Oxidation annealing effects on the spin-glass-like magnetism and appearance of superconductivity in T*-type La$_{1-x/2}$Eu$_{1-x/2}$Sr$_x$CuO$_4$ (0.14 $\leq x \leq$ 0.28)

We investigated the magnetism and superconductivity in as-sintered (AS) and oxidation annealed (OA) T*-type La$_{1-x/2}$Eu$_{1-x/2}$Sr$_x$CuO$_4$ (LESCO) with 0.14 $\leq x \leq$ 0.28 by muon spin rotation/relaxation ($\mu$SR), magnetic susceptibility, and electrical resistivity measurements. In OA superconducting samples, no evidence of magnetic order was observed, whereas AS semiconducting samples exhibited evidence of a disordered magnetic state in the measured temperature range between $\sim$4 K and $\sim$8 K, which potentially developed toward a long-range ordered state at low temperature. Therefore, the ground state in LESCO drastically varies with oxidation annealing and the magnetic phase competitively exists with the superconducting (SC) phase. Furthermore, we clarified the simultaneous development of magnetic properties, that is, the internal magnetic field and the magnetic volume fraction, and the electrical resistivity at a low temperature in AS samples, suggesting the inducement of static magnetism by the suppression of carrier mobility. The magnetic phase in the AS LESCO is quite robust against Sr doping, while the SC phase degrades with increasing $x$. A monotonous decrease of the SC transition temperature from 24.5 K in $x$ = 0.14 to 9.0 K in $x$ = 0.28 suggests the disappearance of the SC phase at $x$ $\sim$ 0.34. These new findings for the T*-type LESCO are discussed by comparing previously reported results for T-type La$_{2-x}$Sr$_x$CuO$_4$ and T'-type $R_{2-x}$Ce$_x$CuO$_4$ ($R$ = rare earth element) to extract common features of magnetism and their relation with superconductivity in cuprates.