近數十年來，過渡金屬氧化物中的物理性質備受矚目。在這些材料中，電子的自旋、電荷與軌道等自由度與晶格緊密的結合，產生了許多豐富而有趣的物理現象。本論文，藉由共振軟X光散射研究量子系統LiCu2O2以及CuO的多鐵相變與電子結構。
第一個研究主題是，LiCu2O2的磁相轉變與基態的性質，從共振軟X光散射結果顯示，沿著 c 軸方向磁矩間的相互耦合是產生鐵電性不可或缺的要素。接著，在CuO方面實驗結果指出，溫度低於230 K以下，長程磁有序形成。溫度介於213 ~ 230 K之間，此磁性結構與晶格不相稱；隨著溫度的降低，磁結構週期變為晶格的整數倍。
同時，一座新的軟X光非彈性散射儀亦被成功的測試完成。我們利用這項新的實驗技術，研究多鐵材料--LiCu2O2 與 CuO 的電子低能激發能譜，進而瞭解這類材料的細部的電子結構。

The physical properties of transition metal oxides have received much attention for decades. The interplay among spin, charge and orbital degrees of freedom coupled with the lattice of these materials results in interesting phenomena. In this thesis, we performed measurements of resonant soft x-ray scattering to investigate the electronic properties and multiferroic transitions of quantum spin systems.
We studied the magnetic transition as well as the ground-state properties of LiCu2O2. The results of soft x-ray scattering indicate that the spin coupling along the c axis is essential for inducing electric polarization. We also found that CuO exhibits a long-range magnetic ordering which is incommensurate with the lattice for temperature between 213 and 230~K. With further cooling, an incommensurate-commensurate transition sets in and the commensurate magnetic order appears.
In addition, a soft x-ray beamline was successfully commissioned for resonant inelastic soft x-ray scattering. With this new technique, we unraveled the dd excitations of multiferroic LiCu2O2 and CuO to understand their detailed electronic structure.

1 Introduction . . . . . . . . . . . . . . 1

2 Low-Dimensional Systems and Magnetoelectric Multiferroicity . . . . . . . . . . . . . 6
2.1 Magnetic Ordering . . . . . . . . . . . . . . . . . . 6
2.2 Low-Dimensional Quantum Spin System . . . . . . 8
2.3 Frustration . . . . . . . . . . . . . . . . . . . . 10
2.4 Magneto-electric Coupling . . . . . . . . . . . 12
2.5 Multiferroics . . . . . . . . . . . . . . . . . . . . 16

3 X-ray Spectroscopic Techniques . . . . . . . . . .35
3.1 Interaction between X-rays and Matters . .. . . . . 35
3.2 X-ray Absorption and Emission . . . . . . . . . . . 39
3.2.1 Photoemission Spectroscopy . . . .. . . . . . 39
3.2.2 X-ray Absorption . . . . . . . . . . . . . . 40
3.3 X-ray Scattering . . . . . . . . . . . . . . 41
3.3.1 Resonant X-ray Magnetic scattering . .. . . . . 47
3.3.2 Resonant Inelastic Soft-X-ray Scattering (RIXS) .. 51
3.4 Instrumentation . . . . . . . . . . . . . . . . . 57
3.4.1 Resonant Soft X-ray Magnetic Scattering . . . . 57
3.4.2 Resonant Inelastic Soft X-ray Scattering—Traditional
Designed . . . . . . . . . . . . . . . . 59
3.4.3 A Novel Design for Resonant Soft X-ray Inelastic Scattering. . . . . . . . . .64
3.4.4 Commissioning Results of Novel Soft X-ray Inelastic
Beamline . . . . . . . . . . . . . 69
3.4.5 Non-Resonant Inelastic Hard X-ray Scattering . . 74

4 Multiferroic Quantum Magnet of LiCu2O2 80
4.1 Introduction . . . . .. . . . . . . . . . . . . . . 80
4.2 Soft X-ray Absorption . . . . . . . . . . . . . . 89
4.3 dd excitations . . . . . . . . . . . . . . . 93
4.4 Multiferroic Transitions . . . . . . .. . . . . . . . 96

5 X-ray Spectroscopy of Cuprate CuO . . . . . . . . . 114
5.1 Introduction . . . . . . . . . . . . . . . . . . . 114
5.2 dd excitations . . . . . . . .. . . . . . . . . . . 118
5.2.1 Soft X-Ray Resonant Inelastic Scattering . . . . 118
5.2.2 Non-Resonant Inelastic X-ray Scattering . .. . 122
5.3 Magnetic Transitions . . . . . . . . . . . . . . 128

6 Conclusion and Future work 134

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