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Using relativistic density-functional calculations, we examine the magneto-crystalline anisotropy and exchange properties of transition-metal atoms adsorbed on 2D-GaAs. We show that single Mn and Mo atom (Co and Os) strongly bind on 2D-GaAs, and induce local out-of-plane (in-plane) magnetic anisotropy. When a pair of TM atoms is adsorbed on 2D-GaAs in a close range from each other, magnetisation properties change (become tunable) with respect to concentrations and ordering of the adatoms. In all cases, we reveal presence of strong Dzyaloshinskii–Moriya interaction. These results indicate novel pathways towards two-dimensional chiral magnetic materials by design, tailored for desired applications in magneto-electronics.

Ginzburg-Landau theory is one of the most powerful phenomenological theories in physics, with particular predictive value in superconductivity. The formalism solves coupled nonlinear differential equations for both the electronic and magnetic responsiveness of a given superconductor to external electromagnetic excitations. With order parameter varying on the short scale of the coherence length, and the magnetic field being long-range, the numerical handling of 3D simulations becomes extremely challenging and time-consuming for realistic samples. Here we show precisely how one can employ graphics-processing units (GPUs) for this type of calculations, and obtain physics answers of interest in a reasonable time-frame - with speedup of over 100x compared to best available CPU implementations of the theory on a 2563grid. (C) 2016 Elsevier Inc. All rights reserved.

We perform the wavepacket dynamics simulation of a graphene-based device where propagating electron trajectories are tamed by an applied magnetic field toward a normal/superconductor interface. The magnetic field controls the incidence angle of the incoming electronic wavepacket at the interface, which results in the tunable electron-hole ratio in the reflected wave function due to the angular dependence of the Andreev reflection. Here, mapped control of the quasiparticle trajectories by the external magnetic field not only defines an experimental probe for fundamental studies of the Andreev reflection in graphene but also lays the foundation for further development of magnetic focusing devices based on nanoengineered superconducting two-dimensional materials.

Over the past few decades, superconducting circuits have been used to realize various novel electronic devices such as quantum bits, SQUIDs, parametric amplifiers, etc. One domain, however, where superconducting circuits fall short is information storage. Superconducting memories are based on the quantization of magnetic flux in superconducting loops. Standard implementations store information as magnetic flux quanta in a superconducting loop interrupted by two Josephson junctions (i.e., a SQUID). However, due to the large inductance required, the size of the SQUID loop cannot be scaled below several micrometers, resulting in low-density memory chips. Here, we propose a scalable memory consisting of a voltage-biased superconducting ring threaded by a half-quantum flux bias. By numerically solving the time-dependent Ginzburg-Landau equations, we show that applying a time-dependent bias voltage in the microwave range constitutes a writing mechanism to change the number of stored flux quanta within the ring. Since the proposed device does not require a large loop inductance, it can be scaled down, enabling a high-density memory technology. (C) 2019 Author(s).

Thin ferromagnetic films with an interfacially induced DMI exhibit nontrivial asymmetric dispersion relations that lead to unique and useful magnonic properties. Here we derive an analytical expression for the magnon propagation angle within the micromagnetic framework and show how the dispersion relation can be approximated with a comprehensible geometrical interpretation in the k-space of the propagation of spin waves. We further explore the refraction of spin waves at DMI interfaces in heterochiral magnetic films, after deriving a generalized Snell's law tunable by an in-plane magnetic field, that yields analytical expressions for critical incident angles. The found asymmetric Brewster angles at interfaces of regions with different DMI strengths, adjustable by magnetic field, support the conclusion that heterochiral ferromagnetic structures are an ideal platform for versatile spin-wave guides., 7 pages, 4 figures

We investigate how the interplay of quantum confinement and level broadening caused by disorder affects superconducting correlations in ultra-small metallic grains. We use the electron-phonon interaction-induced electron mass renormalization and the reduced static-path approximation of the BCS formalism to calculate the critical temperature as a function of the grain size. We show how the strong electron-impurity scattering additionally smears the peak structure in the electronic density of states of a metallic grain and imposes additional limits on the critical temperature under strong quantum confinement.

Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The extension of the crossover regime increases when the pairing strength and/or the characteristic energy of the interaction get larger. Our results indicate the coexistence of large and small Cooper pairs in the crossover regime, leading to the optimal parameter configuration for high transition temperature superconductivity., Comment: 5 pages, 4 figures. Proceedings of the Superstripes 2015 conference to be published in Journal of Superconductivity and Novel Magnetism. MultiSuper collaboration: http://www.multisuper.org

We present an advanced method to study spin fluctuations in superconductors quantitatively, and entirely from first principles. This method can be generally applied to materials where electron-phonon coupling and spin fluctuations coexist. We employ it here to examine the recently synthesized superconductor iron tetraboride (FeB$_4$) with experimental $T_{\mathrm{c}}\sim 2.4$ K [H. Gou \textit{et al.}, Phys. Rev. Lett. \textbf{111}, 157002 (2013)]. We prove that FeB$_4$ is particularly prone to ferromagnetic spin fluctuations due to the presence of iron, resulting in a large Stoner interaction strength, $I=1.5$ eV, as calculated from first principles. The other important factor is its Fermi surface that consists of three separate sheets, among which two nested ellipsoids. The resulting susceptibility has a ferromagnetic peak around $\textbf{q}=0$, from which we calculated the repulsive interaction between Cooper pair electrons using the random phase approximation. Subsequently, we combined the electron-phonon interaction calculated from first principles with the spin fluctuation interaction in fully anisotropic Eliashberg theory calculations. We show that the resulting superconducting gap spectrum is conventional, yet very strongly depleted due to coupling to the spin fluctuations. The critical temperature decreases from $T_{\mathrm{c}}= 41$ K, if they are not taken into account, to $T_{\mathrm{c}}= 1.7$ K, in good agreement with the experimental value., 8 pages, 6 figures

In the quest for miniaturizing magnetic devices, the effects of boundaries and surfaces become increasingly important. Here we show how the recently predicted boundary-induced Dzyaloshinskii-Moriya interaction (DMI) affects the magnetization of ferromagnetic films with a $C_{\infty v}$ symmetry and a perpendicular magnetic anisotropy. For an otherwise uniformly magnetized film, we find a surface twist when the magnetization in the bulk is canted by an in-plane external field. This twist at the surfaces caused by the boundary-induced DMI differs from the common canting caused by internal DMI observed at the edges of a chiral magnet. Further, we find that the surface twist due to the boundary-induced DMI strongly affects the width of the domain wall at the surfaces. We also find that the skyrmion radius increases in the depth of the film, with the average size of the skyrmion increasing with boundary-induced DMI. This increase suggests that the boundary-induced DMI contributes to the stability of the skyrmion., 9 pages, 7 figures

We demonstrate the in situ engineering of superconducting nanocircuitry by targeted modulation of material properties through high applied current densities. We show that the sequential repetition of such customized electro-annealing in a niobium (Nb) nanoconstriction can broadly tune the superconducting critical temperature T-c and the normal-state resistance R-n in the targeted area. Once a sizable R-n is reached, clear magneto-resistance oscillations are detected along with a Fraunhofer-like field dependence of the critical current, indicating the formation of a weak link but with further adjustable characteristics. Advanced Ginzburg-Landau simulations fully corroborate this picture, employing the detailed parametrization from the electrical characterization and high resolution electron microscope images of the region within the constriction where the material has undergone amorphization by electro-annealing.

