Two hundred years ago, Ampère discovered that electric loops in which currents of electrons are generated by a penetrating magnetic field can mutually interact. Here we show that Ampères observation can be transferred to the quantum realm of interactions between triangular plaquettes of spins on a lattice, where the electrical currents at the atomic scale are associated with the orbital motion of electrons in response to the non-coplanarity of neighbouring spins playing the role of a magnetic field. The resulting topological orbital moment underlies the relation of the orbital dynamics with the topology of the spin structure. We demonstrate that the interactions of the topological orbital moments with each other and with the spins form a new class of magnetic interactions − topological-chiral interactions − which can dominate over the Dzyaloshinskii-Moriya interaction, thus opening a path for realizing new classes of chiral magnetic materials with three-dimensional magnetization textures such as hopfions. Exotic magnetic textures with particle-like properties 1-6 offer great potential for innovative spintronic applications 7 and brain-inspired computing 8,9 . Magnetic skyrmions, twodimensional (2D) localized solitons, are a prominent realization of chiral spin structures, first observed in the material class of non-centrosymmetric B20 bulk compounds 1 . The potential of spintronic applications would change fundamentally if the line of thought could be continued to the emergence of three-dimensional (3D) localized magnetic solitons, e.g. hopfions 10-12 . Recently, a 3D lattice of 3D magnetic textures on the nanometer scale was observed in the B20type cubic chiral magnets MnGe 13,14 . Despite the strong interest in this magnet, a complete theoretical model for the underlying magnetic interactions is remarkably elusive until now. While, for instance, the basic magnetic properties of the 2D skyrmions are determined by an intricate competition involving the Heisenberg exchange and the chiral relativistic Dzyaloshinskii-Moriya interaction 15,16 (DMI), such models fail to explain the 3D-magnetic texture observed in MnGe 17 .The 3D magnetization textures of 2D skyrmions gives rise to a scalar spin chirality, a driving force behind a plethora of macroscopic phenomena. Examples are the topological Hall effect 18,19 or a finite topological orbital moment (TOM) 20-25 , which can both serve as experimental fingerprints of skyrmions. Texture-induced contributions to these macroscopic phenomena were also predicted in frustrated magnets 26,27 , where they originate from the non-trivial spin topology associated with the real-space configuration of magnetic moments S i as reflected by the scalar spin chirality χ ijk = S i · (S j × S k ). Although the net spin magnetization might vanish, the symmetry of these chiral systems allows for lowering the energy by preferring orbital currents of specific rotational sense 26,28 . As a consequence, the motion of the electron in the complex magnetic background manifests itself in the finite T...

Magnons, as the most elementary excitations of magnetic materials, have recently emerged as a prominent tool in electrical and thermal manipulation and transport of spin, and magnonics as a field is considered as one of the pillars of modern spintronics. On the other hand, orbitronics, which exploits the orbital degree of freedom of electrons rather than their spin, emerges as a powerful platform in efficient design of currents and redistribution of angular momentum in structurally complex materials. Here, we uncover a way to bridge the worlds of magnonics and electronic orbital magnetism, which originates in the fundamental coupling of scalar spin chirality, inherent to magnons, to the orbital degree of freedom in solids. We show that this can result in efficient generation and transport of electronic orbital angular momentum by magnons, thus opening the road to combining the functionalities of magnonics and orbitronics to their mutual benefit in the realm of spintronics applications.

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FeGe in the B20 phase is an experimentally well-studied prototypical chiral magnet exhibiting helical spirals, skyrmion lattices and individual skyrmions with a robust length of 70 nm. While the helical spiral ground state can be verified by first-principles calculations based on density functional theory, this feature size could not be reproduced even approximately. To develop a coherent picture of the discrepancy between experiment and theory, we investigate in this work the magnetic properties of FeGe from first-principles using different electronic-structure methods. We study atomistic as well as micromagnetic parameters describing exchange and Dzyaloshinskii-Moriya interactions, and discuss their subtle dependence on computational, structural, and correlation parameters. In particular, we quantify how these magnetic properties are affected by changes of the lattice parameter, different atomic arrangements, exchange and correlation effects, finite Fermi-function broadening, and momentum-space sampling. In addition, we use the obtained atomistic parameters to determine the corresponding Curie temperature, which agrees well with experiments. Our results indicate that the well-known and well-accepted relation between the micromagnetic parameters and the period of the helical structure, is not valid for FeGe. This calls for new experiments exploring the relation by measuring independently the spin stiffness, the spiralization and the period of the helical spin spiral. :1909.13545v1 [cond-mat.mtrl-sci] arXiv

B20 compounds are the playground for various non-trivial magnetic textures such as skyrmions, which are topologically protected states. Recent measurements on B20-MnGe indicate no clear consensus on its magnetic behavior, which is characterized by the presence of either spin-spirals or 3-dimensional objects interpreted to be a cubic lattice of hedgehogs and anti-hedgehogs. Utilizing a massively parallel linear scaling all-electron density functional algorithm, we find from full firstprinciples simulations on cells containing thousands of atoms that upon increase of the compound volume, the state with lowest energy switches across different magnetic phases: ferromagnetic, spinspiral, hedgehog and monopole. arXiv:1904.12176v2 [cond-mat.mtrl-sci]

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