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.

By means of an exact diagonalization technique, we analyze the ground state configurations that emerge out of the competition between the octahedral distortions, the Coulomb interactions, and the spin-orbit coupling in the case of two effective $t_{2g}$ sites in $4d^4$ configuration. We show that the crystalline field is a suitable quantum control of the magnetic and orbital correlations, leading to predominant antiferromagnetic (ferromagnetic) exchange with ferro- (antiferro-) like orbital correlations in the flat (elongated) octahedral configuration. Moreover, the role of the spin-orbit coupling is investigated with respect to the character of the octahedral deformations. One of the main findings is the occurrence of anisotropic spin patterns with partially filled orbital occupation and coexisting ferro- and antiferrolike correlations in the spin∕orbital channel. Finally, the possibility of competing states with partial orbital occupation is amplified when a spin polarizing field is added to the system. Its role in controlling magnetic∕orbital correlations is also presented.

We use an exact-diagonalization technique to investigate the phase diagram of correlated $t_{2g}$ electrons within the single-layer Ca-based ruthenates. The interplay between the charge fluctuations, induced by the crystalline field potential, and those due to the Coulomb correlations leads to different magnetic and orbital patterns. We show that the compressive octahedra distortions tend to stabilize an antiferromagnetic state with $C$- or $G$-type structure and different orbital configurations, depending on the degree of flattening. In the case of elongated octahedra, as a consequence of the orbital frustration, a ground state with incomplete ferromagnetism appears, except in the limit of large Coulomb repulsion with respect to the Hund’s rule, where an antiferromagnetic $G$-type state emerges.

A method combining the extended Hückel theory and the tight-binding approximation is proposed to study the electronic properties of the layered noncuprate superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4.$ The band structure close to the Fermi level is obtained by integrating out all low-lying oxygen degrees of freedom allowing the determination of the energy spectra, the Fermi surface, and the total density of states. The results reproduces the main features of local-density approximation calculations near the Fermi energy. As an application of the approach here proposed, we have calculated the temperature dependence of the in-plane Hall coefficient considering the effect of the curvature of the Fermi surface.

We analyze the dc Josephson effect in a ballistic superconductor/ferromagnet/superconductor junction by means of the Bogoliubov\char21{}de Gennes equations in the quasiclassical Andreev approximation. We consider the possibility of ferromagnetism originating from a mass renormalization of carriers of opposite spin, i.e., a spin bandwidth asymmetry. We provide a general formula for Andreev levels that is valid for arbitrary interface transparency, exchange interaction, and bandwidth asymmetry, and we analyze the current-phase relation, free energy, and critical current in the short junction regime. We compare the phase diagrams and the critical current magnitudes of two identical junctions differing only in the mechanism by which the midlayer becomes magnetic. We show that a larger number of 0-$\pi${} transitions caused by a change in junction width or polarization magnitude is expected when ferromagnetism is driven by spin bandwidth asymmetry compared to Stoner magnetism. Moreover, we show that these features can be present also for ferromagnets of the Stoner type having only a partial bandwidth asymmetry.