Structural and magnetic properties of FeMnx_x (x=x=1...6) chains supported on Cu2_2N / Cu (100)

Heterogeneous atomic magnetic chains are built by atom manipulation on a Cu$_2$N/Cu (100) substrate. Their magnetic properties are studied and rationalized by a combined scanning tunneling microscopy (STM) and density functional theory (DFT) work completed by model Hamiltonian studies. The chains are built using Fe and Mn atoms ontop of the Cu atoms along the N rows of the Cu$_2$N surface. Here, we present results for FeMn$_x$ ($x$=1...6) chains emphasizing the evolution of the geometrical, electronic, and magnetic properties with chain size. By fitting our results to a Heisenberg Hamiltonian we have studied the exchange-coupling matrix elements $J$ for different chains. For the shorter chains, $x \leq 2$, we have included spin-orbit effects in the DFT calculations, extracting the magnetic anisotropy energy. Our results are also fitted to a simple anisotropic spin Hamiltonian and we have extracted values for the longitudinal-anisotropy $D$ and transversal-anisotropy $E$ constants. These parameters together with the values for $J$ allow us to compute the magnetic excitation energies of the system and to compare them with the experimental data.Comment: 10 pages 8 figure

Colloquium: Atomic spin chains on surfaces

In the present Colloquium, we focus on the properties of 1-D magnetic systems on solid surfaces. From the emulation of 1-D quantum phases to the potential realization of Majorana edge states, spin chains are unique systems to study. The advent of scanning tunnelling microscope (STM) based techniques has permitted us to engineer spin chains in an atom-by-atom fashion via atom manipulation and to access their spin states on the ultimate atomic scale. Here, we present the current state of research on spin correlations and dynamics of atomic spin chains as studied by the STM. After a brief review of the main properties of spin chains on solid surfaces, we classify spin chains according to the coupling of their magnetic moments with the holding substrate. This classification scheme takes into account that the nature and lifetimes of the spin-chain excitation intrinsically depend on the holding substrate. We first show the interest of using insulating layers on metals, which generally results in an increase in the spin state's lifetimes such that their quantized nature gets evident and they are individually accessible. Next, we show that the use of semiconductor substrates promises additional control through the tunable electron density via doping. When the coupling to the substrate is increased for spin chains on metals, the substrate conduction electron mediated interactions can lead to emergent exotic phases of the coupled spin chain-substrate conduction electron system. A particularly interesting example is furnished by superconductors. Magnetic impurities induce states in the superconducting gap. Due to the extended nature of the spin chain, the in-gap states develop into bands that can lead to the emergence of 1-D topological superconductivity and, consequently to the appearance of Majorana edge states

Visualization of multifractal superconductivity in a two-dimensional transition metal dichalcogenide in the weak-disorder regime

Eigenstate multifractality is a distinctive feature of non-interacting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic weakly disordered single-layer NbSe$_2$ by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. Spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f($\alpha$) shows anomalous scaling behavior typical from 2D weakly disordered systems

Atomic Manipulation of In-gap States on the β\beta-Bi2_2Pd Superconductor

Electronic states in the gap of a superconductor inherit intriguing many-body properties from the superconductor. Here, we create these in-gap states by manipulating Cr atomic chains on the $\beta$-Bi$_2$Pd superconductor. We find that the topological properties of the in-gap states can greatly vary depending on the crafted spin chain. These systems make an ideal platform for non-trivial topological phases because of the large atom-superconductor interactions and the existence of a large Rashba coupling at the Bi-terminated surface. We study two spin chains, one with atoms two-lattice-parameter apart and one with square-root-of-two lattice parameters. Of these, only the second one is in a topologically non-trivial phase, in correspondence with the spin interactions for this geometry

Influence of Magnetic Ordering between Cr Adatoms on the Yu-Shiba-Rusinov States of the β-Bi2Pd Superconductor

