Development of spatial inhomogeneity of internal magnetic field above $T_{\mathrm{c}}$ in Bi${}_2$Sr${}_2$Ca${}_{1-x}$Y${}_x$Cu${}_2$O${}_{8+\delta }$ observed by longitudinal-field muon-spin-relaxation

Longitudinal-field muon-spin-relaxation measurements have revealed inhomogeneous distribution of the internal magnetic field at temperatures above the bulk superconducting (SC) transition temperature, $T_{\mathrm{c}}$, in slightly overdoped Bi${}_2$Sr${}_2$Ca${}_{1-x}$Y${}_x$Cu${}_2$O${}_{8+\delta }$. The distribution width of the internal magnetic field, $\mathrm{\Delta }$, evolves continuously with decreasing temperature toward $T_{\mathrm{c}}$. The origin of the increase in $\mathrm{\Delta }$ is discussed in terms of the creation of SC domains in a sample.