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Correlating magnetic structure and magnetotransport in semimetal thin films of Eu$_{1-x}$Sm$_x$TiO$_3$

We report on the evolution of the average and depth-dependent magnetic order in thin film samples of biaxially stressed and electron-doped EuTiO$_3$ for samples across a doping range $<$0.1 to 7.8 $\times 10^{20}$ cm$^{-3}$. Under an applied in-plane magnetic field, the G-type antiferromagnetic ground state undergoes a continuous spin-flop phase transition into in-plane, field-polarized ferromagnetism. The critical field for ferromagnetism slightly decreases with an increasing number of free carriers, yet the field evolution of the spin-flop transition is qualitatively similar across the doping range. Unexpectedly, we observe interfacial ferromagnetism with saturated Eu$^{2+}$ moments at the substrate interface at low fields preceding ferromagnetic saturation throughout the bulk of the degenerate semiconductor film. We discuss the implications of these findings for the unusual magnetotransport properties of this compound.