以第一原理計算研究雙鈣鈦礦中的反鐵磁半金屬

Abstract

在這篇論文裏，我們以雙鈣鈦(Double Perovskites， DP)結構為主，以第一原理計算研究可能存在的反鐵磁(Antiferromagnet, AFM)半金屬(Half-metal， HM) ，包括LaABB’O6、La2BB’O6及A2BB’O6系列(B，B’=過渡金屬，A=Ca，Sr，Ba)。考慮到過渡金屬氧化物的自旋─軌道耦合(Spin-orbital coupling，SOC)及電子關聯效應(Correlation effect)，我們所使用的計算方法包括GGA(Generalized-Gradient Approximation)、GGA+U、GGA+SOC+U，而使用計算程式包括VASP package(PAW法)及WIEN2k package(FLAPW法)。 在第一章裏，我們簡單介紹反鐵磁半金屬的歷史，以及多少特定的結構已被找尋為可能的反鐵磁半金屬 ?”、”我們找到那些可能的反鐵磁半金屬候選者 ?” 在第二章裏，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)、PAW法、FLAPW法、電子關聯效應(+U計算)、自旋─軌道耦合效應(+SOC計算)。 在第三章裏，我們簡介”什麼是反鐵磁半金屬 ?”，並且對過去十幾年來關於反鐵磁半金屬的理論預測文章作一回顧，以及”為什麼我們要選擇在雙鈣鈦結構中找尋反鐵磁半金屬 ?”，同時介紹兩類的雙鈣鈦堆疊結構 ([111]，[001])、兩類反鐵磁(AF-I，AF-II)、理論計算尋找的策略及計算程序，最後解釋形成反鐵磁之機制。 在第四章裏，針對LaABB’O6 系列，我們找到可能的候選者LaAWXO6 (A=Ca、Sr、Ba；X=Tc、Re)，加上2006年王銀國，郭光宇博士所找到LaAVOsO6，LaAM0XO6，以上為此一系列所有可能的反鐵磁半金屬的候選者。 在第五章裏，針對La2BB’O6系列，除了2009年王銀國、李柏翰、郭光宇博士所到可能的候選者La2VCuO6、La2VTcO6外，我們又找到La2VMnO6 (1998年，Pickett已預測，但Androulkis et al.的實驗顯示為HM-FiM)、La2VReO6、La2CrM0O6為可能的反鐵磁半金屬候選者。 在第六章裏，針對A2BB’O6系列，我們找到A2CrRuO6 (Lee and Pickett在2008年已預測)、A2M0OsO6、A2TcReO6為可能的候選者。 最後，我們總結所有理論預測結果(包括我們及他人的工作)於表7.1，並且以GKA (Goodenough-Kanamori-Anderson) rule給予解釋。而部份候選者如 LaAWTcO6、La2VReO6等等，是GGA+U計算後(即考慮電子關聯效應)才顯現出反鐵磁半金屬特性，但+U計算並非ab-initio計算，而是半經驗式的計算，當U變較大時，它們會變成絶縁體，所以尚待以後實驗証實。

