近期發現稀土鐵石榴石結構(R3Fe5O12, RIG)在低磁場下(2 kOe)具有顯著的磁介電耦合效應，相較於過去多鐵性材料中磁場須達到10 kOe以上才能引發的磁電耦合效應更有廣泛的應用前景。磁電耦合中的鐵電起因是很明確地，但是磁介電耦合中的介電響應具有多種起源，不同的起源將會以不一樣的方式與外加磁場耦合，進而引發不同的磁介電耦合機制，因此探討介電響應的起源則突顯其重要性。除此之外，介電是相對於非金屬材料而言，顯然磁介電材料的選擇必須由磁性氧化物來著手，因此本論文選用具代表性的鐵氧體R3Fe5O12 (RIG, R=Y, Tb, Lu)、R3-xBixFe5O12 (RIG:Bi, R=Y, Lu)以及Y3-xTbxFe5O12 (YIG:Tb)做為研究主軸，利用固相燒結法製備上述磁性氧化物陶瓷，搭配Rietveld方法精算結構原子位置，以利探討結構中多面體的扭曲對磁性的影響以及廣泛的溫度範圍內介電鬆弛的影響機制，企圖揭開多晶RIG材料的介電反應起源，主要成果概述如下。
(1) 所有樣品經由XRD確認後均為純相石榴石結構，並藉由Rietveld法精算結構後，發現氧配位多面體極度不對稱於中心陽離子，而摻雜Bi及Tb後的樣品其晶格常數也隨著濃度提升而逐漸增加，證實Bi與Tb確實進入晶格當中。XPS能譜分析中，除了發現主要的Fe3+外也包含相當多的Fe2+，且Bi2+也在YIG:Bi中被觀察到，但LuIG:Bi則沒有。
(2) 介電性質方面，未摻雜的RIG樣品利用實驗所獲得的介電、modulus以及阻抗數據，參照Debye與Maxwell-Wanger兩種理論模型來擬合並交叉比對，結果顯示在室溫下的介電鬆弛是由Debye模型主導過程，高溫時則是轉由Maxwell-Wanger效應主導。此外，LuIG的介電常數與YIG、TbIG相較起來也明顯大得多，其原因推論是由LuIG結構中FeO6及FeO4多面體的扭曲所造成，導致電子在四面體及八面體中產生躍遷現象時而貢獻出極大的偶極矩。互為固溶體的YIG:Tb，在量測溫度觀察到兩個階梯狀鬆弛，分別位於300-373 K與443-543 K，其中低溫鬆弛的活化能為0.38 eV與Fe2+極化子的熱活化有關，高溫鬆弛的活化能介於1.32-1.01 eV之間則是與氧缺陷有關，且存在於TbIG中的Fe2+/Fe3+發生電荷躍遷時也會比YIG中還快。在摻雜Bi的體系中，LuIG:Bi於室溫下的介電常數以及高溫區Maxwell-Wanger效應皆隨著Bi增加而下降；而YIG:Bi在室溫下的介電常數則是先由低濃度的增加(x<0.4)到最後迅速地下降(x≥0.6)，且階梯狀的鬆弛現象亦隨著摻雜濃度提升後往高溫方向偏移，推論變價離子的濃度主導整體的介電鬆弛行為。
(3) 磁性性質方面，無磁性的Bi離子佔據24c位置時，居禮溫度(Tc)均伴隨著Bi含量提升而增加，而飽和磁化量(Ms)在YIG:Bi中則反之，但是在LuIG:Bi中卻變化不大。藉以Bloch定律擬合YIG:Bi的Ms-T曲線，其中T3/2項的顯著變化證明Bi在晶格內產生強烈的交換偶合。在YIG:Tb中，Ms-T曲線則觀察到補償溫度由x=3的256 K下降到x=1的77 K。
(4) 針對LuIG:Bi進行磁電效應分析，由結果顯示當外加磁場<1500 Oe時，磁電係數隨Bi濃度提升而銳減，由x=0的0.29 mV/cmOe下降至x=0.9的0.012 mV/cmOe。此外，於外加磁場<400 Oe觀察到正磁致伸縮，而高於500 Oe則是發生負磁致伸縮，其結果符合於柯爾效應(MOKE)的Ms-H曲線於400 Oe所觀察到的磁矩翻轉點。

In this study, a range of polycrystalline rare-earth iron garnets (RIG) were synthesized by the solid state reaction method, including R3Fe5O12 (R=Y, Tb and Lu), R3-xBixFe5O12 (R=Y and Lu, x=0.2-1.0) and Y3-xTbxFe5O12 (x=1.0-3.0). The crystal structures of the samples were refined by the Rietveld method, which showed that the oxygen coordination polyhedra in RIG were highly asymmetric against the central cations. X-ray photoelectron spectroscopy showed small amount of Fe2+ in addition to the dominant Fe3+ in most of the obtained samples. A mixed oxidation state of Bi3+/Bi2+ was also observed in Y3-xBixFe5O12 but absent in Lu3-xBixFe5O12. The dielectric responses of the samples were studied in detail by cross examination of the permittivity, modulus and impedance presentations. Fitting the experimental data with the Debye and Maxwell-Wagner models revealed that the dielectric relaxation at room temperature was dominated by the Debye-type process while at elevated temperature the Maxwell-Wagner response gradually took over. Electron hopping between Fe2+/Fe3+ and Bi2+/Bi3+ may be responsible for the observed behaviors. At low temperature, electron hopping was localized and therefore described well by the Debye-type relaxation. As the temperature increased, electron hopping became long-range, crossing over grain boundaries frequently, and hence showed the Maxwell-Wagner response owing to the large difference in impedance between the grain and grain boundary. Compared to YIG and TbIG, the low frequency permittivity of LuIG was much larger. This may be explained by the large difference between the distortions of FeO6 and FeO4 in LuIG and therefore, a large dipole moment was created when the electron hopping between the octahedral and tetrahedral sites took place. In addition to the dielectric properties, the magnetic and magnetoelectric properties were also studied and discussed in correlation with their structure distortions and defects.

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