Tailored flux pinning in superconductor/ferromagnet multilayers with engineered magnetic domain morphology from stripes to skyrmions
X. Palermo, N. Reyren, S. Mesoraca, A. V. Samokhvalov, S. Collin, F. Godel, A. Sander, K. Bouzehouane, J. Santamaría, V. Cros, A. I. Buzdin, Javier E. Villegas
Superconductor/Ferromagnet (S/F) hybrid systems show interesting magneto-transport behaviors that result from the transfer of properties between both constituents. For instance, magnetic memory can be transferred from the F into the S through the pinning of superconducting vortices by the ferromagnetic textures. The ability to tailor this type of induced behavior is important to broaden its range of applications. Here we show that engineering the F magnetization reversal allows tuning the strength of the vortex pinning (and memory) effects, as well as the field range in which they appear. This is done by using magnetic multilayers in which Co thin films are combined with different heavy metals (Ru, Ir, Pt). By choosing the materials, thicknesses, and stacking order of the layers, we can design the characteristic domain size and morphology, from out-of-plane magnetized stripe domains to much smaller magnetic skyrmions. These changes strongly affect the magneto-transport properties. The underlying mechanisms are identified by comparing the experimental results to a magnetic pinning model.
We study the spin-density wave (stripe) instability in lattices with mixed low-temperature orthorhombic (LTO) and low-temperature tetragonal (LTT) crystal symmetry. Within an explicit mean-field model it is shown how local LTT regions act as pinning centers for static stripe formation. We calculate the modulations in the local density of states near these local stripe regions and find that mainly the coherence peaks and the van Hove singularity (VHS) are spatially modulated. Lastly, we use the real-space approach to simulate recent tunneling data in the overdoped regime where the VHS has been …
The evolution of an anelastic relaxation process occurring around 80 K in La{2-x}Sr{x}CuO{4} at a measuring frequency of ~1 kHz has been followed from x = 0.0075 to the overdoped region, x = 0.2, where it disappears. The dependence of the peak intensity on doping is consistent with a polaronic mechanism, identified with the disordered charge stripes overcoming pinning centers. A marked decrease of the peak amplitude occurs at x > 0.045, the same doping range where a change of the stripe order from parallel to diagonal with respect to the Cu-O bonds has been observed by neutron diffraction. Bot…
The response of charge stripes to an external electric field applied perpendicular to the stripe direction is studied within a diagrammatic approach for both weak and strong pinning by random impurities. The sound-like mode of the stripes described as elastic strings moves to finite frequency due to impurity pinning. By calculating the optical conductivity we determine this characteristic energy scale for both a single stripe and an array of interacting stripes. The results explain the anomalous far-infrared peak observed recently in optical-conductivity measurements on cuprates.
We examine the effects of disorder on striped phases in high-temperature superconductors and related materials. In the presence of quenched disorder, pinning by the atomic lattice - which might give rise to commensuration effects - is irrelevant for the stripe array on large length scales. As a consequence, the stripes have divergent displacement fluctuations and topological defects are present at all temperatures. Therefore the positional order of the stripe array is short ranged, with a finite correlation length even at zero temperature. Thus lock-in phenomena can exist only as crossovers bu…
We propose a mechanism for superconductivity suppression in stripe-correlated cuprates based on the pinning of the stripes by impurities, such as Zn. The suppression of superfluid density occurs in the vicinity of the impurity due to the low dimensional character of superfluid carriers on the stripes. Simple geometric argument about the planar fraction of the carriers, affected by stripe pinning, leads to prediction for impurity critical concentration $z_c \sim T^2_c$ and for the linear $T_c$ suppression by Zn doping. We show that our results reproduce the Uemura relation in the pure system an…
We propose a model that explains the reduction of $T_c$ due to the pinning of stripes by planar impurity co-doping in cuprates. A geometrical argument about the planar fraction of carriers affected by stripe pinning leads to a a linear $T_c$ suppression as a function of impurity concentration $z$. The critical value $z_c$ for the vanishing of superconductivity is shown to scale like $T_c^2$ in the under-doped regime and becomes universal in the optimally- and over-doped regimes. Our theory agrees very well with the experimental data in single- and bi-layer cuprates co-doped with Zn, Li, Co, et…
The relationships among charge order, spin fluctuations, and superconductivity in underdoped cuprates remain controversial. We use neutron scattering techniques to study these phenomena in La$_{1.93}$Sr$_{0.07}$CuO$_4$, a superconductor with a transition temperature of $T_c = 20$~K. At $T\ll T_c$, we find incommensurate spin fluctuations with a quasielastic energy spectrum and no sign of a gap within the energy range from 0.2 to 15 meV. A weak elastic magnetic component grows below $\sim10$~K, consistent with results from local probes. Regarding the atomic lattice, we have discovered unexpecte…
We compare the low frequency (~1 kHz) anelastic spectra of La_{2-x}Sr_xCuO_4 and La_{2-x}Ba_xCuO_4 at x = 0.03 and 0.06 in the temperature region where the freezing into the cluster spin-glass (CSG) phase occurs and is accompanied by an increase of the acoustic absorption. The dependence of the amplitude of the anelastic relaxation on doping is explained in terms of movement of the domain walls (DW) in the CSG phase between the Sr (Ba) pinning points. The LBCO sample at x = 0.06 transforms into the LTT structure below 40 K and the amplitude of the anelastic anomaly is 7 times smaller than expe…
We report on the observation of self-organized stripe-like structures on the as-grown surface and in the bulk of (Nd,Eu,Gd)Ba$_2$Cu$_3$O$_y$ single crystals. The periodicity of the stripes on the surface lies between 500 and 800 nm. These are possibly the growth steps of the crystal. Transmission electron microscopy investigations revealed stripes of periodicity in the range of 20 to 40 nm in the bulk. From electron back scattered diffraction investigations, no crystallographic misorientation due to the nanostripes has been found. Scanning tunneling spectroscopic experiments revealed nonsuperc…
We investigate theoretically the equilibrium configurations of many magnetic skyrmions interacting with many superconducting vortices in a superconductor-chiral magnet bilayer. We show that miscible mixtures of vortices and skyrmions in this system breaks down at a particular wave number for sufficiently strong coupling, giving place to remarkably diverse mesoscale patterns: gel, stripes, clusters, intercalated stripes and composite gel-cluster structures. We also demonstrate that, by appropriate choice of parameters, one can thermally tune between the homogeneous and density-modulated phases.
