Inhomogeneous Magnetic-Field Response of YBa2Cu3Oy and La2−xSrxCuO4 Persisting above the Bulk Superconducting Transition Temperature

We report that in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ and ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ there is a spatially inhomogeneous response to the magnetic field for temperatures $T$ extending well above the bulk-superconducting transition temperature ${T}_{c}$. An inhomogeneous magnetic response is observed above ${T}_{c}$ even in ortho-II ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.50}$, which has highly ordered doping. The degree of the field inhomogeneity above ${T}_{c}$ tracks the hole-doping dependences of both ${T}_{c}$ and the density of the superconducting carriers below ${T}_{c}$, and therefore is apparently coupled to superconductivity.