本論文主要針對兩種不同的3d過渡金屬氧化物，La1.66Sr0.33NiO4(LSNO)及SrFeO2.81(SFO)，在低溫下所產生的電荷及電子自旋有序調制結構的相變化進行研究，其中利用硬X光繞射及共振軟X光繞射技術來量測電荷及電子自旋有序調制結構的相變化。在La2-xSrxNiO4系統中，當Sr摻雜量為x = 0.33時，在低溫下所產生的電荷有序波向量及電子自旋有序波向量為QCO(4.66 0 3)及QSO(0.66 0 0)，而其相變溫度分別為TCO = 230 (K)和TSO = 190 (K)，特別的是，電荷有序調制結構的相變化過程中會產生"反向有序到無序"(Inverse Order-Disorder Transition)的相變化，而本論文中亦針對此現象探討。
    而在另一個3d過渡金屬氧化物系統，SrFeO2.81，在低溫下所產生的電荷有序波向量及電子自旋有序波向量為QCO(0 0 3.37)及QSO(0 0 0.5)，而其相變溫度分別為TCO = 110 (K)和TSO = 70 (K)，在此系統中除了有豐富的調制結構的相變化，亦產生四方體轉單斜晶的結構變化，而此結構變化亦伴隨著遲滯現象的發生。針對SFO系統，本論文中利用光譜計算來模擬低溫下Fe L3,2-edge的螢光吸收光譜，並利用低溫下單斜晶的原子結構來做第一原理(LDA+U)的計算，透過態密度(Density of State)及能帶結構(Band Structure)來分析在低溫下SFO系統的電子結構，並確認了反鐵磁相以及電荷轉移的傳導機制。

We report the phase transition of charge and spin modulations in two different kinds of 3d transition metal oxides, La1.66Sr0.33NiO4(LSNO) and SrFeO2.81(SFO). Hard X-Ray and resonant soft X-Ray diffractions were used to measure charge and spin ordering reflections as a function of temperature. In La2-xSrxNiO4, hole doped by strontium, x = 0.33, the wave vector of charge ordering and spin ordering were located at QCO(4.66 0 3) and QSO(0.66 0 0) and their phase transition temperatures were observed to be TCO = 230 (K) and TSO = 190 (K), respectively. Interestingly, the charge ordering was observed to display an inverse order-disorder transition at about 230 K where the spin ordering forms. We show that this inverse transition is due to the interlayer coupling between the charge and spin ordering. This discovery points out the importance of the interlayer correlation in  strongly correlated electron systems.
  The oxygen-defective ferrite, SrFeO2.81, also has both of charge and spin modulated structures at low temperatures, which accompanies with the unusual transport behavior. Using X-Ray scattering, the wave vector changes of reflection were located at QCO(0 0 3.37) and QSO(0 0 0.5) with the transition temperatures of TCO ~ 110 (K) and TSO ~ 70 (K), respectively. In addition, SFO also shows a lattice distortion at around 60 K where a hysteresis transition occurs. For further understanding the electronic structures, we used  the first-principles LDA+U method to simulate the absorption spectrum at the Fe2,3-edge.

Table of Contents

Chapter 1. Introduction	1
Chapter 2. X-Ray Scattering and Density Functional Theory	4
2-1  Synchrotron	4
2-2  Bragg’s Law	7
2-3  Scattering Cross Section	8
2-4  Resonant Soft X-Ray Scattering (RSXS)	11
2-5  Density Functional Theory	20
Chapter 3. Inverse Order-Disorder Transition of Charge Stripe in La1.67Sr0.33NiO4	28
3-1  Introduction	28
3-2  Experiment	32
3-3  Discussion	42
3-4  Conclusion	46
Chapter 4. Spin and Charge Modulation Structures in SrFeO3-δ	47
4-1  Introduction	47
4-2  Experiment	52
4-2-1 Hard X-Ray scattering in SrFeO2.81	54
4-2-2 Resonant Soft X-Ray Scattering in SrFeO2.81	61
4-3 Discussion and First Principle Calculation Results	68
4-4 Conclusions	82
Chapter 5. Summary	95
Reference	98


