The RKKY Interaction in Graphene Proximity Coupled to an Antiferromagnetic Insulator

We study theoretically the long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction mediated by itinerant electrons of graphene between magnetic moments induced by proximity effect of an antiferromagnetic insulator. The antiferromagnetic insulators provides both broken time-reversal symmetry and spin-orbit coupling [1]. We find more spin-spin interaction terms which had not reported previously in other spin-orbit systems[2]. The additional terms could induce a spatially inhomogeneous spin order. We also find a rich texture of the total RKKY range function. With the Fermi energy residing in the band gap induced by the spin-orbit coupling, the RKKY interaction degenerates to the Bloembergen-Rowland (BR) interaction. The BR interaction is a short range exponentially-decay interaction mediated by virtual excitations. We show a possible transformation of anomalous Hall effect to quantum anomalous Hall effect while the RKKY interaction degenerating to the BR interaction.

[1] Z. Qiao, W. Ren, H. Chen et al, Phys. Rev. Lett. 112, 116404(2014).
[2] J.-J. Zhu, D.-X. Yao, S.-C. Zhang, and K. Chang, Phys. Rev. Lett. 106, 097201 (2011).