Strongly anisotropic RKKY interaction in monolayer black phosphorus

We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in two-dimensional black phosphorus, phosphorene. The RKKY interaction enhances significantly for the low levels of hole doping owing to the nearly valence flat band. Remarkably, for the hole-doped phosphorene, the highest RKKY interaction occurs when two impurities are located along the zigzag direction and it tends to a minimum value with changing the direction from the zigzag to the armchair direction. We show that the interaction is highly anisotropic and the magnetic ground-state of two magnetic adatoms can be tuned by changing the rotational configuration of impurities. Owing to the anisotropic band dispersion, the oscillatory behavior with respect to the angle of the rotation is well-described by $\sin(2k_{\rm F}R)$, where the Fermi wavelength $k_{\rm F}$ changes in different directions. We also find that the tail of the RKKY oscillations falls off as $1/R^2$ at large distances.