Signs of high-temperature superconductivity in frustrated manganites La$_{1-y}$Sm$_{y}$MnO$_{3+\delta}$ ($\delta\sim$ 0.1, $y$ = 0.85, 1.0)

The characteristics signs of the coexistence of nanoscale superconductivity and fluctuating antiferromagnetic state of the spin-liquid type have been revealed for the first time in frustrated manganites La$_{1-y}$Sm$_{y}$MnO$_{3+\delta}$ ($\delta\sim$ 0.1, $y$ = 0.85, 1.0) in the form of macroscopic quantization of magnetic properties in weak magnetic fields. A sharp decrease and oscillations of close-in-magnitude critical temperatures of transitions to fluctuating antiferromagnetic $(T_{A})$ and superconducting $(T_{c0})$ states with an increase in the external magnetic field strength have been found. Quantum oscillations of the magnetization and magnetic susceptibility near the critical temperatures of fluctuating antiferromagnetic phase transitions of the $A$- and $CE$-types have been discovered and investigated in detail. It has been shown that the studied samples exhibit properties of a multicomponent composite in which at temperatures $T<$ 60 K in weak magnetic fields, there coexist fluctuating charge and antiferromagnetic correlations of the A- and CE-types with properties of the spin-liquid state and a small fraction of the superconducting phase in the form of individual and Josephsontunnel- junction-coupled superconducting loops with low critical currents. It has been assumed that, in samples with samarium concentrations $y\ge$ 0.8 at temperatures below 60 K, there is a new inhomogeneous state of doped manganites of the magneto-electronic liquid crystal type with strong quantum fluctuations of the magnetic and electronic order parameters, which are similar to electronic liquid crystals in lightly doped high-temperature superconducting cuprates.