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研究生:黃鴻隆
研究生(外文):Hung-Lung Huang
論文名稱:第一原理理論計算研究霍伊斯勒合金與多鐵氧化物之物理特性
論文名稱(外文):First-Principle Studies of Physical Properties of HeuslerAlloys and Multiferroic Oxides
指導教授:郭光宇郭光宇引用關係
口試委員:梁贊全胡崇德薛宏中魏金明
口試日期:2015-07-27
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:98
中文關鍵詞:自旋極化異常霍爾效應自旋霍爾效應電極化
外文關鍵詞:spin polarizationanomalous Hall effectspin Hall effectelectric polarization
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我們利用能帶理論研究霍伊斯勒合金(Heusler arroys) 和多鐵氧化物(Multiferroic oxides) 的物理特性。首先我們以第一原理計算研究霍伊斯勒化合物Co2FeX (X= Al, Ga, In, Si, Ge 和Sn) 的異常霍爾效應及自旋極化。我們發現Co2FeX (X= Al, Ga, In, Al0.5Si0.5 和Sn) 的縱向電流(longitudinal current) 自旋極化(PL) ∼ 100% 。其它化合物雖然不是百分百自旋極化, 亦有相當高的自旋極化PL > 85%。令人感到有趣的是, 計算 Co2FeX (X= Si, Ge 和Sn) PD 值為負的, 其符號與PL 和傳輸實驗結果相反。第二點,計算所得異常霍爾電導(AHCs) 值是適中的, 大約在200 S/cm , 與L21 結構Co2FeSi
的實驗結果高度吻合。第三點, 就計算所得總磁矩而論, 除了Co2FeSi 以外, 所有化合物的總磁矩與實驗結果吻合良好。我們同樣進行了GGA+U 計算, 發現U 值對總磁矩、自旋極化率和AHC 均有明顯影響, 而在大多的系統中計算結果並不符合實驗結果。這些有趣的發現將在本文裡藉由能帶結構來討論。
接著我們研究多鐵材料中鐵電極化的來源及機制。我們選了兩個系統BiMnO3 和Li(Na)Cu2O2 , 分別為C2/c 和Pnma 結構。我們發現BiMnO3 磁結構基態不是共線的(noncollinear), 其在x 和z 方向具有反鐵磁性, 而在y 方向則為鐵磁性。其單位分子式具有的淨磁矩為3.98 μB, 與實驗結果非常吻合。另一方面, 我們亦進行這些材料的電極化計算,發現基態磁結構不具有電極化。然而在磁結構AF2 (反鐵磁) 和Fe2 (亞鐵磁) 下卻得出龐大的電極化。這一有趣現象是由於磁結構AF2 與Fe2 破壞了BiMnO3 空間反轉對稱性所致, 而誘發的電極化大小與反鐵磁磁矩的大小有強烈關聯, 也就是說只要磁結構稍微偏離空間反轉對稱即會產生明顯的電極化。
同樣地使用GGA+U 計算來研究LiCu2O2 和NaCu2O2 , 這兩個化合物在結構上十分相似, 因此計算結果顯示這兩種化合物具有幾乎相同的物理特性, 如電子結構、磁性和鐵電性等。然而這結果與實驗結果卻不相符, 實驗結果指出LiCu2O2 具有鐵電性, NaCu2O2則無。若考慮CuO ribbons 上延著y 軸方向為spin-spiral , 且相鄰ribbon 的chirality相反。NaCu2O2 在這種磁結構下顯示為反鐵電性, 可以成功解釋實驗所得結果。然而不幸的是, LiCu2O2 在這情況下計算結果反而不具鐵電性了, 又與實驗不相符。也許Li 和Cu原子在LiCu2O2 內互相擴散(interdiffusion), 而Na 和Cu 原子在NaCu2O2 內無互相擴散可以用來解釋這一窘境。而GGA+U 計算所得電子結構又與XAS 測量結果高度吻
合, 似乎又駁斥了上述可能的解釋。
綜合上述, 本論文以第一原理能帶理論計算並分析以上霍伊斯勒合金與多鐵氧化物的物理性質, 所得結果在定量上或定性上與既有的實驗值符合。希望這些詳盡完整的能帶計算結果有助於瞭解這些材料的微觀理論機制, 也希望對這些材料在未來的科技應用與發展有所貢獻。

