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Abstract The concept of Berry phase and Berry curvature has become ubiquitous in solid state physics as it relates to variety of phenomena, such as topological insulators, polarization, and various Hall effects. It is well known that large Berry curvatures arise from close proximity of hybridizing bands, however, the vectorial nature of the Berry curvature is not utilized in current research. On bulk bcc Fe, we demonstrate the flow of the Berry curvature vector field which features not only monopoles but also higher dimensional structures with its own topological features. They can provide a novel unique view on the electronic structure in all three dimensions. This knowledge is also used to quantify particular contributions to the intrinsic anomalous Hall effect in a simple analytical form.

Abstract Magneto-optical effects are among the basic tools for characterization of magnetic materials. Although these effects are routinely calculated by the ab initio codes, there is very little knowledge about their origin in the electronic structure. Here, we analyze the magneto-optical effect in bcc Fe and show that it originates in avoided band-crossings due to the spin-orbit interaction. Therefore, only limited number of bands and k-points in the Brillouin zone contribute to the effect. Furthermore, these contributions always come in pairs with opposite sign but they do not cancel out due to different band curvatures providing different number of contributing reciprocal points. The magneto-optical transitions are classified by the dimensionality of the manifold that is formed by the hybridization of the generating bands as one- or two-dimensional, and by the position relative to the magnetization direction as parallel and perpendicular. The strongest magneto-optical signal is provided by two-dimensional parallel transitions.