Modulations of orders around a magnetic impurity in a d-wave superconductor

In this Brief Report we study the effects of a magnetic impurity embedded in a d-wave superconductor based on the t-t'-J-V model by self-consistently solving the Bogoliubov-de Gennes equations. It is found that with the variation of scattering strength, the orders around the impurity exhibit rich and interesting behaviors, including stripes, checkerboard modulations, and Friedel-like oscillations. In particular, the checkerboard modulations in the spin orders appear to be a robust feature, which coincides with that observed in the neutron-scattering experiments. Moreover, an associated charge-density wave is predicted, which is absent in the nonmagnetic case. The implications to high-temperature cuprate superconductors and heavy fermion compounds are discussed.