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Two hundred years ago, Andr\'e-Marie Amp\`ere discovered that electric loopsin which currents of electrons are generated by a penetrating magnetic fieldcan interact with each other. Here we show that Amp\`ere's observation can betransferred to the quantum realm of interactions between triangular plaquettesof spins on a lattice, where the electrical currents at the atomic scale areassociated with a peculiar type of the orbital motion of electrons in responseto the non-coplanarity of neighbouring spins playing the role of a magneticfield. The resulting topological orbital moment underlies the relation of theorbital dynamics with the topology of the spin structure. We demonstrate thatthe interactions of the topological orbital moments with each other and withthe spins of the underlying lattice give rise to a new class of magneticinteractions $-$ topological chiral interactions $-$ which can dominate overthe celebrated Dzyaloshinskii-Moriya interaction, thus opening a path for therealization of new classes of chiral magnetic materials with three-dimensionalmagnetization textures such as magnetic hopfions.

Topological-chiral magnetic interactions driven by emergent orbital magnetism