We report magnetotransport properties of the low-temperature Fermi liquid in SrTiO${}_{3-x}$ single crystals. The classical limit dominates the magnetotransport properties for a magnetic field perpendicular to the sample surface and consequently a magnetic-field induced resistivity minimum emerges. While for the field applied in plane and normal to the current, the linear magnetoresistance (MR) starting from small fields ($<$ 0.5 T) appears. The large anisotropy in the transverse MRs reveals the strong surface interlayer scattering due to the large gradient of oxygen vacancy concentration from the surface to the interior of SrTiO${}_{3-x}$ single crystals. Moreover, the linear MR in our case was likely due to the inhomogeneity of oxygen vacancies and oxygen vacancy clusters, which could provide experimental evidence for the unusual quantum linear MR proposed by Abrikosov [Phys. Rev. B 58, 2788 (1998)].

• Received 19 October 2011

DOI:https://doi.org/10.1103/PhysRevB.85.155114