材料中的豐富的物理特性與微觀尺度下的晶格、電子、自旋和軌道的長程有序有關，這樣的長程有序會在特定條件下產生調製結構。論文為利用中子散射以及X 光散射實驗研究自旋有序的缺氧行鈣鈦礦材料
YBaCuFeO5(YBCFO)以及電荷有序介金屬材料Ir2In8Se(IIS)。
YBCFO的部分，透過中子散射實驗以及共振彈性Ｘ光散射實驗成功建立低溫的雙螺旋磁結構，分別由Fe3+與Cu2+自旋排列組成，外加磁場的中子散射實驗觀察到複雜的磁結構相轉變，推測在相轉變溫度以下，磁域結構形成，磁域間彼此競爭。此外由磁場誘導的記憶效應，也觀察到Fe3+螺旋磁結構對溫度及磁場轉變顯著，而Cu2+則對溫度與磁場相依性低。
IIS的部分，在電阻率觀察到在約200 K 有斜率的改變，比熱結果顯示在約200 K有長程有序的結構存在。透過X 光散射實驗清楚觀察到低溫存在兩種不同的調制結構，分別為qCM = (0.5 0.5 0)以及qICM ~ (0.24 0.24 0)，兩者皆具溫度相依性。溫度相依的X 光散射實驗結果顯示調制結構ICM為二階相轉變，而CM則有Inverse order-disorder 轉變在約150 K，由此推論系統中有兩種不同的order parameter 交互作用。

The modulated structures involving the ordered arrangements of electrons, spins, and orbitals can lead to complex and fascinating physical properties in materials. For this thesis, we focused on the spin-ordered material YBaCuFeO5 (YBCFO) and the charge-ordered material Ir2In8Se (IIS).
In YBCFO, using neutron scattering and resonant elastic x-ray scattering, we demonstrated a low-temperature double-helical magnetic structure composed of the spin
arrangements of Fe3+ and Cu2+. Experiments were also conducted to study the magnetic field effects on the double-helical spin ordering. Using neutron scattering with an applied
magnetic field, we revealed that YBCFO shows the complex magnetic phase transitions,
indicating the formation of magnetic domain structures below the phase transition
temperature, and a field-induced memory effect.
For IIS, high-resolution x-ray scattering experiments identified two distinct modulated structures below T* ~ 200 K with qCM = (0.5, 0.5, 0) and qICM ~ (0.24, 0.24, 0). The ICM phase undergoes a second-order transition, while the CM structure exhibits an inverse order-disorder transition around 150 K, suggesting the interaction of two different order
parameters within the system.

Contents
Contents V
List of Figures VII
List of Tables XII
1 Introduction 1
1.1 Modulated Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Resonant Elastic X-ray Scattering . . . . . . . . . . . . . . . . . . 15
1.3 Modulated Structure of Spin Ordering-YBaCuFeO5 . . . . . . . . . . . . 22
1.4 Modulated Structure of Charge Ordering-Ir2In8Se . . . . . . . . . . . . . 27
2 Experiment 30
2.1 Physical Property Measurement . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.1 Magnetic Susceptibility . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.2 Electrical Transport Measurement . . . . . . . . . . . . . . . . . . 32
2.1.3 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 In-house Diffractometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.1 Four-Circle Diffractometer . . . . . . . . . . . . . . . . . . . . . . 33
2.2.2 Single Crystal Diffractometer . . . . . . . . . . . . . . . . . . . . 34
2.3 Elastic Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Resonant Elastic X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . 36
2.4.1 Photon Factory BL3A . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2 NSRRC TPS09A . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 YBaCuFeO5 39
3.1 Sample Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Elastic Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Resonant Elastic X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Magnetometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5 Elastic Neutron Scattering under a Magnetic Field . . . . . . . . . . . . 63
3.5.1 Thermal Hysteresis Behavior . . . . . . . . . . . . . . . . . . . . . 64
3.5.2 Magnetic Hysteresis Behavior . . . . . . . . . . . . . . . . . . . . 79
3.6 Phase Diagram of Magnetic Structure . . . . . . . . . . . . . . . . . . . . 111
3.7 Resonant Elastic X-ray Scattering under a Magnetic Field . . . . . . . . 115
3.7.1 Thermal Hysteresis Behavior . . . . . . . . . . . . . . . . . . . . . 115
3.7.2 Magnetic Hysteresis Behavior . . . . . . . . . . . . . . . . . . . . 121
4 Ir2In8Se 130
4.1 Physical Property Measurement . . . . . . . . . . . . . . . . . . . . . . . 130
4.2 Single Crystal Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.3 X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5 Summary 140
Bibliography 142

