以第一原理計算探討應力下之複雜氧化物

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黃聖杰(Sheng-Chieh Huang) 查詢紙本館藏

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論文名稱

以第一原理計算探討應力下之複雜氧化物
(First-Principles investigations for complex oxides under stress)

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★ 固態甲烷在行星內部高壓下之熱性質

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摘要(中)

複雜氧化物的新穎性質是來自於電荷、晶格、自旋、和軌域的四個自由度的相互作用。由於此類材料的強關聯性，使得理論計算具有挑戰性。一種有效的方法是密度泛函理論加上 Hubbard U (DFT+U)，其中 Hubbard U 參數從第一原理自洽計算中得到 (Usc)。本論文中，我們展示了對鈷酸鍶 SrCoO3 (塊材與薄膜) 和含鐵菱鎂礦 (Mg,Fe)CO3 的 DFT+Usc 計算結果，如下所述:
(1) 塊材 SrCoO3:近年來，SrCoO3 在催化和燃料電池等領域的潛在應用，以及獨特的磁性性質而受人關注。實驗結果顯示，SrCoO3 在室溫壓下是立方晶系鈣鈦礦結構，具有鐵磁性金屬特性，而且可維持立方晶系鈣鈦礦結構至壓力約 60 GPa。中子粉末繞射實驗結果顯示 SrCoO3 的受壓小於 5.4 GPa 時，沒有自旋轉變的現象。我們的第一原理計算結果顯示，SrCoO3 的基態是具有 d6L 特徵的中自旋態鐵磁性金屬，鈷的價態幾乎像是三價鈷 (Co3+)。在約 7 GPa 壓力時，SrCoO3 會由中自旋態的鐵磁性金屬轉變為低自旋態的鐵磁性半金屬，其中低自旋態的磁矩主要貢獻來自氧原子，也展現了比中自旋態有著更多的 d6L 特徵。除此之外，我們也分析 X 光繞射實驗結果，顯示在自旋轉變時，會有約 1% 的異常體積縮減。(2) 薄膜 SrCoO3:磊晶應變薄膜的物性，相較於塊材，常會有很大的不同。SrCoO3 的高拉伸薄膜 (high tensile strain, ε ≳ 3%) 性質，至今仍不清楚，早期的計算預測此薄膜為反鐵磁性，但是近期實驗結果則顯示其為鐵磁性絕緣體。我們使用第一原理計算，深入研究了 SrCoO3 的拉伸薄膜，包括晶體結構、自旋態、磁性態，以及軌域態等方面。我們計算結果顯示了高拉伸薄膜具有高自旋態鐵磁性絕緣體的獨特性質，這一個獨特性質，必須同時滿足軌域有序、協同楊 − 泰勒效應以及八面體傾斜這些條件才能得到。
(3) 含鐵菱鎂礦 (Mg,Fe)CO3:研究碳礦物的基本物理化學性質，將有助於我們對地球內部碳循環的了解。一般而言，人們相信 (Mg,Fe)CO3 為地球下地函主要攜碳礦物之一，並且是地球內部碳循環的關鍵角色。實驗結果顯示，(Mg,Fe)CO3 是菱形晶系結構，具有絕緣體性質，在約 44−52 GPa 的壓力下，會觀察到異常現象，例如:異常體積縮減和異常彈性下降。我們的第一原理計算結果顯示，(Mg,Fe)CO3 的鐵含量不論是多少，約在 45−50 GPa 的壓力範圍內，會有高 − 低自旋態的轉變，且中自旋態不參與轉變過程。(Mg,Fe)CO3 在自旋轉變的過程中，也伴隨著異常體積縮減與異常彈性下降，並且所有計算結果皆與實驗觀察結果相符合。

摘要(英)

