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研究生： 黃治融
Huang, Jhih-Rong
論文名稱： 利用密度泛函理論計算研究MnFe2O4和NiMn2O4的物理特性
Physical properties of MnFe2O4 and NiMn2O4 using density functional theory calculations
指導教授： 鄭靜
Cheng, Ching
學位類別： 博士
Doctor
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 92
中文關鍵詞： 密度泛函理論 、尖晶石結構 、磁性
外文關鍵詞： density functional theory, spinel structure, magnetic property
相關次數： 點閱：90  下載：5 
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    • MnFe2O4 (MFO) 和 NiMn2O4 (NMO) 一般是由不同反係數(inversion parameters (ν))的正尖晶石結構跟反尖晶石結構共同組成的。藉由密度泛函理論和站點庫倫效應，我們計算了陽離子的分布以及磁偶極矩的排列，並從中找出了最穩定的基態。在MFO中，正間晶石結構的磁偶極矩可以從四面體內的高自旋(high-spin)的Mn2+ 計算得知，而反尖晶石結構的磁偶極矩可以從八面體內的居中自旋(intermediate-spin)的Mn2+ 計算得知。而NMO中，正間晶石結構的磁偶極矩可以從四面體內的Mn3+ 計算得知，而反尖晶石結構的磁偶極矩可以從四面體內的的Mn2+ 與八面體內的Mn4+ 計算得知。這代表在MFO中的Mn是單一價電子，而NMO中的Mn是混合的價電子。在計算了12.5%的交換陽離子的混合態(ν(MFO)=0.125 和 ν(NMO)=0.875)，我們發現NMO的混合態中，在類似參雜的狀態的影響之下，能隙寬度被大大的減少至0.35 電子伏特。這可能是造成NMO的電阻負溫度係數效應的原因。
    關鍵字: 密度泛函理論(density functional theory)，尖晶石結構(spinel structure)，磁性(magnetic property)

    MnFe2O4 (MFO) and NiMn2O4 (NMO) generally crystallize in a mixed phase consisting of both the normal and inverse spinel with different inversion parameters (ν). By employing the density-functional theory (DFT) and the on-site Coulomb effect (U), cation distributions and magnetic ordering of MFO and NMO are explored and then the ground state of these two materials is found. In MFO, the magnetic moment can be calculated by high-spin Mn2+ at the tetrahedral site in the normal spinel and intermediate-spin Mn2+ at the octahedral site in the inverse spinel, while in NMO, the magnetic moment can be calculated by Mn3+ at tetrahedral site in the normal spinel and Mn2+ and Mn4+ at tetrahedral site and octahedral site respectively in the inverse spinel. This means that, the single-valence state is found in MFO while the mixed valence state is found in NMO. As the 12.5% mixed phase (ν(MFO)=0.125 and ν(NMO)=0.875) are calculated, we found that the band gap is strongly reduced to 0.35 eV by the doped-like state in the mixed NMO phase. This may be the origin of the negative temperature coefficient of resistant in NMO.

    1 Introduction 9 1.1 MnFe2O4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 NiMn2O4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Calculation methods 17 2.1 Density functional theory and local density approximation . . . . . . . . . . . . . . 17 2.2 Bloch’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Plane wave expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4 Spin density functional theory and local spin density approximation . . . . . . . . . 24 2.5 Hubbard U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.6 Heisenberg model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Calculation details 33 3.1 Structure and cation distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2 Magnetic configurations and exchange interactions . . . . . . . . . . . . . . . . . . . 36 3.3 Selection of the Hubbard U values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4 Numerical accuracy in the calculations . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 MnFe2O4 41 4.1 Ground state and electronic property of MnFe2O4 . . . . . . . . . . . . . . . . . . 41 4.2 Magnetic property and cation valence of MnFe2O4 . . . . . . . . . . . . . . . . . . 48 4.3 Density of states and the single valence of Mn . . . . . . . . . . . . . . . . . . . . . 51 4.4 Exchange interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.5 Mixed phase of inversion parameter = 0.125 . . . . . . . . . . . . . . . . . . . . . . 60 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5 NiMn2O4 65 5.1 Ground state and electronic property of NiMn2O4 . . . . . . . . . . . . . . . . . . 65 5.2 Magnetic property and cation valence of NiMn2O4 . . . . . . . . . . . . . . . . . . 72 5.3 Mixed state of inversion parameter = 0.875 . . . . . . . . . . . . . . . . . . . . . . . 73 5.4 Exchange interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6 Conclusion 79 A Additional gures and tables in chapter4 81 B Additional gures and tables in chapter5 85 Bibliography 89

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