Magnon-polaron and spin-polaron signatures in the specific heat and electrical resistivity ofLa0.6Y0.1Ca0.3MnO3in zero magnetic field and the effect ofMn—O—Mnbond environment

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$La_{0.6}Y_{0.1}Ca_{0.3}MnO_{3}$, an $ABO_{3}$ perovskite manganite oxide, exhibits a non trivial behavior in the vicinity of the sharp peak found in the resistivity $\rho$ as a function of temperature $T$ in zero magnetic field. The various features seen on $d\rho/dT$ are discussed in terms of competing phase transitions. They are related to the $Mn-O-Mn$ bond environment depending on the content of the $A$ crystallographic site. A Ginzburg-Landau type theory is presented for incorporating concurrent phase transitions. The specific heat $C$ of such a compound is also examined from 50 till 200 K. A log-log analysis indicates different regimes. In the low temperature conducting ferromagnetic phase, a collective magnon signature ($C \simeq T^{3/2}$) is found as for what are called magnon-polaron excitations. A $C \simeq T^{2/3}$ law is found at high temperature and discussed in terms of the fractal dimension of the conducting network of the weakly conducting (so-called insulating) phase and Orbach estimate of the excitation spectral behaviors. The need of considering both independent spin scattering and collective spin scattering is thus emphasized. The report indicates a remarkable agreement for the Fisher-Langer formula, i.e. $C$ $\sim$ $d\rho/dT$ at second order phase transitions. Within the Attfield model, we find an inverse square root relationship between the critical temperature(s) and the total local $Mn-O-Mn$ strain.