Magnetic Field Control of the Fermi Surface Topology in EuTiO₃

Spin-orbit coupling plays a central role in the anomalous Hall effect (AHE) of itinerant ferromagnets and in materials with topologically non-trivial electronic states. Recently, AHE attracted significant attention in antiferromagnetic metals and semiconductors. For example, significant AHEs in non-collinear antiferromagnets have been discovered. The degenerately doped antiferromagnetic semiconductor EuTiO₃ is a unique testbed for these ideas for several reasons. Despite a small net magnetization, it exhibits an intrinsic AHE that changes sign as a function of the carrier density. We report on the symmetry of the anisotropic magnetoresistance (AMR) in doped EuTiO₃ films as a function of the applied magnetic field. Multiple transitions in the AMR symmetry are observed and are attributed to magnetic field induced changes in the band topology. At high fields a transition from positive to negative magnetoresistance coincides with change from four-fold to two-fold symmetry in the AMR. This indicates a non-trivial phase transition in the electronic structure. We discuss the results in the context of Weyl points that form in the band structure of the EuTiO₃.