在這篇論文中，我們以鍶基底的雙鈣鈦(Sr-based Double Perovskites)結構，以第一原理計算找尋可能存在的半金屬。在Sr2BB′O6中(B,B’=過渡金屬)找到三個系列的半金屬組合，另外也A2Fe(Cr)MO6 (A=IVA族元素, M=Mo, Re and W)找到半金屬的一系列候選材料。我們使用的計算程式為VASP根據密度泛函(DFT)理論來計算材料的結構最佳化，從最初的四種磁相態出發：鐵磁(FM)、亞鐵磁(FiM)、反鐵磁(AFM)與無磁性(NM)，其中使用廣義梯度近似(GGA)以及考慮庫倫排斥效應(GGA+U)。

在第一章中，我們簡單介紹磁性半金屬過去的研究發展，以及我們找到那些可能的磁性磁半金屬候選者。

在第二章中，我們簡單介紹相關的理論及計算方法，包括Born-Oppenheimer 近似、密度泛函理論(DFT)。其中包括Hohangberg-Kohn理論、Kohn-Sham方程式
、交換關連效應、侷域密度近似(LDA)與廣義梯度近似(GGA)。使用的計算程式為VASP，其使用擴增平面波方式來計算。並且最後介紹庫倫電子關聯效應(LDA/GGA+U)。

在第三章中，我們簡單介紹磁性半金屬的特性，並且對過去十幾年來關於磁性半金屬材料的研究發展做一些簡介。並且詳細介紹雙鈣鈦結構以及初始的四種磁相態。最後，我們介紹整個研究的計算流程與計算的設定參數以及造成半金屬的重要物理機制-雙交換作用(double exchange)。

在第四章中，將會詳細介紹在緦基底的雙鈣鈦結構(Sr2BB′O6, B,B’=過渡金屬)中，我們找尋到三個系列的半金屬候選人，此分類的方式是根據BB′離子在週期表上分部的組合。第一系列為：Sr2Cr(Co)B′O6 (B′=Sc, Y, La, Ti, Zr 與Hf) 以及 Sr2V(Fe)B′O6 (B′= Zr 與Hf)。在第一系列中最有可能成為半金屬的為Sr2CrScO6、Sr2CrLaO6、Sr2CrTiO6、Sr2VZrO6以及Sr2VHfO6這些材料。第二系列為Sr2BB′O6 (B = Co, Cu 與Ni; B′ = Mo, W, Tc 與Re)，最有可能成為半金屬的是Sr2FeTcO6、Sr2CoWO6 與 Sr2NiTcO6。第三系列為Sr2ZnBO6 (B=Mn, Tc, Re, Fe, Ru, Os, Co, Ni, Pd 與Au)，其中Sr2ZnMnO6與Sr2ZnPdO6是半金屬材料的最佳選擇。整體的篩選是建構在比較不同磁相態的能量，並且同時在GGA與GGA+U兩種不同的情況皆為穩定才能脫穎而出。
在第五章中，我們基於Sr2FeMoO6可以將緦(Sr)置換為IVA族元素的想法，來發展出A2Fe(Cr)MO6(A=IVA族元素, M=Mo, Re 與W)的半金屬系列材料。這樣的想法是基於IIA(s2)族元素與IVA(p2)的外層價電子非常相似的緣故。結果顯示在A為錫(Sn)與鉛(Pb)是較為穩定並且較有可能被合成的半金屬候選材料。

最後，我們總結所有理論預測結果並且重述造成半金屬的物理機制。

我們希望這篇論文可以在尋找半金屬材料方面的研究提供一些有用的訊息，希望對於未來合成半金屬材料的實驗能有所幫助。

In this thesis, we thoroughly investigated three possible candidates series of half-metallic (HM) in the double perovskites structure Sr-based double perovskites Sr2BB′O6 (BB′=transition metal ions) and A-site substitution double perovskites A2Fe(Cr)MO6 (A=IVA group elements, M=Mo, Re and W). The calculation is based on the density functional theory (DFT) with full-structure optimization by generalized gradient approximation (GGA) and consideration of the strong correlation effect (GGA+U) and started with 4 types of initial magnetic states, i.e. ferromagnetic (FM), ferrimagnetic (FiM), antiferromagnetics (AF) and nonmagnetic (NM) using full-potential projector augmented wave (PAW) method within conjugate-gradient (CG) method implemented in VASP package (code).

In the first chapter, we briefly introduced the previous researches of HM compounds and what series investigation that we had done.

In chapter 2, we introduced the Born-Oppenheimer approximation, DFT (including Hohangberg-Kohn theorems, Kohn-Sham equations, exchange-correlation functional, local (spin) density approximation (L(S)DA) and generalized-gradient approximation (GGA)), as well as computational methods we used, including Projector Augmented Wave (PAW) method in VASP code and electron correlation effect (+U calculation).

In chapter 3, we introduced its characteristics and properties of HM materials with reviewing the different structures that had been discovered. The detail of double perovskites structure and the initial magnetic states configurations are also introduced in this chapter. In the end, the calculation procedure with detailed setting parameter and double exchange mechanism of causing HM characteristics are schematic diagramed.

In chapter 4, for Sr-based double perovskites Sr2BB′O6 (BB′=transition metal ions), we classified the possible HM compound into 3 groups according to the electronic configuration of the BB′ ion pairs. In Group 1: Sr2Cr(Co)B′O6 (B′=Sc, Y, La, Ti, Zr, and Hf) and Sr2V(Fe)B′O6 (B′= Zr and Hf), the most promising candidates are Sr2CrScO6, Sr2CrLaO6, Sr2CrTiO6, Sr2VZrO6 and Sr2VHfO6. In Group 2: Sr2BB′O6 (B = Co, Cu, and Ni; B′ = Mo, W, Tc, and Re), Sr2FeTcO6, Sr2CoWO6 and Sr2NiTcO6 are the most possible HM candidates. And for Group 3: Sr2ZnBO6 (B=Mn, Tc, Re, Fe, Ru, Os, Co, Ni, Pd, and Au), the best choices for HM materials are Sr2ZnMnO6 and Sr2ZnPdO6. The selection is based on the energy differences between F(i)M and AF state in both GGA and GGA+U scheme.

In chapter 5, for A-site substitution double perovskites A2Fe(Cr)MO6 (A=IVA group elements, M=Mo, Re and W), based on Sr2FeMoO6, we substituted the Sr ion with IVA group elements according to the similar valence electrons noting as IIA(s2) and IVA(p2). The results shows that choosing A= Sn and Pb can be able to synthesize stable HM double perovskites compounds.

In the last chapter, we will make a summary of our work including the research method, the main results and the mechanism of causing HM compounds.

We hope that this thesis on the searching HM compounds in double perovskites structures are useful for experimental research and bring up the research upsurge of HM materials.

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