Velocity-determined anisotropic behaviors of RKKY interaction in 8-textit{Pmmn} borophene

As a new two-dimensional Dirac material, 8-\textit{Pmmn} borophene hosts novel anisotropic and tilted massless Dirac fermions (MDFs) and has attracted increasing interest. However, the potential application of 8-\textit{Pmmn} borophene in spin fields has not been explored. Here, we study the long-range RKKY interaction mediated by anisotropic and tilted MDFs in magnetically-doped 8-\textit{Pmmn} borophene. To this aim, we carefully analyze the unique real-space propagation of anisotropic and tilted MDFs with noncolinear momenta and group velocities. As a result, we analytically demonstrate the anisotropic behaviors of long-range RKKY interaction, which have no dependence on the Fermi level but are velocity-determined, i.e., the anisotropy degrees of oscillation period and envelop amplitude are determined by the anisotropic and tilted velocities. The velocity-determined RKKY interaction favors to fully determine the characteristic velocities of anisotropic and tilted MDFs through its measurement, and has high tunability by engineering velocities shedding light on the application of 8-\textit{Pmmn} borophene in spin fields.