 List of Figures

FIG. 2-1-1 The synchrotron light source.	5
FIG. 2-1-2 The spectrum of light of synchrotron.	5
FIG. 2-2-1 The diagram of geometry of Bragg's Law.	7
FIG. 2-4-1 The diagram shows the interaction between electric field and dipole moment.	12
FIG. 2-4-2 The diagram shows the solution of the real part and the imaginary part.	13
FIG. 3-1-1 The atomic structure of LSNO.	29
FIG. 3-1-2 The pattern of domains of spin and charge stripes.	30
FIG. 3-1-3 The spin and charge reflections for LSNO (x=0.33) in reciprocal space.	31
FIG. 3-1-4 The electronic state of Ni2+ and Ni3+.	31
FIG. 3-2-1 Sample of La1.67Sr0.33NiO4	32
FIG. 3-2-2 The resolution function of Bargg peak (0 0 4)	33
FIG. 3-2-3 The resistivity versus temperature measurement for La1.67Sr0.33NiO4. The hollow black circle and the hollow red circle are E parallel and perpendicular to a-b plane.	34
Fig 3-2-4 The temperature evolution of ratio of the correlation lengths along the K and H-axis.	35
FIG. 3-2-5 The temperature evolution of the correlation lengths along the L-axis.	35
FIG. 3-2-6 Peak profiles of charge reflection around (4.66 0 3) along H and K-axis at different temperature points.	36
FIG. 3-2-7 Peak profiles of charge reflection around (4.66 0 3) along L-axis at different temperature points.	36
FIG. 3-2-8 The peak intensity versus temperature of charge and spin ordering.	38
FIG. 3-2-9 The peak width versus temperature of charge and spin ordering.	38
FIG. 3-2-10 The energy scan in π-channel and the Q dependent energy scan of QSO (0.66 0 0) with different polarizations at Ni L3,2-edge.	39
FIG. 3-2-11 Peak profiles at Ni L3,2-edge in π- and σ-channel.	39
FIG. 3-2-12 Q The energy scan in π-channel and the Q dependent energy scan of QCO (0.72 0 1) with different polarizations at Ni L3,2-edge.	41
FIG. 3-3-1 The thermal effects on the charge stripe modulation along L direction.	43
FIG. 3-3-3 Temperature dependence of peak widths of charge stripes with different hole concentrations .	45
FIG. 4-1-1 The Atomic Structure for Sr8Fe8O23.	48
FIG. 4-1-2. The FIG. 4-1-2(a) is Ref.[45] and (b) is SQUID measurement for our sample.	50
FIG. 4-1-3. Resistivity warming up and cooling down measurements without magnetic field which shows a non-linear transition and hysteresis behavior at TCO=110 (K) and T=50 (K)	50
FIG. 4-1-4. MR measurement, the block ball is for cooling down process, and the red hollow circle is for warming up process. (a) shows the measurement which is parallel to the c-axis, and (b) is perpendicular to the c-axis.	51
FIG.4-2-1 Foating-Zone.	52
FIG.4-2-2 SrFeO2.81 single crystal.	52
FIG. 4-2-2 SrFeO2.81 high quality single crystal with (0 0 1) normal direction.	53
FIG.4-2-3. L-scan peak profile of Bragg peak (0 0 4).	53
FIG.4-2-4. L-scan peak profile of Bragg peak (0 0 4).	54
FIG. 4-2-5. Long range linear L-scan at T=20 (K).	55
FIG. 4-2-6. SQUID and RT measurements.	56
FIG. 4-2-7. The charge ordering peak (0 0 0.66) which was obtained in resonant soft X-Ray diffraction experiment for warming up.	56
FIG. 4-2-8. The process of hysteresis behavior of cooling down and warming up for FWHM which are as function of temperature.	57
FIG. 4-2-9. The temperature dependence of charge ordering (0 0 3.37) is as function of temperature.	57
FIG. 4-2-10. The diagram shows the commensurate position is as function of temperature.	58
FIG. 4-2-11. The lattice constant of c-axis length is as function of temperature.	58
FIG. 4-2-12. The temperature dependence of FWHM and L-position are shown in this diagram.	59
