrate the almost fixed valence state Mn3+/4+ in thin films between 30 and 300K. ........................ 73
Figure 4-5 
The Polarization-dependent Mn L3,2 XLD spectra of S20 and S72 samples measured at both 30 and 300K [upper panel]. The lower panel shows the difference plot. ................. 75
Figure 4-6 
Plot showing a comparison between experimental results and simulated results were done using atomic multiplet simulation at (a) 30±2K and (b) 300K. .................. 79
Figure 4-7 
(a) The plot of Mn L3,2-edge XMCD spectra for samples S20 and S72 at 300K [upper panel]. The lower panel shows the difference plot. (b) The plot of Mn L3,2-edge XMCD spectra for samples S20 and S72 at 30 K [upper panel]. The lower panel shows the difference plot. (c) The plot of Ti L3,2-edge XMCD spectra of S20 sample taken at 300K and 30K temperatures. The lower panel shows the difference plot. ........................................................ 82
Figure 5-1 
Schematic illustration of Hettirck-Underwood optical scheme. ................................................ 92
Figure 5-2 
SHADOW simulations showing the scattered dot images at the detector plane at selected photon energies: (a) 225 eV, (b) 300 eV, (c) 420 eV, (d) 750 eV. In each panel, three photon energies (one central and two detuned) are used to show the
energy resolution. Panel (e) is the result at 225 eV, same as panel (a), except rGD is kept at 1.275 m. ........... 96
Figure 5-3 
Photograph showing the internal construction of the optics chamber with Ni coated LEG and Au coated HEG. .......... 98
Figure 5-4 
The calculated (lines) and measured (markers) grating efficiency curves. The red and blue curves are for Au coated HEG and Ni coated LEG, respectively. ............ 99
Figure 5-5 
CAD models showing (a) the optics carriage, and (b) the interior view of the optics chamber. .................. 103
Figure 5-6 
Photograph showing (a) the spectrometer developed for a beamline at Taiwan Photon Source (TPS). ............... 103
Figure 5-7 
Photographs showing the commissioning setup of the TKU-SXE
spectrometer at BL8.0.2, Advanced Light Source (ALS). ....................................................... 106
Figure 5-8 
(a) Straight beam test results at selected photon energies for LEG. (b) RP of spectrometer as a function of photon energy determined from the Gaussian fittings to the curves in panel (a). Two sets of curves correspond to two repeated
measurements. ......................................... 107

List of Tables
Table 3-1 
Parameters used in atomic multiplet calculations (in units of eV). ................................................ 34
Table 4-1 
Parameters used in atomic multiplet calculations (in units of eV). ................................................ 61

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