| 摘要: | 多鐵性材料的多項新奇物理性質，主要與其特殊的電子結構有關。拜最近發展的 LDA+U 方法之賜，我們才得以一窺多鐵性材料中，同時具備鐵電性與鐵磁(或反鐵磁) 特性之奧妙。LDA+U 計算方法，主要是在靜態密度泛函理論(static DFT)的基礎上，加 入哈柏(Hubbard)形式之局域庫倫位勢U。雖然，過去研究顯示，透過LDA+U 計算方 法，能清楚地說明多鐵性材料中的鐵電性，可能由晶體結構效應或更複雜的電子相關 作用(例如:電子軌道有序、電子電荷有序及電子自旋有序)所引起。然而，一般計算中， 局域庫倫位勢U 與交換強度J，皆被定位為可調整之參數；而設定不同的參數值，常 會導致不同的計算結果。如此缺乏嚴格的定義，使得LDA+U 計算在多鐵性材料所得 之結果，引起相當爭議。為了解決這個難題，近年來新發展的限制RPA 方法，提供直 接由第一原理方法計算參數U 與J。事實上，這些參數皆與多電子遮蔽庫倫位勢W 有 關。因此，在本計畫中，我們將首先利用限制RPA 方法，由第一原理計算包含d 電子 的多鐵性材料(YMnO3 及其掺雜系統)中，U 與J 的參數值。其中，因為在多鐵性材料 中，局域分佈之d 電子，扮演關鍵性的角色。所以，我們採用最大局域化之Wannier 函數作為基底，以反應d 電子的局域性；進一步而言，為了瞭解多鐵性材料中電子軌 道再耦合現象，我們必須考慮多電子遮蔽效應，以計算更準確的電子結構。因此，進 行多鐵性材料的準粒子GW 計算，遂成為不可或缺的工作。我們相信此計畫之研究成 果，對於未來多鐵性材料之第一原理研究，將產生相當重要之影響。
The fascinating physical properties of multiferroic materials are originated from their unique electronic structures. Thanks to the state-of-the-art LDA+U method which including on-site Hubbard Coulomb potential U in the framework of static DFT, the coexistence of ferroelectric and ferro-/antiferro- magnetic characters in multiferroics can be understood comprehensively. Indeed, first-principles LDA+U calculations elucidate the origin of ferroelectricity in multiferroic materials can be either structural effect or more complicated correlation effects, such as orbital ordering, charge ordering , and spin ordering. However, the key empirical parameters, on-site Coulomb interaction U and exchange parameter J, obtained from different approaches sometimes yield to very different results. Actually, the lack of well-defined parameters provokes the ambiguity of LDA+U results in multiferroic materials. According to the recent development of constrained random phase approximation (cRPA) method, parameters U and J, mainly related to the screened Coulomb interaction W, can be calculated from first-principles. Therefore, in this project, we will firstly calculate the U and J in a typical multiferroics, YMnO3 and its doping system, by performing cRPA calculation. Taking into account the localized character of the d electron which plays an essential role in multiferroic compounds, maximally localized Wannier functions are used as the basis set to evaluate the parameters U and J for d-electrons. Furthermore, in order to understand the insight of the vital rehybridization effects in multiferroic structure, the accurate electronic structure including many-body screening effects is necessary. Thus, based on the appropriate LDA+U results, we will carry out the quasiparticle GW calculations of YMnO3 and related doping systems. A significant impact of this work on the first-principles study on multiferroics is promising. |
