Relativistic bandstructure of solids generates functionalities of modern quantum, topological and spintronics materials . Common collinear antiferromagnets exhibit Kramers spin degenerate bands  and for many decades were believed to be excluded from spin splitting physics and spontaneous Hall effects. Our recent prediction of crystal time-reversal symmetry breaking by anisotropic magnetization densities (see picture) due to the collinear antiferromagnetism combined with nonmagnetic atoms  changes this perspective. Unlike the conventional relativistic spin-orbit interaction induced spin splitting, our crystal antiferromagnetic spin splitting is of exchange origin, can reach giant eV values, and can preserve spin quantum number.
In this talk, we will discuss the basic properties of this new type of antiferromagnetic spin splitting, its local magnetic symmetry origin and symmetry criteria for its emergence and we will catalogue broad class of material candidates. Furthermore, we will show that this antiferromagnetic spin splitting can generate a crystal Hall effect controllable via rearrangement of nonmagnetic atoms . Finally, we will present an experimental discovery of crystal Hall effect in ruthenium dioxide antiferromagnet .
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