We report the Hall resistivity, $rho_{xy}$ of polycrystalline SmFeAsO$_{1-x}$F$_{x}$ for four different fluorine concentrations from the onset of superconductivity through the collapse of the structural phase transition. For the two more highly-doped samples, $rho_{xy}$ is linear in magnetic field up to 50 T with only weak temperature dependence, reminiscent of a simple Fermi liquid. For the lightly-doped samples with $x<0.15$, we find a low temperature regime characterized $rho_{xy}(H)$ being both non-linear in magnetic field and strongly temperature dependent even though the Hall angle is small. The onset temperature for this non-linear regime is in the vicinity of the structural phase (SPT)/spin density wave (SDW) transitions. The temperature dependence of the Hall resistivity is consistent with a thermal activation of carriers across an energy gap. The evolution of the energy gap with doping is reported.
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