List of Figures
1.1 Schematic diagram of the scattering experiment . . . . . . . . . . . . . . 2
1.2 A schematic illustration that shows the scattering interactions of neutrons,
x-rays, and electrons within materials . . . . . . . . . . . . . . . . . . . . 4
1.3 The magnetic structure of ErPd3 below TN = 3 K . . . . . . . . . . . . . 12
1.4 Neutron diffraction patterns of polycrystalline ErPd3 at T = 1.5 K . . . 13
1.5 A schematic diagram illustrating the spiral magnetic structure of Ho . . . 14
1.6 The rocking curve around the atomic structure reflection (100) of Ho at T
= 77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7 The rocking curve around the atomic structure reflection (100) of Ho at T
= 77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 X-ray-induced transitions of E1 and E2 for d- and f -elements . . . . . . 20
1.9 The coordinate system used to evaluate the polarization dependence of
resonant scattering amplitudes . . . . . . . . . . . . . . . . . . . . . . . . 21
1.10 The crystal structure and temperature-dependent magnetic susceptibility
of YBCFO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.11 The neutron diffraction patterns at 300 K and 80 K . . . . . . . . . . . . 24
1.12 The diffraction patterns of q = (0.5 0.5 0.5) along L-direction as a function
of temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.13 Simulated incommensurate magnetic reflection patterns at 3.5 K and temperaturedependent
rotation angle Φ with incommensurability δ . . . . . . . . . . 25
1.14 The magnetic structure at 200 K and 3.5 K . . . . . . . . . . . . . . . . 26
1.15 The crystal structure of Ir2In8Se . . . . . . . . . . . . . . . . . . . . . . . 27
1.16 Temperature-dependent resistivity and heat capacity of IIS . . . . . . . . 28
1.17 The single crystal diffraction patterns of IIS . . . . . . . . . . . . . . . . 29
2.1 Schematic diagram of the SQUID magnetometer . . . . . . . . . . . . . . 31
2.2 Four-wire resistance measurement on PPMS puck . . . . . . . . . . . . . 33
2.3 Specific heat puck schematic diagram . . . . . . . . . . . . . . . . . . . . 33
2.4 Prof. Du lab’s in-house four-circle diffractometer . . . . . . . . . . . . . . 34
2.5 Single crystal diffractometer Synergy-S . . . . . . . . . . . . . . . . . . . 34
2.6 TAIPAN triple-axis spectrometer: top-down schematic view . . . . . . . 36
2.7 PF BL3 endstation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.8 TPS09A endstation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.9 TPS09A endstation with horizontal scattering plane . . . . . . . . . . . . 38
3.1 Diffraction pattern and temperature-dependent magnetization of single
crystal YBCFO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Temperature-dependent elastic neutron diffraction pattern . . . . . . . . 40
3.3 Fitting results of temperature-dependent elastic neutron scattering . . . . 42
3.4 Temperature-dependent rotation angle and pitch length . . . . . . . . . . 44
3.5 Schematic diagram of Φ and Pitch Length. The double spiral magnetic
structures at 10 K, 100 K, and 150 K. . . . . . . . . . . . . . . . . . . . . 45
3.6 Slice scan around Fe K-edge at 250 K (PF) . . . . . . . . . . . . . . . . 47
3.7 Temperature-dependent x-ray diffraction pattern (PF) . . . . . . . . . . 48
3.8 Slice scan around Fe K-edge at 300 K (TPS) . . . . . . . . . . . . . . . . 49
3.9 Comparison of NS and REXS data (TPS) . . . . . . . . . . . . . . . . . 50
3.10 The schematic diagram of the superlattice of Fe3+ and Cu2+ . . . . . . . 52
3.11 Temperature-dependent magnetization under various magnetic fields . . . 54
3.12 The difference between in magnetization . . . . . . . . . . . . . . . . . . 55
3.13 The M(H) curve at 5K and PUND method . . . . . . . . . . . . . . . . 56
3.14 The remnant magnetization at various temperatures . . . . . . . . . . . . 57
3.15 Temperature-dependent AC susceptibility at H = 4T . . . . . . . . . . . 58
3.16 Magnetic field-dependent magnetization at various temperatures . . . . . 59
3.17 ∂M/∂H at various temperatures . . . . . . . . . . . . . . . . . . . . . . . 60