We perform a systematic ab initio study of two principal spin-related phenomena,namely, anomalous Hall effect and current spin polarization, in Co2Fe-based Heusler compounds Co2FeX (X = Al, Ga, In, Si, Ge, Sn) in the cubic L21 structure. First, we find that the spin-polarization of the longitudinal current (PL) in Co2FeX (X = Al, Ga, In, Al0.5Si0.5 and Sn) approximately equals to 100 % The other compounds also have a high current spin polarization with PL larger than 85%. Interestingly, PD is negative in Co2FeX (X = Si, Ge and Sn), differing in sign from the PL as well as that from the results of transport experiments. Second, the calculated anomalous Hall conductivities (AHCs) are moderate, being within 200
S/cm, and agree well with the results of experiments on highly L21 ordered Co2FeSi specimen. Third, the calculated total magnetic moments are consistent with the
corresponding experimental ones in all the studied compounds except Co2FeSi.
We also performed the GGA plus on-site Coulomb interaction U calculations. We found that including the U affects the calculated total magnetic moment, spin polarization and AHC significantly. Meanwhile, unfortunately, this results in a disagreement with the available experimental results. All these interesting findings are discussed in terms of the underlying band structures.
We also study the physical mechanism for ferroelectric polarization of multiferroic oxide, such as BiMnO3 and Li(Na)Cu2O2 with C2/c and Pnma structures. We found that the ground state of magnetic structure of BiMnO3 is noncollinear, the x- and z-directions are antiferromagnetic, the y-direction is ferromagnetic. The net magnetic dipole moment is 3.98 μB per chemical formula and it is consistent with experiment results. We also performed the electric polarized calculations using Berry phase method. The findings indicate that there is significant electric-polarization at both antiferromagnetism (AF2) and ferrimagnetism (Fe2), but there is no electricpolarization at the ground state of FM. This interesting phenomenon comes from the breaking of the spacial inversion symmetry. The magnitude of electric polarization is related strongly with the magnitude of antiferromagnetic moment.
We also perform the GGA+U method to study both LiCu2O2 and NaCu2O2. Their structures are very similar, Therefore, both compounds exhibit almost identical
physical properties, such as electronic structure, magnetism and ferroelectricity. However, experimental results show that LiCu2O2 is multiferroic, but NaCu2O2 is
not. Antiferroelectricity in NaCu2O2 could be explained by multiple spin-spiral CuO ribbons along the y-axis with opposite chiralities. However, this would leave the ferroelectricity in LiCu2O2 unexplained. Interdiffusion of Li and Cu in LiCu2O2 while no interdiffusion of Na and Cu in NaCu2O2 could be a resolution. However, the
good agreement in electronic structure between the XAS measurement and GGA+U calculation suggest that this is unlikely the explanation.
We have carried out a systematic ab initio study of the magnetic properties of Heusler compounds and multiferroic oxide. These findings suggest that our simulation results are consistent with that of experiments. We hope that our systematic studies can help to understand the microscopic mechanism and have some benefits to the development of related applications.

誌謝vii
摘要ix
Abstract xi
1 緒論1
1.1 自旋電子學概論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 半金屬材料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 多鐵材料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 本論文章節安排. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 能帶理論與計算方法9
2.1 密度泛函理論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Hohenberg-Kohn 原理. . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Kohn-Sham 方程式. . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.4 交換關聯泛函近似. . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 求解晶體電子本微方程. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 擴增平面波方法(APW method) . . . . . . . . . . . . . . . . . 19
2.2.2 線性擴增平面波方法(LAPW method) . . . . . . . . . . . . . . 20
2.2.3 全位勢線性擴增平面波(FLAPW) 方法及所有電子(all-electron)
計算. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 簡介自旋極化與LDA+U 計算方法. . . . . . . . . . . . . . . . . . . . 22
3 霍伊勒合金之自旋極化與異常霍爾效應29
3.1 引言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 理論和計算方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 異常及自旋霍爾電導率. . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 電流自旋極化率. . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 磁矩與能帶結構. . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 異常與自旋霍爾電導. . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.3 電流自旋極化. . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.4 晶格點上庫侖作用力效應(Effect of on-site Coulomb interaction) 44
3.4 小結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4 BiMnO3 之鐵磁與鐵電性質51
4.1 背景與研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2 結構簡介與計算方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.1 共線磁結構的穩定性(stability) 分析. . . . . . . . . . . . . . . 56
4.3.2 非共線磁結構的穩定性分析. . . . . . . . . . . . . . . . . . . . 60
4.3.3 鐵電極化. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Li(Na)Cu2O2 的物理性質65
5.1 背景簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 結構簡介與計算細節. . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6 結論與展望75

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