Structural and superconducting properties of high-quality niobium nanofilms with different thicknesses are investigated on silicon oxide (SiO2) and sapphire substrates. The role played by the different substrates and the superconducting properties of the Nb films are discussed based on the defectivity of the films and on the presence of an interfacial oxide layer between the Nb film and the substrate. The X-ray absorption spectroscopy is employed to uncover the structure of the interfacial layer. We show that this interfacial layer leads to a strong proximity effect, especially in films deposited on a SiO2 substrate, altering the superconducting properties of the Nb films. Our results establish that the critical temperature is determined by an interplay between quantum-size effects, due to the reduction of the Nb film thicknesses, and proximity effects. The detailed investigation here provides reference characterizations and has direct and important implications for the fabrication of superconducting devices based on Nb nanofilms.

Spin-triplet chiral p-wave superconductivity is typically described by a two-component order parameter, and as such is prone to unique emergent effects when compared to the standard single-component superconductors. Here we present the equilibrium phase diagram for small mesoscopic chiral p-wave superconducting disks in the presence of magnetic field, obtained by solving the microscopic Bogoliubov-de Gennes equations self-consistently. In the ultrasmall limit, the cylindrically symmetric giant-vortex states form the ground state of the system. However, with increasing sample size, the cylindrical symmetry is broken as the two components of the order parameter segregate into domains, and the number of fragmented domain walls between them characterizes the resulting states. Such domain walls are topological defects unique for the p-wave order, and constitute a dominant phase in the mesoscopic regime. Moreover, we find two possible types of domain walls, identified by their chirality-dependent interaction with the edge states.

The magnetic flux domains in the intermediate state of type-I superconductors are known to resemble fluid droplets, and their dynamics in applied electric current is often cartooned as a "dripping faucet". Here we show, using the time-depended Ginzburg-Landau simulations, that microfluidic principles hold also for the determination of the size of the magnetic flux-droplet as a function of the applied current, as well as for the merger or splitting of those droplets in the presence of the nanoengineered obstacles for droplet motion. Differently from fluids, the flux-droplets in superconductors are quantized and dissipative objects, and their pinning/depinning, nucleation, and splitting occur in a discretized form, all traceable in the voltage measured across the sample. At larger applied currents, we demonstrate how obstacles can cause branching of laminar flux streams or their transformation into mobile droplets, as readily observed in experiments. Fil: Berdiyorov, G. R.. Hamad Bin Khalifa University; Qatar Fil: Milošević, Milorad V.. Universiteit Antwerp; Bélgica Fil: Hernandez Nieves, Alexander David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB). Grupo de Teoría de Sólidos; Argentina Fil: Peeters, F. M.. Universiteit Antwerp; Bélgica Fil: Domínguez, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB). Grupo de Teoría de Sólidos; Argentina

Magnetic skyrmions are nanoscale windings of the spin structure that can be observed in chiral magnets and hold promise for potential applications in storing or processing information. Pinning due to ever-present material imperfections crucially affects the mobility of skyrmions. Therefore, a proper understanding of how magnetic skyrmions pin to defects is necessary for the development and performance of spintronic devices. Here we present a fundamental analysis on the interactions of single skyrmions with atomic defects of distinctly different origins, in a Co monolayer on Pt, based on minimum-energy paths considerations and atomic-spin simulations. We first report the preferred pinning loci of the skyrmion as a function of its nominal size and the type of defect being considered, to further reveal the manipulation and "breathing" of skyrmion core in the vicinity of a defect. We also show the behavior of skyrmions in the presence of an extended defect of particular geometry, that can lead to ratcheted skyrmion motion or a facilitated guidance on a defect "trail." We close the study with reflections on the expected thermal stability of the skyrmion against collapse on itself for a given nature of the defect, and discuss the applications where control of skyrmions by defects is of particular interest.

