Large Rashba Spin-Orbit Effect by Orbital Engineering at SrTiO3–based Correlated Interfaces-猫眼课题宝

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2021

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G. J. Omar;W. Kong;H. Jani;M. S. Li;J. Zhou;Z. Lim;S. Prakash;S. Zeng;S.;Hooda;T. Venkatesan;Y. Feng;S. Pennycook;L. Shen;A. Ariando

大的自旋轨道效应是有效利用电荷与自旋自由度相互作用的自旋轨道电子学的必要因素。这种自旋轨道效应在重金属- 1-7基的异质结构中通常很小，或者在复杂的氧化物基异质结构中需要很大的外部施加电压8。在这里，我们通过轨道杂化的界面原子控制，在srtio3基界面上引入了Ti-O晶格极化，在零施加电压下产生了大的Rashba自旋轨道效应。观察到的自旋轨道效应（~ 3.5×10-12 eV-m）比在零偏置电压下观察到的传统srtio3基界面大4倍。通过从头算电子结构计算和高分辨率原子显微镜验证了轨道杂化和Ti-O晶格极化。我们的研究结果提供了一种在SrTiO3界面上实现Ti-O晶格极化的独特方法，并通过轨道工程开辟了迄今为止尚未探索的产生和控制Rashba自旋轨道效应的途径，以设计下一代自旋轨道电子学。在凝聚态物理中，自旋-轨道耦合（SOC）是材料的固有性质，与量子粒子的自旋σσ和动量kk有关。这种SOC效应及其可调性被认为是开发利用自旋自由度的功能器件的潜在途径，这降低了自旋电子器件的能量效率9,10。这种SOC效应调节了自旋居数的衰减，从而定义了它在新的器件结构（即自旋轨道电子）中的适用性。特别令人感兴趣的是Rashba SOC12，这是一种相对论性效应，通常与二维或界面系统中发现的反转对称性破缺有关。由于垂直于界面的对称破缺电场（E0），这种效应提升了布里渊区k点处的自旋简并态。在Rashba SOC中，哈密顿量定义为HHRR = ααRRzz∙(kk × σσ)，其中ααRR为Rashba SOC系数，zz为面向界面的Rashba单位向量。它是各种凝聚态系统（如石墨烯、拓扑绝缘体和冷原子）中出现现象的原因13,14。LaAlO3 （LAO）和绝缘体SrTiO3 （STO）界面上的二维电子系统（2DES）的规范模型显示出具有长载流子寿命（对低功率自旋电子学至关重要）的强Rashba SOC。人们普遍认为，当LAO晶体沉积在非极性STO上时，其极性性质会导致内部电位的发散和电子重构。电子重构导致电荷从LAO转移到STO，从而在LAO/STO复合氧化物异质结构上形成2DES。通过识别界面体系的轨道杂化，可以从能带结构中读出Rashba强度。这种轨道杂化对STO界面的局部轨道和晶格极化非常敏感。这里，Ti原子在STO界面的tt2gg电子杂化起了重要作用，定义哈密顿HH为HH = HH0 + HHAAAAAA + HHzz。其中，HH0为轨道内跳变（轨道空间对角线），HHAAAAAA为现场原子SOC， HHzz为反对称轨道间跳变19-22。这些不同的轨道内和轨道间的微扰跳变项影响着能量色散和SOC。特别是，在二阶扰动中，HHzz项通过ppxx沿yy方向产生从ddxxxx到ddzzxx的电子跳变，通过ppxx沿xx方向产生从ddxxxx到ddxxzz的电子跳变，在STO界面产生类似rashba的SOC效应。垂直于STO界面的电场的建立对Ti阳离子和氧阴离子产生相反的力（图1）。TiO2平面上的极化引起了TiO2 - ti键角，导致了层相关的离子位移。离子位移与界面波函数的不对称和杂化有关，控制着Rashba SOC的强度。在电子晶体动量kk = (kkxx kkxx 0),泡利矩阵σσ=(σσxx,σσxx,σσzz),和轨道基础(yyyy, yyxx xxyy),反对称跳跃哈密顿项HHzz形式,HHzz =∆zz�0 0 iikkxx 0 0 iikkxx−iikkxx−iikkxx 0�⨂σσ0�yyyy yyxx xxyy�,(1)∆zz =γγ1 ttppppe0 _ppppΔlog⁄+�nttpppp 2 _ppppΔlog��与诱导轨道极化引起的附加电场(跳跃幅度E0γγ1)和键角,n,或离子极化/位移（ΔδδTi−O）沿yy方向，由跳跃幅度为ttpppp的pp-dd杂化轨道介导。∆pppp是o和ti轨道之间的分裂。∆zz是一个与层相关的参数，在界面处有最大值，在较深层处迅速减小。轨道网络Ti(3ddzzxx) - O(2ppxx) - Ti（3ddxxxx）中tt2gg流形内的杂化直接促成了HHAAAA，从而导致了Rasbha分裂。对所有哈密顿量的简要描述见补充资料S1。图1(a)显示了TiO2层的Ti(3ddzzxx) - O(2ppxx) - Ti（3ddxxxx）轨道的晶格位移。轨道位移越大，产生的内建电场越大，导致Rashba SOC增强。本文主要从tt2gg Rashba界面理论出发，通过反对称轨道杂化，提供了在LAO/STO界面中控制Rashba SOC（零偏置）的实验证据。为了检验反对称跳变的显著贡献，使用厚度为dd = 0至6个单元格（uc）的LaFeO3 （LFO）缓冲层调制LAO和STO接口。我们展示了Rashba SOC的四倍增强，可以用LFO工程层进行调制。因此，我们利用脉冲激光沉积（PLD）系统制备了具有LFO缓冲层的LAO和STO复合氧化物异质结构。使用反射高能电子衍射（RHEED）方法来确认沉积过程中逐层生长（见补充信息）。利用扫描隧道电镜（STEM）的横截面高角环形暗场（HAADF）模式对界面的原子结构进行了表征。STEM图像一致地呈现出相干和外延生长，具有原子锐界面，dd = 0,2和4uc（示意图图1(b)和补充）

