Colossal magnetoresistance effect and spin-dependent variable-range hopping in the charge ordered phase of overdoped (La,Ca)MnO3 manganites

Manganese oxides or manganites, widely known for their colossal magnetoresistance (CMR) effect, are systems in which spin, charge, lattice, and orbital interactions are simultaneously active, resulting in a complex phase diagram. Considerable research done mostly at low doping suggested that the CMR effect is the manifestation of the interplay of these interactions that occur in the phase-separated state composed of coexisting clusters of ferromagnetic and paramagnetic and antiferromagnetic phases. In order to get deeper insight in the physics at high doping, we have undertaken magnetoresistance and magnetization measurements of ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ thin-film samples with $x=0.5$, 0.52, 0.58, 0.62, 0.66, and 0.75, in the temperature range 1.5--300 K and in magnetic fields up to 16 T. We have observed similar characteristics of the phase diagram as for low doping: the CMR effect, ferromagnetism, and even metallic behavior for certain temperature, magnetic field, and doping values, demonstrating that the phase separation into ferromagnetic and antiferromagnetic clusters is here also in play. We find that the charge transport in the charge ordered phase takes place via spin-dependent variable-range hopping (VRH), which points towards Anderson-type localization of conducting electrons in a spin-disordered background of Mn magnetic moments. We also find a close relationship between the VRH activation energy, the CMR effect, the fraction of ferromagnetic clusters, and the charge ordering temperature, which implies that, aside from the spin disorder, the electron-electron and Jahn-Teller interactions also play an important role in the charge localization.