Inhomogeneous magnetic-field response of YBa2Cu3Oy and La2-xSrxCuO4 persisting above the bulk superconducting transition temperature

We report that in YBa2Cu3Oy and La2-xSrxCuO4 there is a spatially inhomogeneous response to the magnetic field for temperatures T extending well above the bulk-superconducting transition temperature Tc. An inhomogeneous magnetic response is observed above Tc even in ortho-II YBa2Cu3O6.50, which has highly ordered doping. The degree of the field inhomogeneity above Tc tracks the hole-doping dependences of both Tc and the density of the superconducting carriers below Tc, and therefore is apparently coupled to superconductivity.