Large spin-orbit effect is an essential element for efficient spin-orbitronics that utilizes the interplay between charge and spin degree of freedom. This spin-orbit effect is generally small in heavy-metal1-7-based or requires large external applied voltages in complex-oxide-based heterostructures8. Here, we present a large Rashba spin orbit effect at zero applied voltages by interfacial atomic control of orbital hybridization that introduces Ti-O lattice polarization at the SrTiO3-based interfaces. The observed spin orbit effect (~ 3.5×10-12 eV-m) is four-fold larger than that observed in conventional SrTiO3-based interfaces at zero bias voltage. The orbital hybridization and Ti-O lattice polarization are verified through ab initio electronic structure calculations and high-resolution atomic microscopy. Our results present a unique approach to achieve Ti-O lattice polarization at SrTiO3 interfaces and open hitherto unexplored avenues of generating and controlling Rashba spin orbit effect via orbital engineering to design nextgeneration spin-orbitronics. In condensed matter physics, spin-orbit coupling (SOC) is intrinsic property of material and links to the quantum particle’s spin σσ and momentum kk. This SOC effect and its tunability have been proposed to be a potential route for developing function devices utilizing spin degrees of freedom, which reduces the energy efficiency of spintronic devices9,10. This SOC effect regulates the spin population decay and thus defines its suitability in new device architecture, namely spin-orbitronics11. Of particular interest is the Rashba SOC12, which is a relativistic effect associated with an inversion symmetry breaking typically found in a two-dimensional or an interfacial system. This effect lifts the spin degeneracy states at kk-points in the Brillouin zone due to a symmetry-breaking electric field (E0) normal to the interface. In Rashba SOC, the Hamiltonian is defined by HHRR = ααRRzz� ∙ (kk × σσ), where ααRR is the Rashba SOC coefficient and zz� is the Rashba unit vector normal to the interface. It is responsible for the emergent phenomena in various condensed matter systems such as graphene, topological insulators, and cold atoms13,14. The canonical model of the two-dimensional electron system (2DES) at the interface between LaAlO3 (LAO) and insulators SrTiO3 (STO) have been shown to exhibit a strong Rashba SOC with long carrier lifetimes (crucial for low power spintronics15-18). It is well accepted that the polar nature of the LAO crystal can lead to a diverging internal potential and electronic reconstruction when the LAO is deposited onto a nonpolar STO. The electronic reconstruction results in a charge transfer from the LAO into STO and thus forms 2DES at the LAO/STO complex oxide heterostructures. Rashba strength can be read off the band structure by identifying the orbital hybridization of interfacial systems. This orbital hybridization is strongly sensitive to local orbital and lattice polarization of STO interface19. Here, the hybridization of tt2gg electron of Ti atoms at STO interface plays an important role and the Hamiltonian HH is defined as HH = HH0 + HHAAAAAA + HHzz. Here, HH0 is the intra-orbital hopping (diagonal in the orbital space), HHAAAAAA is the on-site atomic SOC, and HHzz is the antisymmetric interorbital hopping19-22. These various