臺灣博碩士論文加值系統

過渡金屬氧化物中，電子的電荷、軌域以及自旋之間的交互作用與其豐富的物理現象有著緊密的關係。本論文研發共振軟X光磁散射技術，並直接量測過渡金屬氧化物中，3d電子的電荷、軌域以及自旋有序。
利用共振軟X光散射技術，本論文的實驗結果提供四氧化三鐵(Fe3O4) 的電荷及軌域有序排列的決定性證據，並探討其Verwey 相變與電荷軌域有序的關係。在Verwey 相變溫度附近，Fe3O4的電阻值有一熱滯後(thermal hysteresis)現象，與共振軟X光散射強度對溫度的變化一致，說明Verwey 相變為電荷軌域有序相變。
我們亦闡明鋱錳氧化物(TbMn2O5)的多鐵電性現象 (multiferroicity) 之微觀機制的基本對稱性，實驗結果顯示鋱錳氧化物的多鐵電性現象決定於材料的磁結構與對稱性。TbMn2O5的有序反鐵磁結構產生一個等效「內電場」，進一步藉由磁電效應(magnetoelectric effect)產生電極化，而形成多鐵電性現象。
本論文的第三個主題是半摻雜單層錳氧化物的反鐵磁相變，與其電荷軌域有序的陽離子半徑效應。共振軟X光散射結果顯示，釙鈣錳氧化物的電荷軌域有序現象比鑭鍶錳氧化物更具有三維的特性。我們並發現鑭鍶錳氧化物在三維反鐵磁相變溫度以上時，具有二維短程反鐵磁有序排列。隨著溫度下降，二維反鐵磁有序相關長度（correlation length）呈現指數函數形式的增加，然後轉變成三維反鐵磁有序。

ABSTRACT

In some transition-metal oxides, strong interactions among electronic spins, charge,
and orbitals are intimately connected to a rich variety of physical phenomena. We
developed an experimental technique of resonant soft x-ray scattering to detect charge,
orbital and spin ordering of novel oxides. With the photon energy about the L-edge (2p →
3d) of transition metal ions, resonant soft-x-ray scattering is a dipole-allowed transition
and suitable for probing the ordering of 3d states directly and with high sensitivity.
Magnetite exhibits a metal-to-insulator transition known as the Verwey transition.
Although magnetite is believed to be a classic example of charge ordering, the existence of
its charge ordering has been an issue for longer than half a century. We report experimental
evidence for the charge-orbital ordering in magnetite below the Verwey transition.
Measurements of O K-edge resonant x-ray scattering on magnetite reveal that the O 2p
states in the vicinity of the Fermi level order along the c axis with a spatial periodicity
twice the lattice parameter in the undistorted cubic phase. Such a charge-orbital ordering
vanishes abruptly above the transition and exhibits a thermal hysteresis, correlating closely
with the Verwey transition.
We also present studies on the multiferroelectric phenomenon of frustrated magnets
derived from magnetism. Based on measurements of soft-x-ray magnetic scattering and
symmetry considerations, we demonstrate that the magnetoelectric effect in TbMn2O5
arises from an internal field determined by Sq × S-q with Sq being the magnetization at
modulation vector q. Our results set fundamental symmetry constraints on the microscopic
mechanism of multiferroicity in frustrated magnets.
The third subject is on the quasi-2D magnetic ordering of layered manganites and

their charge-orbital ordering associate with different sizes of cations. Orbital ordering of
Pr0.5Ca1.5MnO4 exhibits a stronger three-dimensional character and a dramatically
enhanced transition temperature, as compared with those of La0.5Sr1.5MnO4. The
correlation length of orbital ordering along the c-axis in Pr0.5Ca1.5MnO4 is about half of the
in-plane one. Our results indicate that reductions in the one-electron bandwidth and
quenched disorder strongly enhance the stabilization of charge-orbital ordering. In addition,
we investigated the antiferromagnetic (AFM) transition of La0.5Sr1.5MnO4 and found that
quasi-2D incommensurate AFM short-range order exhibits at temperatures above the Neel
temperature (TN). The spin correlation follows the same exponential growth in inverse
temperature as those observed in quantum Heisenberg antiferromagnets. When the
temperature cools across TN, on top of the dimensional crossover, the 2D incommensurate
AFM order collapses to stabilize the 3D commensurate AFM order.

1 Strongly Correlated Electronic System 6
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Mott-Hubbard Insulator . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Jahn-Teller Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Charge-Orbital Order . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Experimental Techniques and Setup 12
2.1 Resonant Soft x-ray Scattering . . . . . . . . . . . . . . . . . . . . . . 12
2.1.1 Azimuthal-Dependence of Scattering Intensity . . . . . . . . . 16
2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 The EPU Beamline . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 The UHV Diffractometer . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Detector and Electronics . . . . . . . . . . . . . . . . . . . . . 20
2.2.4 Sample Manipulator . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.5 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Charge-Orbital Order in Magnetite 26
3.1 Fundamental Issues about Magnetite . . . . . . . . . . . . . . . . . . 26
3.1.1 Verwey Transition . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Experimental Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Fe L-edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 O K-edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Antiferromagnetic order in TbMn2O5 38
4.1 Introduction of Multiferroelectric . . . . . . . . . . . . . . . . . . . . 38
4.1.1 The Structure of TbMn2O5 . . . . . . . . . . . . . . . . . . . 39
4.2 Experimental Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1
CONTENTS 2
5 Charge, Orbital, and Spin Order in Layered Manganite 48
5.1 Effect of One-electron Bandwidth and Quenched Disorder . . . . . . . 48
5.1.1 Charge, Orbital, and Antiferromagnetic order of La0.5Sr1.5MnO4
and Pr0.5Ca1.5MnO4 . . . . . . . . . . . . . . . . . . . . . . . 50
5.1.2 Experimental Result . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Quasi-Two-Dimensional Antiferromagnetism in LSMO . . . . . . . . 65
5.2.1 Low-Dimensional Quantum Magnetism . . . . . . . . . . . . . 65
5.2.2 Antiferromagnetic Transitions of LSMO . . . . . . . . . . . . 68
5.2.3 Resonant Soft x-ray Scattering . . . . . . . . . . . . . . . . . . 70
5.2.4 Incommensurate AFM Order above the Neel Temperature . . 72
5.2.5 Incommensurate-to-Commensurate AFM Transition . . . . . . 77
6 Conclusions 80
Bibliography 82
A Comparison of Magnetic Soft X-Ray and Neutron Scattering 92
B List of Publications 94

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