We show that the magnetic ordering of coupled atomic dimers on a superconductor is revealed by their intragap spectral features. Chromium atoms on the superconductor β-Bi2Pd surface display Yu-Shiba-Rusinov bound states, detected as pairs of intragap excitations in tunneling spectra. By means of atomic manipulation with a scanning tunneling microscope's tip, we form Cr dimers with different arrangements and find that their intragap features appear either shifted or split with respect to single atoms. These spectral variations are associated with the magnetic coupling, ferromagnetic or antiferromagnetic, of the dimer, as confirmed by density functional theory simulations. The striking qualitative differences between the observed tunneling spectra prove that intragap Shiba states are extremely sensitive to the magnetic ordering on the atomic scaleWe thank Javier Zaldivar and Joeri de Bruijckere for developing the deconvolution process and Sebastian Bergeret for discussions. D.-J. C. and J. I. P. thank the European Union for support under the H2020-MSCA-IF-2014 Marie-Curie Individual Fellowship program (Proposal No. 654469), Spanish MINECO (MAT2016-78293-C6-1-R), Diputacion Foral de Gipuzkoa for Grant No. 64/15, and the European Regional Development Fund (ERDF). N. L. thanks Spanish MINECO (Grant No. MAT2015-66888-C3-2-R). M. M. U. acknowledges Spanish MINECO (MAT2014-60996-R). E. H., I. G., and H. S. acknowledge FIS2014-54498-R and MDM-2014-0377, COST MP16218 nanocohybri, ERC PNICTEYES Grant Agreement No. 679080, and Departamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS (Colombia), Programa doctorados en el exterior and convocatoria 568-2012, as well as Comunidad de Madrid through program Nanofrontmag-CM (Grant No. S2013/MIT-2850

Coexistence of elastic modulations in the charge density wave state of 2H-NbSe₂

Bulk and single-layer 2H-NbSe₂ exhibit identical charge density wave order (CDW) with a quasi-commensurate 3 × 3 superlattice periodicity. Here we combine scanning tunnelling microscopy (STM) imaging at T = 1 K of 2H-NbSe₂ with first-principles density functional theory (DFT) calculations to investigate the structural atomic rearrangement of this CDW phase. Our calculations for single-layers reveal that six different atomic structures are compatible with the 3 × 3 CDW distortion, although all of them lie on a very narrow energy range of at most 3 meV per formula unit, suggesting the coexistence of such structures. Our atomically resolved STM images of bulk 2H-NbSe₂ unambiguously confirm this by identifying two of these structures. Remarkably, these structures differ from the X-ray crystal structure reported for the bulk 3 × 3 CDW which in fact is also one of the six DFT structures located for the single-layer. Our calculations also show that due to the minute energy difference between the different phases, the ground state of the 3 × 3 CDW could be extremely sensitive to doping, external strain or internal pressure within the crystal. The presence of multiphase CDW order in 2H-NbSe₂ may provide further understanding of its low temperature state and the competition between different instabilities

Orbital-selective spin excitation of a magnetic porphyrin

Scattering of electrons by localized spins is the ultimate process enabling detection and control of the magnetic state of a spin-doped material. At the molecular scale, scattering is mediated by the orbitals hosting the spin. Here we report the selective excitation of a molecular spin by tunneling through different molecular orbitals. Spatially resolved tunneling spectra on iron-porphyrins reveal that the inelastic spin excitation extends beyond the iron site, changing shape and symmetry along the molecule. Combining density functional theory simulations with a phenomenological scattering model, we show that the extension and lineshape of the inelastic signal are due to excitation pathways assisted by different frontier orbitals. By selecting the intramolecular site for electron injection, the relative weight of iron and pyrrole orbitals in the tunneling process is modified. Thus, the excitation mechanism, reflected by its spectral lineshape, depends on the degree of localization and energy alignment of the chosen molecular orbital.This work has been funded by the COST 15128 Molecular Spintronics project, by Marie Curie IF ARTE, by the Spanish Ministerio de Economía y Competitividad (MINECO) through the cooperative grant No. MAT2016-78293 and grant No. FIS2016-75862-P, and by the Basque Government (Dep. Industry, Grant PI-2015-1-42, Dep. Education, Grant PI-2016-1-27 and Grant IT-756-13), the EU project PAMS (610446), and the European Regional Development Fund (ERDF)

Magnetic field dependence of magnetic impurities on superconductors

Resumen del trabajo presentado a la International Conference on Nanoscience + Technology (ICN+T), celebrada en Brno (Czech Republic) del 22 al 27 de julio de 2018.Magnetic adatoms can be considered as impurities that weaken the binding of superconducting Cooper pairs leading to impurity levels in the gap: so-called Yu-Shiba-Rusinov (YSR) states. In-gap states caused by a Cr magnetic impurity on a superconducting Pb (111) thin film are studied in the presence of an external magnetic field using a scanning tunneling microscope. We show that the lifetimes of these states can be considerably modified by applying magnetic fields. The result shows that the magnetic impurity does not alter the superconducting gap however, it enhances the rate of Cooper-pair dissociation by a constant value. Surprisingly, the large Pb spin-orbit coupling does not influence the field-induced depairing and we show that only orbital effects intervene in the effective destruction of Pb superconductivity by an external magnetic field.Peer reviewe