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We study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two contact magnetic
impurities placed on bilayer graphene (BLG). We compute the interaction mediated by the carriers
of the pristine and biased BLG as well as the conduction electrons of the doped system. The
results are obtained from the linear-response expression for the susceptibility written in terms of
the integral over lattice Green's functions. For the unbiased system, we obtain some analytical
expressions in terms of the Meijer G-functions, which consist of the product of two oscillatory terms,
one coming from the interference between the two Dirac points and the second coming from the
Fermi momentum. In particular, for the undoped BLG, the system exhibits the RKKY interaction
commensurate with its bipartite nature as expected from the particle-hole symmetry of the system.
Furthermore, we explore a beating pattern of oscillations of the RKKY interaction in a highly doped
BLG system within the four-band continuum model. Besides, we discuss the discrepancy between
the short-range RKKY interaction calculated from the two-band model and that obtained from the
four-band continuum model. The nal results for the applied gate voltage are obtained numerically
and are tted with the functional forms based on the results for the unbiased case. In this case, we
show that the long-range behavior is scaled with a momentum that depends on Fermi energy and
gate voltage, allowing the possibility of tuning of the RKKY interaction by gate voltage.
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