Chiral spin textures such as skyrmions are of interest to the field of spintronics for their potential use in future computing devices. Hall effect measurements are a simple and powerful method to probe the electronic and magnetic properties of materials. The topological Hall effect, which appears as anomalies in Hall resistance versus magnetic field measurements compared to magnetic measurements, has frequently been used to establish the occurrence of chiral spin textures. However, in addition to experimental issues, intrinsic electronic mechanisms combined with inhomogeneity in materials and at interfaces can lead to an inhomogeneous anomalous Hall effect which could be mistaken for a topological Hall signal. This review covers recent research using Hall effect measurements to probe chiral spin textures, focusing on SrRuO₃ as a model system. The ambiguity between Hall effects due to topological sources has led to disagreement in the interpretation of experimental results and casts doubts on the effectiveness of these techniques for investigating chiral spin textures.

Three-dimensional strontium ruthenate (${\mathrm{SrRuO}}_3$) is an itinerant ferromagnet that features Weyl points acting as sources of emergent magnetic fields, anomalous Hall conductivity, and unconventional spin dynamics. Integrating ${\mathrm{SrRuO}}_3$ in oxide heterostructures is potentially a novel route to engineer emergent electrodynamics, but its electronic band topology in the two-dimensional limit remains unknown. Here we show that ultrathin ${\mathrm{SrRuO}}_3$ exhibits spin-polarized topologically nontrivial bands at the Fermi energy. Their band anticrossings show an enhanced Berry curvature and act as competing sources of emergent magnetic fields. We control their balance by designing heterostructures with symmetric (${\mathrm{SrTiO}}_3$/${\mathrm{SrRuO}}_3$/${\mathrm{SrTiO}}_3$ and ${\mathrm{SrIrO}}_3$/${\mathrm{SrRuO}}_3$/${\mathrm{SrIrO}}_3$) and asymmetric interfaces (${\mathrm{SrTiO}}_3$/${\mathrm{SrRuO}}_3$/${\mathrm{SrIrO}}_3$). Symmetric structures exhibit an interface-tunable single-channel anomalous Hall effect, while ultrathin ${\mathrm{SrRuO}}_3$ embedded in asymmetric structures shows humplike features consistent with multiple Hall contributions. The band topology of two-dimensional ${\mathrm{SrRuO}}_3$ proposed here naturally accounts for these observations and harmonizes a large body of experimental results.

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO₃/SrTiO₃ interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

We investigate the physical mechanisms for achieving an electrical control of conventional spin-singlet superconductivity in thin films by focusing on the role of surface orbital polarization. Assuming a multiorbital description of the metallic state, due to screening effects the electric field acts by modifying the strength of the surface potential and, in turn, yields nontrivial orbital Rashba couplings. The resulting orbital polarization at the surface and in its close proximity is shown to have a dramatic impact on superconductivity. We demonstrate that, by varying the strength of the electric field, the superconducting phase can be either suppressed, i.e., turned into normal metal, or undergo a 0-$\pi$ transition with the $\pi$ phase being marked by nontrivial sign change of the superconducting order parameter between different bands. These findings unveil a rich scenario to design heterostructures with superconducting orbitronics effects.