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arXiv 1607.08008cond-mat.mes-hall
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hBN /(Co,Ni)上石墨烯的邻近诱导交换耦合理论

Theory of proximity-induced exchange coupling in graphene on hBN/(Co, Ni)

Klaus Zollner, Martin Gmitra, Tobias Frank, Jaroslav Fabian

摘要:

我们进行系统的邻近交换耦合的第一性原理计算,诱导钴(Co)和镍(Ni)在石墨烯中,通过几个(多达三个)层的六方氮化硼(hBN)。我们发现,诱导的石墨烯带的自旋分裂的数量级为10毫电子伏的hBN单层,减少的幅度,但交替的符号,通过添加每个新的绝缘层。我们发现,如果在狄拉克点附近存在过渡金属的$d$共振能级,邻近交换可以是巨大的。我们的计算表明,这种效应可能存在于钴异质结构,其中$d$水平强烈杂交与石墨烯的价带轨道。由于这种杂交依赖于自旋,因此邻近自旋分裂异常大,即使对于两层hBN也约为10 meV。外部电场可以改变石墨烯和过渡金属轨道的偏移,并且可以导致交换参数的符号反转。我们预测这将发生在hBN的两个单层的情况下,使得能够在石墨烯/hBN/Co结构中对邻近自旋极化(但也是自旋注入)进行电控制。镍基异质结显示较弱的邻近效应比钴异质结。我们引入两个唯象模型来描述第一性原理数据。极小模型包括石墨烯(有效)$p_z$轨道,可用于研究具有邻近交换的石墨烯中的输运,而$p_z$ - $d$模型还包括与$d$轨道的杂交,这对于捕获巨大的邻近交换很重要。这两个模型的关键是赝自旋相关的交换耦合,需要描述不同的自旋分裂的价带和导带。

英文摘要:

We perform systematic first-principles calculations of the proximity exchange coupling, induced by cobalt (Co) and nickel (Ni) in graphene, via a few (up to three) layers of hexagonal boron nitride (hBN). We find that the induced spin splitting of the graphene bands is of the order of 10 meV for a monolayer of hBN, decreasing in magnitude but alternating in sign by adding each new insulating layer. We find that the proximity exchange can be giant if there is a resonant $d$ level of the transition metal close to the Dirac point. Our calculations suggest that this effect could be present in Co heterostructures, in which a $d$ level strongly hybridizes with the valence-band orbitals of graphene. Since this hybridization is spin dependent, the proximity spin splitting is unusually large, about 10 meV even for two layers of hBN. An external electric field can change the offset of the graphene and transition-metal orbitals and can lead to a reversal of the sign of the exchange parameter. This we predict to happen for the case of two monolayers of hBN, enabling electrical control of proximity spin polarization (but also spin injection) in graphene/hBN/Co structures. Nickel-based heterostructures show weaker proximity effects than cobalt heterostructures. We introduce two phenomenological models to describe the first-principles data. The minimal model comprises the graphene (effective) $p_z$ orbitals and can be used to study transport in graphene with proximity exchange, while the $p_z$-$d$ model also includes hybridization with $d$ orbitals, which is important to capture the giant proximity exchange. Crucial to both models is the pseudospin-dependent exchange coupling, needed to describe the different spin splittings of the valence and conduction bands.

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