Complex oxides are considered promising functional materials, owing to their unique properties emerging from the intricate interplay between charge, lattice, spin, and orbital degree of freedom exhibited in this class of materials. Theoretical treatment for these materials has been challenging due to their strongly correlated nature. One promising approach is the density functional theory plus Hubbard U (DFT+U) method with the Hubbard U parameter computed from the first principles self-consistently (Usc). In this dissertation, we present our DFT+Usc calculation results for strontium cobaltite SrCoO3 (bulk and thin films) and ferromagnesite (Mg,Fe)CO3, as described below:
(1) Bulk SrCoO3: In recent years, SrCoO3 has attracted significant attention due to its potential applications in catalysis, fuel cells, and other fields, as well as its unique magnetic properties. In experiments, bulk Sr- CoO3 has been confirmed to be a ferromagnetic (FM) metal at ambient conditions and remains in cubic perovskite structure up to 60 GPa. Our calculations show the ground state of bulk SrCoO3 is a FM metal in an intermediate-spin (IS) state with d6L character: nearly trivalent cobalt (Co3+) accompanied by spin-down O-2p electron holes. We also show that SrCoO3 undergoes a transition from IS state FM metal to a low-spin state (LS) FM half-metal at around 7 GPa. Compared to the metallic IS state, the half-metallic LS state exhibits even more prominent d6L character, in- cluding nearly nonmagnetic Co3+ and exceptionally large oxygen magnetic moments. By analyzing x-ray diffraction data of compressed single-crystal SrCoO3, we point out an anomalous volume reduction of 1% when IS-LS spin transition.
(2) SrCoO3 thin film: Materials properties can be dramatically altered by strains. With epitaxial strain, thin-film materials often exhibit novel properties not found in their bulk counterparts. Bulk SrCoO3 has been known a ferromagnetic metal. The magnetic properties of epitaxial SrCoO3 thin films, particularly under high tensile strain (ε ≳ 3%), remain unclear. Previous calculations had predicted antiferromagnetic (AFM) states to be more energetically favorable in this regime, but recent experiments have suggested a FM insulating state. Using first-principles calculations, we perform an extensive search for the structural, spin, magnetic, and orbital states of SrCoO3 thin films. Our calculations present a novel state ex- hibiting FM insulating behavior, and this FM insulating state is achieved through complicated orbital ordering, cooperative Jahn−Teller distortion, and octahedral tilts.
(3) (Mg,Fe)CO3: Knowledge of carbon minerals in the Earth’s interior is key to understanding the Earth’s deep carbon cycle. (Mg,Fe)CO3 is believed to be the major carbon carrier in the earth’s lower mantle and play a key role in the earth’s deep carbon cycle. Experiments reveal that (Mg,Fe)CO3 has a trigonal crystal structure (R ̄3c) and exhibits insulat- ing properties. At pressures around 44−52 GPa, anomalous behavior are observed, including volume reduction and elastic anomalies. Our calculations indicate a high-spin (HS) to LS transition at 45−50 GPa without passing through the IS state, regardless of the iron concentration. All key calculation results, including the transition pressure, volume and elastic anomalies associated with the HS-LS transition, are in great agreement with experiments.

關鍵字(中)

★ 八面體傾斜
★ 自旋轉變
★ 軌域有序
★ 楊泰勒效應
★ 金屬-絕緣體轉變

關鍵字(英)

★ Spin transition
★ Metal−insulator transition
★ Orbital ordering
★ Octahedral tilt
★ Cooperative Jahn−Teller distortion

論文目次

目錄
頁次摘要 iii Abstract v
誌謝目錄圖目錄表目錄
ix
xi xv
xxvii
一、緒論 1
1.1 氧化物 ..................................................................... 1
1.2 Glazer notation .......................................................... 5
1.3 自旋態 ..................................................................... 8
1.4 楊 − 泰勒效應 ........................................................... 11
1.5 軌域有序與協同楊 − 泰勒效應 ...................................... 12
1.6 磁性 ........................................................................ 14
1.7 居里溫度 .................................................................. 17
1.8 塊材鈷酸鑭與塊材鈷酸鍶 ............................................. 18
1.9 論文架構 .................................................................. 19
二、計算方法 21 2.1 Density Functional Theory............................................ 21 2.1.1 Born-Oppenheimer Approximation ........................ 23
2.1.2 Hohenberg−Kohn Theorem.................................. 24
2.1.3 Kohn−Sham equation ......................................... 26
2.1.4 Exchange-Correlation Energy ............................... 29
2.2 Force and Stress ......................................................... 31 2.2.1 Force .............................................................. 31 2.2.2 Stress.............................................................. 32
2.3 DFT+U method......................................................... 33
2.3.1 Hubbard model ................................................. 34
2.3.2 Formulation...................................................... 34
2.3.3 Compute U (Linear response approach) .................. 38
2.3.4 Computation .................................................... 40
三、塊材鈷酸鍶 41
3.1 簡介 ........................................................................ 41
3.2 計算結果與討論 ......................................................... 43
3.3 小結 ........................................................................ 54
四、薄膜鈷酸鍶 55
4.1 簡介 ........................................................................ 55
4.2 計算結果與討論 ......................................................... 61
4.3 小結 ........................................................................ 72
五、含鐵菱鎂礦 73
5.1 簡介 ........................................................................ 73
5.2 計算結果與討論 ......................................................... 76
5.2.1 結論 ............................................................... 84
六、總結參考文獻
85 87
附錄 A 補充資料 99 A.1 Thermodynamic of the mixed spin state........................... 99
A.2 塊材鈷酸鍶的補充資料 ................................................ 101
A.2.1 磁矩 ............................................................... 101
A.2.2 U 值對轉換壓力的影響....................................... 102
A.2.3 實驗 XRD 數據................................................. 102
A.3 薄膜鈷酸鍶的補充資料 ................................................ 103
A.3.1 Pseudopotential convergence test...........................103 A.3.2 無八面體傾斜條件下的相對能量表與投影狀態密度
圖 ........................................................................... 105 A.3.3 IS-hm and HS-o3 在平衡體積下的電子結構與自旋
密度 ........................................................................ 107
A.3.4 HS-o3 在拉伸 3% 下的狀態密度............................ 110
A.3.5 HS-o3, HS-rs, and HS-c 在拉伸 3% 下的總磁化強度 . . 112
A.3.6 U 值是否對總能量高低排序與能帶結構有影響......... 114
A.3.7 居里溫度 ......................................................... 116
A.4 Calculation of exchange interaction and curie temperature ... 118
A.4.1 Exchange interaction (J).....................................118
A.4.2 Curie temperature..............................................124

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指導教授

徐翰

審核日期

2024-1-31

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