在此論文中，我們以共振非彈性X光散射(RIXS)來研究兩種代表性的樣品：高溫超體Bi1.5Pb0.6Sr1.54CaCu2O8+δ (Bi2212) 以及第一個被人類發現的磁性物質- 四氧化三鐵。由於自旋波動被認為是高溫超導機制的一個重要因素，因此探測高溫超導體的磁性激發成為此領域的重要課題。然而理論上對於此磁性激發的成因仍存有爭論。藉由不同入射光偏振，我們發現兩種截然不同磁性激發 - Raman形式和Fluorescence 形式。當入射光偏振方向在散射光平面時，其磁性激發為Raman形式，也就是其激發態能量不隨著入射光能量改變。結合RIXS和精確對角化計算，我們證明Raman形式的磁性激發本質上確實是集體磁性激發態(collective magnetic excitation)。

從發現四氧化三鐵的Verwey 相變以來，其引起電導率異常降低與同時結構改變的機制引發了許多研究。在此我們使用RIXS探測四氧化三鐵中的局部電子結構。藉由其共振特性我們觀測到Fe3+的定域磁性激發以及由自旋與軌域交互作用形成的Fe2+ dd激子。藉由multiplet 理論計算我們得到 FeO6的tetragonal變形其強度為Δt2g=-80meV。RIXS的溫度變化結果顯示此變形在四氧化三鐵的高溫態就已存在。

Resonant inelastic X-ray scattering (RIXS), a photon-in and photon-out spectroscopy method, has been used to probe two representative compounds, the optimally doped superconducting cuprate Bi1.5Pb0.6Sr1.54CaCu2O8+δ (Bi2212) and the first magnetic material found by mankind - magnetite Fe3O4. Investigation of collective magnetic excitations in cuprate superconductors is an important subject in searching the paring mechanism of high Tc superconductivity. In comparison with inelastic neutron scattering, RIXS reveals the existence of high-energy magnetic excitations in doped superconducting cuprates.
However, the interpretation of such excitations remains in dispute. Here we show the dependence of Cu L3 RIXS on the energy and polarization of incident photons in optimally doped high-Tc cuprate superconductors Bi2212. Two distinct types of excitations, Raman-like and
fluorescence-like, were observed by using π- and σ-polarized incident X-rays, respectively. Combined with calculations of exact diagonalization, we demonstrate
the nature of collective damped magnetic excitations measured with -polarized RIXS.

Fe3O4 has been studied for decades to understand the Verwey transition. The mech-
anism of the simultaneous drop of electric conductivity and a complex structural phase
transition has been one of the most extensively studied problems in condensed matter physics. We used RIXS to unravel the local electronic structures of different Fe sites in Fe3O4. Local spin excitations are observed on the octahedral Fe3+ sites with an effective exchange field of 90 meV. Markedly we found a broad excitation feature with an energyof 200 meV for Fe2+. With the help of multiplet calculations, a tetragonal distortion of
strength t2g = 􀀀24 meV on the t2g orbitals was deduced. Our temperature-dependent RIXS spectra indicate that such local distortion already exists above the Verwey transition temperature and even up to 475 K.

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