3.18 Field-dependent AC susceptibility at 110 K, 135 K, 150 K, and 166 K . . 61
3.19 Magnetic phase diagram from magnetic magnetization . . . . . . . . . . 62
3.20 The measurement paths of neutron scattering with H field . . . . . . . . 64
3.21 Temperature-dependent elastic neutron diffraction pattern at H = 4 T
(Warming) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.22 Temperature-dependent elastic neutron diffraction pattern at H = 4 T
(Cooling) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.23 Neutron diffraction pattern at T = 110 K and H = 0 T and 4T. . . . . . 66
3.24 Fitting results of temperature-dependent elastic neutron scattering at H
= 4 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.25 Temperature-dependent L-value during warming at H = 4 T . . . . . . . 68
3.26 Temperature-dependent integrated intensity during warming at H = 4 T 69
3.27 Temperature-dependent peak width (FWHM) during warming at H = 4 T 70
3.28 Temperature-dependent L-value during cooling at H = 4 T . . . . . . . . 71
3.29 Temperature-dependent integrated intensity during cooling at H = 4 T . 72
3.30 Temperature-dependent peak width (FWHM) during cooling at H = 4 T 73
3.31 Temperature-dependent rotation angle Φ and pitch length at H = 4 T . 73
3.32 The H(T) diagram with the measurement paths at H = 4 T . . . . . . . 74
3.33 Fitting results of the CM and ICM1 component at H = 4 T . . . . . . . 76
3.34 Fitting results of the ICM2 component at H = 4 T . . . . . . . . . . . . 77
3.35 Fitting results of the S component at H = 4 T . . . . . . . . . . . . . . . 78
3.36 Field-dependent elastic neutron diffraction pattern at T = 110 K (H increased)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.37 Field-dependent elastic neutron diffraction pattern at T = 110 K (H decreased)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.38 Neutron diffraction pattern at T = 110 K at different field condition . . 81
3.39 Filed-dependent diffraction patterns of (H H L)-plane at T = 110 K . . 82
3.40 Fitting results of field-dependent elastic neutron scattering at T = 110 K 83
3.41 Field-dependent L-value with increasing H filed at T = 110 K . . . . . . 84
3.42 Field-dependent integrated intensity with increasing H field at T = 110 K 85
3.43 Field-dependent peak width (FWHM) with increasing H field at T = 110 K 85
3.44 Field-dependent L-value with decreasing H filed at T = 110 K . . . . . . 86
3.45 Field-dependent integrated intensity with decreasing H filed at T = 110 K 87
3.46 Field-dependent peak width (FWHM) with decreasing H filed at T = 110 K 88
3.47 Field-dependent rotation angle Φ and pitch length at T = 110 K . . . . 89
3.48 The H(T) diagram with the measurement paths at T = 110 K . . . . . . 89
3.49 The neutron diffraction pattern at T = 110 K and H = 4 T at different
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.50 Fitting results of the CM and ICM1 components at H = 4 T . . . . . . . 93
3.51 Fitting results of the ICM2 component at H = 4 T . . . . . . . . . . . . 94
3.52 Fitting results of the S component at H = 4 T . . . . . . . . . . . . . . . 95
3.53 Field-dependent elastic neutron diffraction pattern at T = 135 K . . . . 96
3.54 Fitting results of field-dependent elastic neutron scattering at T = 135 K 97
3.55 The H(T) diagram with the measurement paths at T = 135 K . . . . . . 98
3.56 Field-dependent elastic neutron diffraction pattern at T = 150 K . . . . 99
3.57 Fitting results of field-dependent elastic neutron scattering at T = 150 K 100
3.58 The H(T) diagram with the measurement paths at T = 150 K . . . . . . 101
3.59 Field-dependent elastic neutron diffraction pattern at T = 160 K . . . . 102
3.60 Fitting results of field-dependent elastic neutron scattering at T = 160 K 103
3.61 The H(T) diagram with the measurement paths at T = 160 K . . . . . . 104
3.62 Field-dependent elastic neutron diffraction pattern at T = 170 K . . . . 105
3.63 Fitting results of field-dependent elastic neutron scattering at T = 170 K 106
