第一原理計算研究多層鐵磁Fe3GeTe2 之磁光效應及類霍爾電荷和自旋傳導

Abstract

二維材料Fe3GeTe2 的薄膜在近期被實驗成功撕出並且其鐵磁性也被成功證實。這提供了研究低維度磁性和發展自旋相關科技或是磁性奈米裝置一個極佳的平台。本碩士論文將系統地研究各個層數之下Fe3GeTe2 的磁性性質以及三個磁性引導出的現象: 首先是自旋相關的傳輸性質如反常霍爾效應，反常能斯特效應，自旋霍爾效應，自旋能斯特效應; 再來是磁性異相能，最後是磁光效應。在鐵磁性基態之下，我們發現了Fe3GeTe2 存在極大的磁晶異相能，從1 至5 層直到塊材，皆存在大約3(毫電子伏特/化學式) 的磁晶異相能。這表示Fe3GeTe2在二維情況下可以存在穩定的鐵磁性。接下來，我們發現了與層數相關的反常霍爾電導率，反常能斯特電導率，自旋霍爾電導率，自旋能斯特電導率。其中單層Fe3GeTe2 具有最大的反常霍爾電導率247(歐姆/公分)，以及在180 凱爾文下的反常能斯特電導率0.67(安培/公尺凱爾文)。此等反常能斯特電導率超過非共線反鐵磁Mn3Sn，甚至可與傳統上有較大反常能斯特係數的金屬導體，例如多層鉑鐵合金或是金屬鐵，競爭。甚者，我們還發現不僅僅反常霍爾電導率和反常能斯特電導率，自旋霍爾電導率和自旋能斯特電導率可以藉由調動費米能級來使其有較大的變化，例如在單層Fe3GeTe2，經過上調費米能級我們可以在實驗可行的摻雜範圍內得到提升的反常霍爾電導率337(歐姆/公分) 和在180 凱爾文下的反常能斯特電導率2.28(安培/公尺凱爾文)。在沒有磁性，室溫300 凱爾文下，1 至4 層的Fe3GeTe2 在自旋能斯特效應比起鐵磁性下更顯著，有著0.3(¯h/e)(安培/公尺凱爾文)。藉由貝瑞曲率分析，我們發現了在Fe3GeTe2 系統中存在的兩種貝瑞區率源頭。在偶數層Fe3GeTe2，我們發現由自旋軌到偶合所產生的能帶間隙所產生的貝瑞區率峰值。另一種則是在奇數層Fe3GeTe2 發現由兩條相近並且共同穿過費米能級後得到較小的貝瑞區率值但是較大的積分面積所產生對於霍爾電導率的巨大貢獻。另外，我們藉由對稱性分析發現了單層Fe3GeTe2 的巨大反常霍爾和能斯特電導率緣於一圈連續的貝瑞區率，並且這環是由兩條被對稱性所保護而成，並未因為自旋軌道偶合而被破壞。這形成了一個節環並且還給予了電導率等等巨大的貢獻。最後，在光學分析方面，在可見光區間，我們發現了三層的Fe3GeTe2 最大到約2.7 度的磁光克爾旋轉角。這個大小的磁光克爾旋轉角與歷史上有名的3d 過度金屬合金MnBi 或是被大量實驗運用的半導體Y3Fe5O12 都還要大。另外Fe3GeTe2 也有極大的磁光法拉第旋轉角，尤其單層的Fe3GeTe2 有約156 度/微米的磁光法拉第旋轉角，這個數值三倍大於Bi3Fe5O12，也大於其他最近被報導的二維磁性半導體Cr2Ge2Te6 或CrI3。綜合來說這份研究使我們預測Fe3GeTe2 可以成為好的磁性自旋，光電，電熱相關科技的優良載體，並且我們提出了一個新的對稱性保護拓樸金屬的可能性。

Atomically thin Fe3GeTe2 was recently prepared and confirmed to be ferromagnetic. This provides a platform to study two-dimensional magnetism and also stimulate the application to spintronics and magnetic nanodevices. In this master thesis, we systematically study the magnetism, magnetic anisotropy energy(MAE), the spin transport properties including anomalous Hall effect (AHE), anomalous Nernst effect (ANE), spin Hall effect (SHE) and spin Nernst effect (SNE), as well as the magneto-optical(MO) effects for few layers Fe3GeTe2 by first principle calculation. The ferromagnetic state is calculated and a large magnetocrystalline anisotropy energy of nearly 3 (meV/f.u.) is found for 1-5 layers and also bulk Fe3GeTe2. Such large MAE stabilizes the magnetism till two-dimensional limit. For anomalous Hall conductivity (AHC), monolayer Fe3GeTe2 has the largest AHC of 247(S/cm). The AHC decreases as the number of layer increases which eventually converges to bulk Fe3GeTe2 with AHC 167(S/cm). Nonetheless, monolayer Fe3GeTe2 also has a large anomalous Nernst conductivity (ANC) of 0.67 (A/m-K) at 180 K. Such ANC is larger than that of noncollinear antiferromagnet Mn3Sn, and is comparable to that of metallic conductors Pt/Fe multilayers or metal iron with large anomalous Nernst coefficient. Furthermore, we discover not only the AHC and ANC but also spin Hall conductivity (SHC) and spin Nernst conductivity (SNC) of Fe3GeTe2 to be highly tunable via slightly changing the Fermi level. Big enhancement for ML Fe3GeTe2 can be performed up to 337 (S/cm) for AHC by electron doping of 0.50 e/f.u., and 2.28 (A/m-K) for ANC by electron doping of 0.26 e/f.u. These doping level are within possible experimental doping level (1.6 e/f.u.). For nonmagnetic Fe3GeTe2, SNC is of value of roughly 0.3 (¯h /e)(A/m-K) for 1-4 layers Fe3GeTe2 in 300 K, which is larger than that in ferromagnetic state (0.009 -0.24 (¯h /e)(A/m-K)). Via Berry curvature analysis, we discover two different origins of large AHC in Fe3GeTe2 with an odd number and even number of layers, respectively. In the case of even-number-layers, Fermi level crosses multiple spin-orbit-coupling-induced band-gaps, thus results in large Berry curvature peaks in the Brillouin zone. On the other hand, in the case of odd-number-layers, pairs of neighbouring bands straddle the Fermi level. Therefore, large-area Berry curvature plateaus appear in the Brillouin zone, which gives large AHC in total. Surprisingly, we identify especially the origin of the continuous Berry curvature plateau around Γ point for monolayer Fe3GeTe2 to be a mirror symmetry protected gapless nodal ring. On the other hand, through linear optics response calculation, in visible frequency range, huge Kerr rotation angle up to ∼2.7◦ for trilayer Fe3GeTe2 is found, and the value is larger than famous 3d transition alloy MnBi. Also, a large Faraday rotation angle is predicted for all considered Fe3GeTe2 structures. Especially, monolayer Fe3GeTe2 has a Faraday rotation angle of 156◦/μm, which is three times larger than famous Bi3Fe5O12 or recently reported 2D magnetic semiconductors Cr2Ge2Te6 and CrI3. Our work not only suggests atomically thin Fe3GeTe2 to become candidate for two-dimensional magnetic or MO nanodevice, and spin caloritronics, but also proposes a new possibility of two dimensional symmetry protected topological metal.