Magnetic property and phase diagram of single-crystalline over-doped Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_2$As$_2$

Sizable single-crystalline samples of hole-doped Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_2$As$_2$ with x \textgreater\ 0.4 have been grown and characterized via magnetic measurements. Tc of our samples decreases from that of optimal doping as doping rate of K increases. Sharp transitions in M(T) curves indicate high quality of our sizable crystals which has never succeeded in over-doped region due to extreme nonhomogeneous property of this kind of material. With increasing K content, electron Fermi surface diminishing and nesting between hole FS and electron FS disappearing consequently, it is predicted that there exists a transition from s-wave superconducting state to d-wave yet without sufficient experimental evidences. Our results made it possible to further study on the hole-overdoped Ba$_{\mathrm{1-x}}$K$_{\mathrm{x}}$Fe$_2$As$_2$ series and provide a significant platform to test and verify these current theories and understand the underlying pairing mechanism in iron-based superconductors.