We study exchange interaction between two magnetic impurities, i.e. (the Ruderman-Kittel-Kasuya-Yosida [RKKY]), in doped biased bilayer graphene by directly computing Green’s function within full band method. Tight binding model Hamiltonian in the presence of magnetic long range ordering has been applied to describe electron dynamics. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a field induced ferromagnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. Such field induced ferromagnetic ordering is due to external magnetic field. The exchange interaction along arbitrary direction between two magnetic moments, has been obtained using the static spin susceptibilities of gapped graphene structure. The effects of spin polarization on the the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the chemical potential impacts the spatial behavior of RKKY interaction. Moreover bias voltage effects on RKKY interaction have been investigated for both stacking types of bilayer graphene.

我们通过直接在全频带方法中计算格林函数来研究掺杂的偏置双层石墨烯中两种磁性杂质（Ruderman-Kittel-Kasuya-Yosida [RKKY]）之间的交换相互作用。在存在磁性长程有序的情况下，紧密结合模型哈密顿量已用于描述电子动力学。分析了RKKY相互作用与局部力矩之间距离的关系。研究表明，磁场沿z方向感应铁磁有序轴介导的各向异性相互作用对应于两个磁矩之间的XXZ模型相互作用。这种磁场感应的铁磁排序是由于外部磁场引起的。利用有间隙的石墨烯结构的静态自旋磁化率，获得了两个磁矩之间沿任意方向的交换相互作用。通过计算自旋密度算子的相关函数，研究了自旋极化对交换相互作用对矩之间距离的依赖性的影响。我们的结果表明，化学势会影响RKKY相互作用的空间行为。此外，已经针对两种堆叠类型的双层石墨烯研究了偏压对RKKY相互作用的影响。