Electric- and magnetic-field-driven nonlinear charge transport and magnetic ordering in epitaxial films of ${\mathrm{Pr}}_{0.7}{\mathrm{Ca}}_{0.3-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$

Electric- and magnetic-field-dependent resistivity, and magnetization are studied in epitaxial films of ${\mathrm{Pr}}_{0.7}{\mathrm{Ca}}_{0.3-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3$ between 4.2 and 300 K. Attention is focused on how the substitution of Sr at the Ca sites of the parent compound ${\mathrm{Pr}}_{0.7}{\mathrm{Ca}}_{0.3}{\mathrm{MnO}}_3$ affects the electrical and magnetic states of this canonical charge-ordered (CO) insulator. The resistivity (ρ) of the parent compound is characterized by a gradual increase on cooling below 300 until 205 K, where it shows a steplike enhancement. We identify this step as the onset temperature ${(T}_{\mathrm{CO}})$ of the CO state. Below 205 K, a well-defined Arrhenius-type of resistivity with activation energy of 0.13 eV suggests excitation of holes across the CO gap as the mechanism of charge transport in the parent compound. In the films with $x=0.03\mathrm{}$ and 0.07, this band-to-band excitation process gives way to a Mott-type, spin-dependent hopping transport from $T_{\mathrm{CO}}$ to a crossover temperature $T_2(<\mathrm{}{T}_{\mathrm{CO}}).\mathrm{}$ Over a narrow temperature range below $T_2$ and a second crossover temperature $T_3,$ the films show a metallic character followed by the onset of a second insulating state, which persists down to the lowest temperature of measurement (4.2 K). In the regime of temperature between $T_2$ and 4.2 K, the transport in films with $x=0.03\mathrm{}$ and 0.07 is highly nonlinear in electric field, and displays hysteretic and history effects. In this regime of temperature, the resistivity also shows a large drop on application of a magnetic field. In samples with $x>~0.1,$ while the large magnetoresistance in the vicinity of $T_2$ and the minimum in ρ at $T_3$ persist, the transport remains Ohmic. Our magnetization measurements show the onset of ferromagnetic ordering in the vicinity of $T_2$ in all Sr-substituted films. However, for $x<\mathrm{}0.1,$ a low value of the field-cooled moment and a spin-glass type of behavior seen at temperatures below $T_3$ suggest formation of ferromagnetic clusters whose moment is gradually blocked with decreasing temperature. We argue that the nonlinear and hysteretic effects seen in samples with $x<~0.1$ are a result of classical percolation and quantum transport in a topologically inhomogeneous medium.