FIG. 4-2-13. The architecture of EPU beamline.	62
FIG. 4-2-14. The geometry of EPU beamline chamber from top view.	62
FIG. 4-2-15. Sample geomtry.	63
FIG. 4-2-16 EPU beamline end-station chamber.	63
FIG.4-2-17. The magnetism measurment shows the G-type[42] anti-ferromagnetic. phase transition is about at 70 (K), and the inset graph shows the quality of SFO single crystal which the FWHM of rocking curve is about 0.112°.	64
FIG. 4-2-18. The Qso (0 0 0.5) peak is as function of temperature and the phase transition is about at 70 (K).	64
FIG. 4-2-19. The energy scan in π-channel and the Q dependent energy scan of QSO (0 0 0.5) with different polarizations at Fe L3,2-edge.	65
FIG. 4-2-20. The energy scan in π-channel and the Q dependent energy scan of QSO (0 0 0.5) with different polarizations at O K-edge.	66
FIG. 4-2-20. The energy scan in π-channel and the Q dependent energy scan of QCO (0 0 0.63) in π- and σ-channel at Fe L3,2-edge.	67
FIG. 4-3-1. shows a monoclinic phase of SFO at T = 2 (K) in space group, I2/m.	68
FIG. 4-3-2. Charge reflection (0 0 3.37) is as a function of azimuthal angel Ψ.	70
FIG. 4-3-3. The solid circle is XAS result and the color lines are FDMNES simulation results.	71
FIG. 4-3-4 Total density of state of Sr, Fe and O for FM phase.	73
FIG. 4-3-5 s-orbit projected density of Sr, Fe and O for FM phase.	74
FIG. 4-3-6 p-orbit projected density of Sr, Fe and O for FM phase.	75
FIG. 4-3-7 d-orbit projected density of Sr, Fe and O for FM phase.	76
FIG. 4-3-8 Total density of state of Sr, Fe and O for AFM phase.	77
FIG. 4-3-9 s-orbit projected density of Sr, Fe and O for AFM phase.	78
FIG. 4-3-10 p-orbit projected density of Sr, Fe and O for AFM phase.	79
FIG. 4-3-11 d-orbit projected density of Sr, Fe and O for AFM phase.	80
FIG. 4-4-1 The Brillouin zone is considered in VASP calculating process.	82
FIG. 4-4-2 the total PDOS and Fe 3d-orbit and O 2p-orbit for FM phase by LDA+U calculation.	83
FIG. 4-4-3 the total PDOS and Fe 3d-orbit and O 2p-orbit for AFM phase by LDA+U calculation.	83
FIG. 4-4-4 The PDOS of O 2p-orbit for FM phase by LDA+U calculation.	84
FIG. 4-4-6 The PDOS of Fe 3d-orbit for FM phase by LDA+U calculation.	85
FIG. 4-4-7 The PDOS of Fe 3d-orbit for AFM phase by LDA+U calculation.	85
FIG. 4-4-8 Comparing with O 2p-orbit and Fe 3d-orbit for FM phase by LDA+U.	86
FIG. 4-4-9 Comparing with O 2p-orbit and Fe 2p, 3d-orbit for AFM phase by LDA+U.	86
FIG. 4-4-10 PDOS of Fe(1), Fe(21), Fe(22) and Fe(3) 3d-orbit for FM by LDA+U.	88
FIG. 4-4-11 PDOS of Fe(1), Fe(21), Fe(22) and Fe(3) 3d-orbit for AFM by LDA+U.	88
FIG. 4-4-12 Total band structure for FM phase by LDA and LDA+U calculation.	89
FIG. 4-4-13 Partial band structure for FM phase by LDA and LDA+U calculation.	89
FIG. 4-4-14 Total band structure for AFM phase by LDA and LDA+U calculation.	90
FIG. 4-4-15 Partial band structure for AFM phase by LDA and LDA+U calculation.	90
FIG. 4-4-16 Total band structure for tetragonal phase by LDA and LDA+U calculation.	93
FIG. 4-4-17 Partial band structure for tetragonal phase by LDA and LDA+U calculation.	93






List of Tables

Table 2-4-1 the calculated value of scattering amplitude is obtained by resonant scattering which is coming from different bands.	19
Table. 4-2-1. Polarization of EPU phase.	62
Table 4-4-1. The net magnetic moment and total energy by LDA calculation.	91
Table 4-4-2. The net magnetic moment and total energy by LDA+U calculation.	91

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