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Magnetic vortices are topological spin structures frequently found in ferromagnets, yet novel to antiferromagnets. By combining experiment and theory, it is demonstrated that in a nanostructured antiferromagnetic‐ferromagnetic NiO(111)‐Fe(110) bilayer, a magnetic vortex is naturally stabilized by magnetostatic interactions in the ferromagnet and is imprinted onto the adjacent antiferromagnet via interface exchange coupling. Micromagnetic simulations are used to construct a corresponding phase diagram of the stability of the imprinted antiferromagnetic vortex state. The in‐depth analysis reveals that the interplay between interface exchange coupling and the antiferromagnet magnetic anisotropy plays a crucial role in locally reorienting the Néel vector out‐of‐plane in the prototypical in‐plane antiferromagnet NiO and thereby stabilizing the vortices in the antiferromagnet. Nanoscale magnetic vortex is naturally stabilized by magnetostatic interactions in the ferromagnet and is imprinted onto the adjacent antiferromagnet via interface exchange coupling. The interplay between interface exchange coupling and the antiferromagnet magnetic anisotropy plays a crucial role in locally reorienting the Néel vector out‐of‐plane in the prototypical in‐plane antiferromagnet NiO and thereby stabilizing the vortices in the antiferromagnet.

Let V be a pseudo-Riemannian n -dimensional manifold or, more generally, let ( ξ , Q ) be a real fibre bundle whose base space is a paracompact space endowed with a non-degenerate quadratic form Q , (that is, with a structure group O ( p , q ) , n = p + q .) Let K p , q denote the obstruction class for the existence of a Pin ( p , q ) -spin structure on V or over ξ . Let K Conf ( p , q ) denote the obstruction class for the existence of a conformal spin structure in a strict sense on V or over ξ , (simply: a C n s ( p , q ) -spin structure), if n = 2 r , or of a conformal special spin structure, if n = 2 r + 1 . This short self-contained paper will recall the determination of the obstruction class K p , q on V ,  or over ξ , for n even or odd. Then, the obstruction class K p + 1 , q + 1 for the existence of a Pin ( p + 1 , q + 1 ) -spin structure over ξ j , (Greub’s j -extension of ξ , where j denotes the identity mapping from O ( p , q ) into O ( p + 1 , q + 1 ) ), will be determined in order to express K Conf ( p , q ) , for n = 2 r or n = 2 r + 1 , in terms of the Stiefel–Whitney classes w i ( p , q ) , i = 1 , 2 , of ξ , decomposed as the Whitney sum ξ = ξ + ⊕ ξ - , where the restriction of Q to ξ + is positive definite and the restriction of Q to ξ - is negative. If n = 2 r , we find again results obtained in previous publications [ 4 , 5 , 7 ], by different methods.

We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this classification in two different ways; through examining the differential of the actions and through representation theory.

I propose a novel physically based and pedagogically motivated approach to description of the electron spin origin and its Dirac Hamiltonian operator representation. There electron symmetry properties and related conservation laws are treated from mathematical physics point of view, having put into background the algebraic description of the corresponding physically observed representations. There are also analyzed in detail the spin structure and its crucial dependence on the SU(2)-symmetry properties of the related representations of the basic Clifford algebra, generated by creation-annihilation operators on the Fock space and the related chirality symmetry of the Pauli spin operators. Based on the physically confirmed conservation law of the electron spin projection on its momentum there is proposed a new derivation of the Dirac Hamiltonian operator, whose Lorentz invariance follows naturally from its structure as that naturally related to the fundamental Maxwell equations, whose quanta are carriers of interaction between electrons.

The spin structures of Bose-Einstein condensates (BEC) with three kinds of spin-1 atoms are studied. The many-body Hamiltonian is diagonalized in the spin space via a strict numerical approach to obtain eigen-energies and eigen-states. The emphasis is to clarify the effect of the singlet pairing force with the strength Γ. This force has been neglected in previous studies on 3-species BEC. We found that the classification scheme for the phases of the ground state (g.s.) found previously with Γ = 0 remains to be valid if the total spin of each species (which is conserved previously but not now) is replaced by its average S J ¯ . Accordingly, the phase-diagrams for the g.s. remain qualitatively unchanged except for a shift of the boundaries (critical surfaces) separating the zones (each for a phase). However, neighboring to the critical surface which designates the breakdown of the ppp-phase (all the three species are in the polar phase), we found that there is a narrow zone in which the spin structure is extremely sensitive to the variation of the parameters if Γ is negative. It implies that, once the ppp-phase is broken, a great adjustment in spin structure will follow. This highly sensitive narrow zone does not exist if Γ = 0 .

