The quantum coupling of fully di erent degrees of freedom is a challenging path towards new functionalities for quantum electronics [1][2][3] . Here we show that the localized classical spin of a magnetic atom immersed in a superconductor with a twodimensional electronic band structure gives rise to a long-range coherent magnetic quantum state. We experimentally evidence coherent bound states with spatially oscillating particle-hole asymmetry extending tens of nanometres from individual iron atoms embedded in a 2H-NbSe 2 crystal. We theoretically elucidate how reduced dimensionality enhances the spatial extent of these bound states and describe their energy and spatial structure. These spatially extended magnetic states could be used as building blocks for coupling coherently distant magnetic atoms in new topological superconducting phases 4-11
ARTICLES 546nature materials | VOL 2 | AUGUST 2003 | www.nature.com/naturematerials E xploring the ultimate density limits of magnetic information storage, whether on computer hard disks or in MRAMs (magnetic random access memories), requires elaborate tuning of the preferred (easy) magnetization axis, of the magnetic anisotropy energy, and of the magnetic moment in the units used to store a bit. These units are single-domain particles (with diameter d < 20 nm) where the magnetic moments of all atoms are ferromagnetically aligned 1 to form the overall magnetic moment of the particle M, which is also called the macrospin. The preferred orientations of M, and the anisotropy energy barriers K separating them, are given by the delicate balance between several competing energies. These are the magnetocrystalline bulk anisotropy, its surface and step counterparts, and the shape anisotropy, or demagnetizing energy, resulting from the interaction of M with its own dipolar stray field. Unravelling the anisotropy's origin is far from trivial due to the competition between these energies 2 . This is unfortunate because the anisotropy is one of the key quantities: it defines the stability of the magnetization direction against thermal excitation,and therefore the minimum particle size for which non-volatile information storage may be achieved (at 300 K this requires K ≥ 1.2 eV). A further key parameter is the modulus of M, M defining the dipolar stray field used to read and write, but also mediating interactions between adjacent bits. These interactions are minimized for out-of-plane magnetization, and because the ultimate limit of single-particle bits may only be achieved for uniaxial systems, uniaxial out-of-plane systems are best suited to explore the ultimate density limit of magnetic recording 3,4 . Current studies attempting to identify the origin of magnetic anisotropy mainly deal with two model systems. These are colloids or three-dimensional (3D) nanoparticles, and 2D nanostructures created by molecular-beam epitaxy at single-crystal surfaces. For colloid particles, remarkable progress has been achieved in monodispersity 5 , their self-assembly into 2D superlattices 6,7 and in the accomplished anisotropy energies per constituent atom 8 . Despite their promising properties for applications,3D nanoparticles present several difficulties for tracing back the origin of anisotropy. First, although the magnetism of a single particle can be addressed 9 , it is almost impossible to study the morphology of the very same particle in conjunction with its magnetism. Second, the particles frequently have a few atomic layers of oxide at their surface, which is not ferromagnetic
Just like insulators can present topological phases characterized by Dirac edge states, superconductors can exhibit topological phases characterized by Majorana edge states. In particular, one-dimensional topological superconductors are predicted to host zero-energy Majorana fermions at their extremities. By contrast, two-dimensional superconductors have a one-dimensional boundary which would naturally lead to propagating Majorana edge states characterized by a Dirac-like dispersion. In this paper we present evidences of one-dimensional dispersive in-gap edge states surrounding a two-dimensional topological superconducting domain consisting of a monolayer of Pb covering magnetic Co–Si islands grown on Si(111). We interpret the measured dispersive in-gap states as a spatial topological transition with a gap closure. Our method could in principle be generalized to a large variety of heterostructures combining a Rashba superconductor with a magnetic layer in order to be used as a platform for engineering topological quantum phases.
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