Coexistence of the spin and electron-hole quantum liquids in frustrated manganites La$_{1-y}$Sm$_y$MnO$_{3+\delta}$

The structural, electronic, and magnetic phase transformations induced in the temperature range of 4.2–300 K by the isovalent substitution of the rare-earth Sm$^{3+}$ ion for the La$^{3+}$ ion with a larger radius have been investigated in the system of self-doped manganites La$_{1-y}$Sm$_y$MnO$_{3+\delta}$ ($\delta\sim$ 0.1, 0 $\le y\le$ 1). It has been found using the X-ray diffraction analysis that the substitution La $\to$ Sm is accompanied by a significant increase of the GdFeO$_3$-type and Jahn–Teller-type lattice distortions. At a temperature of 300 K, an increase in the Sm concentration $y$ leads to a concentration phase transition from the pseudocubic $O^*$ phase to the orthorhombic $O’$ phase, as well as to the appearance of an $s$-shaped anomaly of the lattice parameter a at concentrations $y\ge$ 0.4 and an anomalous peak in the concentration dependence of the electrical resistance $R(y)$ near $y\approx$ 0.85. The magnetic $T$–$y$–$\langle r_A\rangle$ phase diagrams of the La$_{1-y}$Sm$_y$MnO$_{3+\delta}$ system in the temperature range of 4.2–250 K have been constructed according to the results of measurements of the temperature dependences of the direct-current (dc) magnetization $M(T)$. It has been revealed that the samples with $y\ge$ 0.8 exhibit signs of the melting of the $A$- and CE-type modulated antiferromagnetic (AFM) structures in the form of an anomalous decrease both in the critical temperature of the transition to a frustrated AFM state and in the magnetization of the samples with an increase in the concentration $y$. The anomalies observed in the temperature dependences of the alternating-current (ac) dielectric permittivity of the La$_{1-y}$Sm$_y$MnO$_{3+\delta}$ samples have been explained within the existing concepts of the Bose–Einstein condensation of an electron-hole liquid in the form of metallic droplets in an excitonic insulator.