This self-contained paper wants to precise the study of a real conformal spin structure in a strict sense over a pseudo-Riemannian or Riemannian 2 r -dimensional manifold V already made in previous publications (Anglès in Studia Scientiarum Mathematicarum Hungarica 23:115–139, 1988 ; Anglès in Progress in Mathematical Physics, vol 50. Birkhäuser, Boston, 2008 ). We give a fundamental diagram (A) concerning U (1)-spin geometry, a notion which has been initiated in Atiyah et al. (Topology 3(suppl 1):3–38 (Pergamon Press), 1964 ), in a special case. The obstruction class for the existence of a conformal spin structure in a strict sense over V is studied. Necessary and sufficient conditions for the existence of such a structure are recalled, using groups called conformal spinoriality groups in a strict sense. The notion of a conformal U (1)-spin structure over a pseudo-Riemannian or Riemannian 2 r -dimensional manifold V is defined and studied. Two fundamental diagrams (B) and (C), relative to the conformal U (1)-spin geometry are given. We study the obstruction class for the existence of a conformal U (1)-spin structure over V . New fiber bundles are defined.

Reservoir computing (RC) has been considered as one of the key computational principles beyond von-Neumann computing. Magnetic skyrmions, topological particle-like spin textures in magnetic films are particularly promising for implementing RC, since they respond strongly nonlinearly to external stimuli and feature inherent multiscale dynamics. However, despite several theoretical proposals that exist for skyrmion reservoir computing, experimental realizations have been elusive until now. Here, we propose and experimentally demonstrate a conceptually new approach to skyrmion RC that leverages the thermally activated diffusive motion of skyrmions. By confining the electrically gated and thermal skyrmion motion, we find that already a single skyrmion in a confined geometry suffices to realize nonlinearly separable functions, which we demonstrate for the XOR gate along with all other Boolean logic gate operations. Besides this universality, the reservoir computing concept ensures low training costs and ultra-low power operation with current densities orders of magnitude smaller than those used in existing spintronic reservoir computing demonstrations. Our proposed concept is robust against device imperfections and can be readily extended by linking multiple confined geometries and/or by including more skyrmions in the reservoir, suggesting high potential for scalable and low-energy reservoir computing. Magnetic skyrmions, due to their strongly nonlinearity and multiscale dynamics, are promising for implementing reservoir computing. Here, the authors experimentally demonstrate skyrmion-based spatially multiplexed reservoir computing able to perform Boolean Logic operations, using thermal and current driven dynamics of spin structures.

The interconversion of charge and spin currents via spin-Hall effect is essential for spintronics. Energy-efficient and deterministic switching of magnetization can be achieved when spin polarizations of these spin currents are collinear with the magnetization. However, symmetry conditions generally restrict spin polarizations to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced. Here, we show control of the spin polarization direction by using a non-collinear antiferromagnet Mn 3 GaN, in which the triangular spin structure creates a low magnetic symmetry while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn 3 GaN/permalloy heterostructures can generate unconventional spin-orbit torques at room temperature corresponding to out-of-plane and Dresselhaus-like spin polarizations which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spin-orbit torque, enabling high-efficient antiferromagnetic spintronics. In the typical spin-hall effect, spin-current, charge current, and spin polarisation are all mutually perpendicular, a feature enforced by symmetry. Here, using an anti-ferromagnet with a triangular spin structure, the authors demonstrate a spin-hall effect without a perpendicular spin alignment.

SignificanceThe exactly solvable Kitaev model of bond-dependent near-neighbor interactions has drawn attention to quantum spins on the honeycomb lattice. But exotic quantum magnetism may also arise from competing interactions beyond nearest neighbors. Combining state-of- the-art theory and neutron scattering, we show that ferromagnetic nearest-neighbor interactions between effective spin-1/2 Co2+ spins in BaCo2(AsO4)2 are frustrated by antiferromagnetic third neighbor interactions. While an in-plane field suppresses the resulting incommensurate order, a ĉ−oriented field enhances quantum fluctuations. The spin Hamiltonian that we obtain will inform the search for quantum spin liquid physics in BaCo2(AsO4)2 subjected to tilted fields. Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid (KSL) state. One of the front-runners is BaCo2(AsO4)2 (BCAO), where it was suggested that the exchange processes between Co2+ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze a comprehensive inelastic neutron scattering (INS) study of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelastic spin structure factor measured in zero magnetic field, we examine two leading theoretical models: the Kitaev-type JKΓΓ′ model and the XXZ-J1-J3model. We show that the existing experimental data can be consistently accounted for by the XXZ-J1-J3model but not by the JKΓΓ′ model, and we discuss the implications of these results for the realization of a spin liquid phase in BCAO and more generally for the realization of the Kitaev model in cobaltates.

In this paper, we obtain explicit expressions for Pandharipande-Pixton-Zvonkine relations in the second rational cohomology of \\(M_g,n\\) and comparing the result with Arbarello-Cornalba's theorem we prove Pixton's conjecture in this case.