In this thesis, we thoroughly investigated all the possible (C_2^29=406) candidates of half-metallic (HM) antiferromagnet (AFM) with the double Perovskites (DP) structure LaSrBB'O6, La2BB'O6 and Sr2BB'O6, where BB' pairs are any combination of two 3d, 4d and 5d transition elements except for La. Sr could also be replaced by Ca or Ba whenever HM-AFM was found and similar calculation was performed in order to probe more possibilities. Our calculations were based on density functional theory (DFT) with GGA, GGA + U and GGA + SOC approaches, where + U is the correction for electron correlation effect and + SOC is the correction for electron spin-orbit coupling effect. The crystal shapes and ionic positions were fully optimized using full-potential projector augmented wave (PAW) method within conjugate-gradient (CG) method implemented in VASP package (code). And we used the WIEN2k package with the all electron full-potential linearized augmented plane wave (FLAPW) method for calculating the electronic structures and magnetic properties. In the first chapter, we briefly introduced the history of HM-AFM, as well as 'how many HM-AFMs with specific structure has been found theoretically ?' and 'what we got in this series investigation ?' In chapter 2, we briefly 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, Full Linear Augmented Plane Wave (FLAPW) method, electron correlation effect (+ U calculation), spin-orbit coupling effect (+ SOC calculation). In chapter 3, we introduced 'what is HM-AFM', including its characteristics and properties. We also reviewed possible HM-AFM candidates hitherto 2010, 'why we search HM-AFMs on double perovskites (DP) structure ?' and introduce two kinds of DP stacked structures, AFMs, as well as our theoretical search strategy and calculation procedure and explained the formation of AFM. In chapter 4, for DP structure LaABB'O6 (A=Ca,Sr,Ba; B,B'=transition elements), we present LaAWXO6 where A=Ca, Sr, Ba and X=Tc, Re are potential candidates of HM-AFM. Among those HM-AFM candidates, LaAWReO6 (A=Sr, Ba) are more robust than others for the structural optimization. Including the previous Wang and Guo's work in 2006, we believe that we have found all possible HM-AFM candidates in LaABB'O6 compounds. In Chapter 5, for DP structure La2BB'O6, in 2009, while Wang, Lee and Guo found that La2VTcO6 and La2VCuO6 are promising candidates for HM-AFM, the search continued to other potential candidates of HM-AFM in the DP structure La2BB'O6. In this chapter, we present other two materials, La2VReO6 and La2CrMoO6 which are very likely candidates of HM-AFM. The DP La2VMnO6 with a $Fm bar{3}m$ structure was predicted by Pickett et al. as a HM-AFM based on first principle calculations, while Androulakis et al.'s experimental result showed that La2VMnO6 also exhibits the same structure as a ferrimagnetic (FiM) state. For thoroughly understanding what happens in the DP La2VMnO6 with a $Fm bar{3}m$ structure, we first calculated the fixed cubic $Fm bar{3}m$ structure before recalculating the structure through an optimization process. Our results show that La2VMnO6 is a FiM state in the fixed and volume-relaxed cubic $Fm bar{3}m$ structure. However, after full relaxation, it becomes a HM-AFM and remains the same even +U is taken into consideration. This recalculation illustrates that the magnetic state of the Mn ion is sensitive to the crystal field of MnO6 octahedron, and is the main reason behind the transformation of the magnetic state of La2VMnO6 from a FiM to a AFM state after full relaxation. Because the difference of total energy $ riangle$$E^{FiM-AFM}$ is small (merely about 57.1 meV/f.u.) and their space group in both FiM and AFM states La2VMnO6 are similar, we conclude that the decisive factor is the crystal field of the MnO6 octahedron, i.e. the distortion magnitude of the MnO6 octahedron, which is related to the process of synthesis and the presence of defects. Although Androulakis et al.'s experimental result show that this is a $Fm bar{3}m$/FiM state, we think that it is still possible for a I4/mmm/AFM state to exists. i.e. a HM-AFM La2VMnO6.

In chapter 6, for DP structures A2BBO6, we present A2MoOsO6, A2TcReO6, A2CrRuO6, where A=Ca, Sr, Ba, are potential candidates for HM-AFM. Also considered were the effects of spin-orbit coupling (SOC) and correlation by introducing +SOC and +U corrections. It is found that the SOC effect has much less influence than the correlation effect on the HM property of the compounds. For A2TcReO6 and A2CrRuO6 (A=Ca, Sr, Ba), after +U, they become Mott-Insulators. In the future, it is hoped that there will be further experimental confirmation for these possible HM-AFM candidates. In chapter 7, we listed all theoretical prediction results of DP structures LaABB'O6, La2BB'O6 and A2BB'O6 in Table ef{tb-conclusion}, including our works and others. We tried to give a explaination by GKA (Goodenough-Kanamori-Anderson) rule. For less robust HM-AFM candidates, such as LaAWTcO6, La2VReO6 $cdots$ etc, they exhibit the HM-AFM's characteristic after considering correlation effect. Since + U calculation is a semi-emperical calculation method, not eactly so-called $ab-initio$ calculation, and theoretical prediction for them will go to insulators if choose higher U value, the value of U need more accurate calculation or relevant experimental data.