Magnetoresistance scaling in MBE-grown ${\mathrm{La}}_{0.7}$${\mathrm{Ca}}_{0.3}$Mn${\mathrm{O}}_3$ thin films

We present a detailed analysis of magnetoresistance in tetragonal thin films of ferromagnetic ${\mathrm{La}}_{0.7}{\mathrm{Ca}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{\delta }$ grown by atomic layer-by-layer molecular-beam epitaxy. The field and temperature dependence of the resistivity $\rho$ show an explicit dependence only on the fractional magnetization $\frac{M}{M_{\mathrm{sat}}}$ and are consistent with a single approximate form $\rho \approx \rho \mathrm{}\left(0\right)\mathrm{}\exp [-C{\left(\frac{M}{M_{\mathrm{sat}}}\right)}^2]$ for small and intermediate magnetization both above and below the Curie temperature ($T_C$). The microscopic magnetization and susceptibility ($\chi$) have been inferred from the low-field magnetoresistance above $T_C$ with $\chi$ following a Curie-Weiss form. We observe a sharp transition in the low-field ($H$) dependence of $\rho$ from quadratic ($\propto H^2$) above $T_C$ to linear ($\propto H$) below, consistent with a temperature-independent $\rho \mathrm{}\left(M\right)\mathrm{}$. Finally we show that within a simple model this temperature-independent form for $\rho$ reproduces the behavior of the measured low-field sensitivity below $T_C$.