3.64 The H(T) diagram with the measurement paths at T = 170 K . . . . . . 107
3.65 Field-dependent elastic neutron diffraction pattern at T = 180 K . . . . 108
3.66 Fitting results of field-dependent elastic neutron scattering at T = 180 K 109
3.67 The H(T) diagram with the measurement paths at T = 180 K . . . . . . 110
3.68 Phase Diagram of YBCFO . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.69 Phase Diagram of YBCFO . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.70 Temperature-dependent x-ray diffraction patterns under H = 4 T . . . . 116
3.71 Comparison of NS and REXS data under H = 4 T . . . . . . . . . . . . 116
3.72 Temperature-dependent x-ray diffraction pattern with fitting curves under
H = 4 T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.73 Fitted q-value of the REXS patterns under H = 4 T . . . . . . . . . . . 118
3.74 Fitted integrated intensity of the REXS patterns under H = 4 T . . . . . 118
3.75 Fitted FWHM of the REXS patterns under H = 4 T . . . . . . . . . . . 119
3.76 Comparison of NS, REXS and EXS data under H = 4 T and T = 110 K 120
3.77 Field-dependent x-ray diffraction patterns at T = 140 K . . . . . . . . . 121
3.78 Field-dependent x-ray diffraction pattern with fitting curves at T = 140
K with increasing field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.79 Field-dependent x-ray diffraction pattern with fitting curves at T = 140
K with decreasing field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.80 Fitted q-value of the REXS patterns at T = 140 K . . . . . . . . . . . . 123
3.81 Fitted integrated intensity of the REXS patterns at T = 140 K . . . . . 124
3.82 Fitted FWHM of the REXS patterns at T = 140 K . . . . . . . . . . . . 125
3.83 Field-dependent x-ray diffraction patterns at T = 135 K . . . . . . . . . 126
3.84 Field-dependent x-ray diffraction pattern with fitting curves at T = 135
K with increasing field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
3.85 Field-dependent x-ray diffraction pattern with fitting curves at T = 135
K with decreasing field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
3.86 Fitted q-value of the REXS patterns at T = 135 K . . . . . . . . . . . . 128
3.87 Fitted integrated intensity of the REXS patterns at T = 135 K . . . . . 128
3.88 Fitted FWHM of the REXS patterns at T = 135 K . . . . . . . . . . . . 129
4.1 The temperature-dependent resistance and heat capacity of IIS . . . . . . 130
4.2 The diffraction patterns of HK-, HL-, and KL-plane at 300 K . . . . . . 131
4.3 The diffraction patterns of HK-, HL-, and KL-plane at 100 K . . . . . . 131
4.4 Temperature-dependent diffraction patterns of HK-planes at L = 0, 1, 2
at T = 300 K, 250 K, 220 K . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.5 Temperature-dependent diffraction patterns of HK-planes at L = 0, 1, 2
at T = 200 K, 180 K, 160 K . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.6 Temperature-dependent diffraction patterns of HK-planes at L = 0, 1, 2
at T = 140 K, 120 K, 100 K . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.7 Temperature-dependent diffraction patterns of (H K 1) planes . . . . . . 135
4.8 The diffraction pattern of (H K 1) planes at T = 100 K and linear scan 136
4.9 The reciprocal space diffraction pattern of HK-plane around (11 -1 0) . . 137
4.10 The integrated intensity, FWHM, and correlation length as a function of
the temperature the ICM and CM modulated structures . . . . . . . . . 138

List of Tables
1.1 Comparison of the properties of neutrons and x-rays . . . . . . . . . . . . 3
1.2 Resonant enhancement for REXS . . . . . . . . . . . . . . . . . . . . . . 19
3.1 The Δq value table for each component at H = 4 T (NS) . . . . . . . . . 75
3.2 The Δq value table for each component at T = 110 K (NS) . . . . . . . 91
3.3 The Δq value table for each component at H = 4 T (NS) . . . . . . . . . 92
3.4 The Δq value table for each component at T = 140 K (REXS) . . . . . . 125
3.5 The Δq value table for each component at T = 135 K (REXS) . . . . . . 129

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