第10 卷 第19 期 Vol.10 No.19 2017 年 10 月 October 2017 自旋轨道耦合下铁磁单层石墨烯结的自旋输运 陈宪章,包 瑞,刘郴荣,黄 亮 * (兰州大学物理科学与技术学院,磁学与磁性材料教育部重点实验室,兰州 730000) 摘要: 为实现铁磁机理,需提高单层石墨烯结中自旋轨道耦合强度,因此在研究石墨烯结的自旋输运时需考虑 自旋轨道耦合。利用格林函数计算不同形式的自旋轨道耦合对铁磁单层石墨烯结极化作用的影响,发现铁磁 单层石墨烯结中起过滤自旋电子作用的交换场与 Rashba 和内禀的自旋轨道耦合存在相互竞争的关系,而在相 同耦合参数下,内禀自旋轨道耦合是一种抑制作用更强的机制。此外,利用 Rashba 自旋轨道耦合强度受外加 电场调制的特性可以实现可控的自旋过滤。 关键词:凝聚态物理学;自旋输运;铁磁单层石墨烯结;自旋轨道耦合;自旋极化 中图分类号:O469 文献标识码:A 文章编号:1674-2850(2017)19-2178-08 Spin transport of ferromagnetic monolayer graphene junction under the spin-orbit coupling CHEN Xianzhang, BAO Rui, LIU Chenrong, HUANG Liang (Key Laboratory for Magnetism and Magnetic Materials of MOE, School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China) Abstract: In order to realize the ferromagnetic mechanism, it is needed to improve the spin-orbit coupling in graphene. Thus, it is unavoidable to consider the spin-orbit coupling in the spin transport of graphene junctions. Focusing on the ferromagnetic monolayer graphene’s spin polarization induced by spin-orbit coupling in different types, which calculated by the non-equilibrium Green’s function, we find that there is competition between the exchange field in ferromagnetic monolayer graphene junction and Rashba, as well as that between the exchange field and intrinsic spin-orbit coupling. The inhibition induced by intrinsic spin-orbit coupling is stronger than Rashba spin-orbit coupling with the same coupling parameter. In addition, a controllable spin filter can be realized by adjusting the Rashba spin-orbit coupling via tuning the external electric field. Key words: condensed matter physics; spin transport; ferromagnetic monolayer graphene junction; spin-orbit coupling; spin polarization 0 引言 自旋电子学旨在利用电子自旋而非传统的电子电荷作为载体,以便实现信息的记录、存储和传输。 由于改变电子自旋所需的能量远比改变电子运动要小,而且时间更短、效率更高,因此在过去的几年里, 自旋电子学的研究已成为凝聚态物理领域的热点课题 [1~3] 。单层石墨烯结的发现使其自旋极化输运成为自 旋输运领域的研究热点 [4] 。相关文献报道,已经成功实现了室温环境下在单层石墨烯结上自旋注入 [5] 和 自旋输运功能 [4, 6~7] 。原生的单层石墨烯结为内禀非铁磁性 [8] ,而铁磁单层石墨烯结在自旋电子器件和信 息存储方面有广泛的应用前景 [9~10] 。研究者们利用分子外延术在氢化单层石墨烯结上实现了居里温度高 基金项目:高等学校博士学科点专项科研基金(20130211110008);国家自然科学基金(11375074,11422541) 作者简介:陈宪章(1993—),男,硕士研究生,主要研究方向:电子输运、混沌散射等 通信联系人:黄亮,教授,主要研究方向:量子混沌、非线性等. E-mail: [email protected]
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Spin transport of ferromagnetic monolayer graphene junction under the spin-orbit coupling
CHEN Xianzhang, BAO Rui, LIU Chenrong, HUANG Liang
(Key Laboratory for Magnetism and Magnetic Materials of MOE, School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China)
Abstract: In order to realize the ferromagnetic mechanism, it is needed to improve the spin-orbit coupling in graphene. Thus, it is unavoidable to consider the spin-orbit coupling in the spin transport of graphene junctions. Focusing on the ferromagnetic monolayer graphene’s spin polarization induced by spin-orbit coupling in different types, which calculated by the non-equilibrium Green’s function, we find that there is competition between the exchange field in ferromagnetic monolayer graphene junction and Rashba, as well as that between the exchange field and intrinsic spin-orbit coupling. The inhibition induced by intrinsic spin-orbit coupling is stronger than Rashba spin-orbit coupling with the same coupling parameter. In addition, a controllable spin filter can be realized by adjusting the Rashba spin-orbit coupling via tuning the external electric field. Key words: condensed matter physics; spin transport; ferromagnetic monolayer graphene junction; spin-orbit coupling; spin polarization
Fig. 2 Spin polarization PZ (a-d) under different Rashba spin-orbit coupling and the corresponding spin conductance (e-h) of the ferromagnetic monolayer graphene
及其所对应的自旋分解电导分量(d~f) Fig. 3 Spin polarization PZ (a-c) under different intrinsic spin-orbit coupling and the corresponding spin conductance (d-f) of the
便起见,取铁磁交换能 h=−0.05 t 和 h=−0.1 t,并分别计算在两种轨道耦合情况下自旋极化的输运行为,
其计算结果如图 4 所示。
图 4 铁磁单层石墨烯结上在不同费米能下自旋极化度 PZ 随自旋轨道耦合强度 tR 和 tI 的变化
Fig. 4 Spin polarization PZ under different Fermi energy (Ef), Rashba (tR) and intrinsic (tI) spin-orbit coupling of the ferromagnetic monolayer graphene
由图 4 可以看出,不论是哪种类型的自旋轨道耦合,在自旋轨道耦合参数较小的情况下自旋极化度
均没有被严重抑制住。但当耦合参数强度逐步增大时,极化度逐步开始出现退步行为,这一点符合上述
分析结果,并与物理直觉相符。特别地,对于 Rashba 情形,在铁磁交换能 h=−0.05 t 时,自旋极化度 PZ
在 3 个费米能参数的情形下,在 tR<0.05 t 时变化较小,一旦当参数 tR>0.05 t 时,自旋极化出现了迅速衰
减,如图 4a 所示。将自旋极化度开始出现明显衰减的自旋轨道耦合参数值称为阈值。当铁磁交换能 h=0.1 t时,在 Rashba 自旋轨道耦合情形下得到了类似的结果,自旋极化度均在阈值 tR≈0.05 t 出现了迅速衰减,如