Topological phase transition of decoupling quasi-two-dimensional vortex pairs in La$_{1-y}$Sm$_{y}$MnO$_{3+\delta}$ ($y$ = 0.85, 1.0)

Characteristic signs of the universal Nelson–Kosterlitz jump of the superconducting liquid density in the temperature dependences of the magnetization of La$_{1-y}$Sm$_{y}$MnO$_{3+\delta}$ samples with samarium concentrations $y$ = 0.85 and 1.0, which are measured in magnetic fields 100 Oe $\le H\le$ 3.5 kOe, are detected. As the temperature increases, the sample with $y$ = 0.85 exhibits a crescent-shaped singularity in the dc magnetization curve near the critical temperature of decoupling vortex–antivortex pairs ($T_{\mathrm{KT}}\equiv T_{c}\cong$ 43 K), which is independent of measuring magnetic field H and is characteristic of the dissociation of 2D vortex pairs. A similar singularity is also detected in the sample with a samarium concentration $y$ = 1.0 at a significantly lower temperature ($T_{\mathrm{KT}}\cong$ 12 K). The obtained experimental results are explained in terms of the topological Kosterlitz–Thouless phase transition of dissociation of 2D vortex pairs in a quasi-two-dimensional weak Josephson coupling network.