Spin-glass behavior in Ni-doped high-$T_{C}$ cuprate La$_{1.85}$Sr$_{0.15}$CuO$_{4}$

We report the dc and ac magnetic properties of La$_{1.85}$Sr$_{0.15}$Cu$_{1-y}$Ni$_{y}$O$_{4}$ ($0\leq y\leq0.5$), investigated in the field up to 5 T and in the temperature range 2 K - 400 K. For y$\geq$0.06 the system exhibits irreversibility of dc susceptibility $\chi(T)$ below $T_ {irr}(y)$ and a cusp at $T_{g}(y)$ in $\chi(T)$ measured after zero-field cooling. The decay of remnant magnetization with time is described by a stretched-exponential function. In accordance with the scaling theory, all the $\chi(T)$ data for a given sample taken in the vicinity of $T_{g}$ at different fields collapse onto two separate curves when plotted as $q/|t|^{\beta} $ vs. $B^{2}/|t|^{\beta+\gamma}$, where $q$ is the spin-glass (SG) order parameter, $t$=$(T-T_{g})/T_{g}$, and $\beta$ and $\gamma$ are the critical exponents. The temperature of the peak in the real part of $\chi_{ac}$ vs. $T$ curve increases with increased frequency according to the critical slowing-down formula. The obtained parameters do not exclude the presence of spin clusters. Variation of $T_{g}$ with $y$ is linear for $y<0.25$ and $T_{g}$ extrapolates to 0 K for $y\rightarrow0$, what strongly suggests that the SG phase extends into the superconducting region of the phase diagram.