The optical response of a charge stripe in the presence of pinning impurities is investigated. We address the issue of a discrete description of the stripe, and discuss its quantitative relevance with respect to a continuum one in the light of recent optical-conductivity measurements in cuprate compounds.
An advanced mask-less nanofabrication technique, focused electron beam-induced deposition (FEBID), has been employed on epitaxial Nb thin films for their ferromagnetic decoration by an array of Co stripes. These substantially modify the non-patterned films' superconducting properties, providing a washboard-like pinning potential landscape for the vortex motion. At small magnetic fields B<0.1T, vortex lattice matching effects have been investigated by magneto-transport measurements. Peculiarities in the field dependencies of the films resistivity R(B) have been observed in particular for the vo…
The evolution of stripe patterns in type-I superconductors subject to a rotating in-plane magnetic field is investigated magneto-optically. The experimental results reveal a very rich and interesting behavior of the patterns. For small rotation angles, a small parallel displacement of the main part of the stripes and a co-rotation of their very ends is observed. For larger angles, small sideward protrusions develop, which then generate a zigzag instability, ultimately leading to a breaking of stripes into smaller segments. The short segments then start to co-rotate with the applied field altho…
We study striped morphologies induced by magnetic impurities in d-wave superconductors (DSCs) near optimal doping by self-consistently solving the Bogoliubov-de Gennes equations based on the $t-t^{\prime }-U-V$ model. For the single impurity case, it is found that the stable ground state is a modulated checkerboard pattern. For the two-impurity case, the stripe-like structures in order parameters are induced due to the impurity-pinning effect. The modulations of DSC and charge orders share the same period of four lattice constants (4$a$), which is half the period of modulations in the coexisti…
We have investigated the vortex dynamics in superconducting thin film devices with non-uniform patterns of artificial pinning centers (APCs). The magneto-transport properties of a conformal crystal and a randomly diluted APC pattern are compared with that of a triangular reference lattice. We have found that in both cases the magneto-resistance below the first matching field of the triangular reference lattice is significantly reduced. For the conformal crystal, the magneto-resistance is below the noise floor indicating highly effective vortex pinning over a wide magnetic field range. Further,…
We study the transport properties of vortex matter in a superconducting thin film separated by a thin insulator layer from a ferromagnetic layer. We assume an alternating stripe structure for both FM and SC layers as found in [7]. We calculate the periodic pinning force in the stripe structure resulting from a highly inhomogeneous distribution of the vortices and antivortices. We show that the transport properties in FM-SC bilayer are highly anisotropic. In the absence of random pinning it displays a finite resistance for the current perpendicular to stripes and is superconducting for the curr…
We discuss recent elastic neutron scattering and scanning tunneling experiments on high-T_c cuprates exposed to an applied magnetic field. In particular we show that a physical picture consisting of antiferromagnetic vortex cores operating as pinning centers for surrounding stripes is qualitatively consistent with the neutron data provided the stripes have the usual antiphase modulation. Further, we calculate the electronic structure in such a region using a T-matrix method, and find a checkerboard interference pattern consistent with recent scanning tunneling experiments.
The influence of high electric fields on the charge stripe order in Nd1.67Sr0.33NiO4 was studied by means of simultaneous hard x-ray diffraction and electrical transport experiments. Direct measurements of the charge stripe satellite peaks in zero and high electric fields provide no evidence for a deformation or a sliding of the stripe lattice, which contradicts previous indications from non-linear conductance effects. By using the order parameter of a structural phase transition for instant sample temperature measurements, non-linear transport effects can be attributed to resistive heating. I…
Within a Green's function formalism we calculate the electronic structure around static extended magnetic and non-magnetic perturbations in a d-wave superconductor. In partucular, we discuss recent elastic neutron scattering and scanning tunneling experiments on High-T_c cuprates exposed to an applied magnetic field. A physical picture consisting of antiferromagnetic vortex cores operating as pinning centers for surrounding stripes is qualitatively consistent with the neutron data provided the stripes have the usual antiphase modulation. The low energy electronic structure in such a region rev…
Magnetic skyrmions are particle-like objects with topologically-protected stability which can be set into motion with an applied current. Using a particle-based model we simulate current-driven magnetic skyrmions interacting with random quenched disorder and examine the skyrmion velocity fluctuations parallel and perpendicular to the direction of motion as a function of increasing drive. We show that the Magnus force contribution to skyrmion dynamics combined with the random pinning produces an isotropic effective shaking temperature. As a result, the skyrmions form a moving crystal at large d…
We study the influence of disorder and lattice pinning on the dynamics of a charged stripe. Starting from a phenomenological model of a discrete quantum string, we determine the phase diagram for this system. Three regimes are identified, the free phase, the flat phase pinned by the lattice, and the disorder pinned phase. In the absence of impurities, the system can be mapped onto a 1D array of Josephson junctions. The results are compared with measurements on nickelates and cuprates and a good qualitative agreement is found between our results and the experimental data.