intraand inter-orbital perturbed hopping terms between the energy bands influence the energy dispersion and SOC. In particular, the HHzz term generates electronic hopping from ddxxxx to ddzzxx along the yy direction via ppxx and from ddxxxx to ddxxzz along the xx direction via ppxx in the second-order perturbation producing a Rashba-like SOC effect at the STO interface. The building up of the electric field perpendicular to the STO interface produces opposite forces on the Ti cations and oxygen anions (Figure 1). The polarization in the TiO2 plane induces TiO-Ti bond angle resulting in a layer dependent ionic displacement. The ionic displacement is related to the asymmetric features and hybridization of the interface wave functions, which controls the strength of the Rashba SOC. In the electron crystal momentum kk = (kkxx,kkxx, 0), Pauli matrices σσ = (σσxx,σσxx,σσzz), and orbital basis (yyyy, yyxx, xxyy), the antisymmetric hopping Hamiltonian term HHzz takes the form, HHzz = ∆zz � 0 0 iikkxx 0 0 iikkxx −iikkxx −iikkxx 0 �⨂σσ0 � yyyy yyxx xxyy � , (1) where ∆zz= γγ1ttppppE0 Δpppp ⁄ + �nttpppp 2 Δpppp � � is related to the induced orbital polarization arising from the additional electric field (with hopping amplitude E0γγ1) and bond angle, n, or ionic polarization/ displacement (ΔδδTi−O) along the yy direction, mediated by the pp-dd hybridized orbitals with the hopping amplitude ttpppp. Here ∆pppp is the splitting between the Oand Ti-orbitals. The ∆zz is a layerdependent parameter, having a maximum value at the interface and decreasing rapidly at the deeper layers. This hybridization within the tt2gg manifold, in the orbital network Ti(3ddzzxx) – O(2ppxx) – Ti(3ddxxxx), directly contributes to HHAAAA and consequently leads to a Rasbha splitting. A brief description of all the Hamiltonians is described in Supplementary information S1. Figure 1(a) illustrate the lattice displacement of the Ti(3ddzzxx) – O(2ppxx) – Ti(3ddxxxx) orbitals of the TiO2 layer. Larger the orbital displacement induces more built-in electric field, results in enhancing the Rashba SOC. This present work focuses on providing experimental evidence of controlling Rashba SOC (at zero bias) in LAO/STO interfaces from the theory of tt2gg Rashba interfaces via antisymmetric orbital hybridization. To examine the pronounced contribution of the antisymmetric hopping, LAO and STO interface is modulated with a LaFeO3 (LFO) buffer layer with thickness of dd = 0 to 6-unit cells (uc). We demonstrate a fourfold enhancement of the Rashba SOC that can be modulated with LFO engineering layer. We, therefore, fabricated LAO and STO complex oxide heterostructures with LFO buffer layer via pulsed laser deposition (PLD) system. A reflection high-energy electron diffraction (RHEED) method was used to confirm the layer-by-layer growth during the deposition (see Supplementary Information). The atomic structure of the interfaces was characterized using a crosssectional high-angle annular dark-field (HAADF) mode of the scanning tunnelling electron microscopy (STEM). STEM images consistently present a coherent and epitaxial growth with atomically sharp interfaces with dd = 0, 2, and 4 uc (schematic Figure 1(b) and Supplementary

Large Rashba Spin-Orbit Effect by Orbital Engineering at SrTiO3–based Correlated Interfaces

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