Abstract
The phase separation (PS) effect in superconducting ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4+x} (x<~0.04)$ single crystals with low oxygen mobility was studied via $\ensuremath{\mu}\mathrm{SR}$ spectroscopy, high-resolution neutron diffraction, and magnetic susceptibility. Despite the fact that all crystals are inside the miscibility gap $(0.01<x<0.06),$ only crystals with a sufficiently large excess oxygen concentration $x=0.04$ show a macroscopic phase separation according to the neutron-diffraction data. However, in all samples a phase transition to an ordered magnetic state was observed by $\ensuremath{\mu}\mathrm{SR}$ spectroscopy concomitantly with the onset of superconductivity. This effect is treated as a microscopic phase separation which is possibly driven by superconductivity.
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