Starting from first principles, we show the formation and evolution of superconducting gaps in MgB$_2$ at its ultrathin limit. Atomically thin MgB$_2$ is distinctly different from bulk MgB$_2$ in that surface states become comparable in electronic density to the bulk-like $\sigma$- and $\pi$-bands. Combining the ab initio electron-phonon coupling with the anisotropic Eliashberg equations, we show that monolayer MgB$_2$ develops three distinct superconducting gaps, on completely separate parts of the Fermi surface due to the emergent surface contribution. These gaps hybridize nontrivially with every extra monolayer added to the film, owing to the opening of additional coupling channels. Furthermore, we reveal that the three-gap superconductivity in monolayer MgB$_2$ is robust over the entire temperature range that stretches up to a considerably high critical temperature of 20 K. The latter can be boosted to $>$50 K under biaxial tensile strain of $\sim$ 4\%, which is an enhancement stronger than in any other graphene-related superconductor known to date., Comment: To appear in Phys. Rev

Superconducting circuits represent a versatile playground to explore novel quantum phenomena and a platform to realize quantum bits (qubits). Superconducting qubits hinge on the coherent tunneling of Cooper pairs across the insulating barrier of a Josephson junction. This qubit implementation is, however, plagued with the variability of the fabricated junction, along with the need for magnetic tunability of the qubit transition frequency. Alternatively, a dual to the Josephson effect--referred to as quantum phase slips--allows for a coherent coupling of flux states and has been used to build phase-slip qubits. In this paper, we propose coupling flux states of a superconducting ring using a bias voltage. By solving the time-dependent Ginzburg-Landau equations, we demonstrate that the bias voltage locally suppresses the density of Cooper pairs, thereby forming a weak link where phase slips occur. Moreover, we show that a voltage-biased superconducting ring serves as an electrically-controlled magnetic memory. The work presented in this paper is an important step towards realizing electrically-tunable superconducting devices, such as qubits and SQUIDs.

We theoretically investigate, through Ginzburg–Landau simulations, the possibility to induce an open circuit voltage in absence of applied current, by dragging superconducting vortices with a dynamic pinning array as for instance that created by a nearby sliding vortex lattice or moving laser spots. Different dynamic regimes, such as synchronous vortex motion or dynamic vortex chains consisting of laggard vortices, can be observed by varying the velocity of the sliding pinning potential and the applied magnetic field. Additionally, due to the edge barrier, significantly different induced voltage is found depending on whether the vortices are dragged along the superconducting strip or perpendicular to the lateral edges. The output voltage in the proposed mesoscopic superconducting dynamo can be tuned by varying size, density and directions of the sliding pinning potential.

Quantized magnetic vortices driven by electric current determine key electromagnetic properties of superconductors. While the dynamic behavior of slow vortices has been thoroughly investigated, the physics of ultrafast vortices under strong currents remains largely unexplored. Here, we use a nanoscale scanning superconducting quantum interference device to image vortices penetrating into a superconducting Pb film at rates of tens of GHz and moving with velocities of up to tens of km/s, which are not only much larger than the speed of sound but also exceed the pair-breaking speed limit of superconducting condensate. These experiments reveal formation of mesoscopic vortex channels which undergo cascades of bifurcations as the current and magnetic field increase. Our numerical simulations predict metamorphosis of fast Abrikosov vortices into mixed Abrikosov-Josephson vortices at even higher velocities. This work offers an insight into the fundamental physics of dynamic vortex states of superconductors at high current densities, crucial for many applications., Ultrafast vortex dynamics driven by strong currents define eletromagnetic properties of superconductors, but it remains unexplored. Here, Embon et al. use a unique scanning microscopy technique to image steady-state penetration of super-fast vortices into a superconducting Pb film at rates of tens of GHz and velocities up to tens of km/s.

Superconducting and normal state properties of sputtered Niobium nanofilms have been systematically investigated, as a function of film thickness in a d=9-90 nm range, on different substrates. The width of the superconducting-to-normal transition for all films remained in few tens of mK, thus remarkably narrow, confirming their high quality. We found that the superconducting critical current density exhibits a pronounced maximum, three times larger than its bulk value, for film thickness around 25 nm, marking the 3D-to-2D crossover. The extracted magnetic penetration depth shows a sizeable enhancement for the thinnest films, aside the usual demagnetization effects. Additional amplification effects of the superconducting properties have been obtained in the case of sapphire substrates or squeezing the lateral size of the nanofilms. For thickness close to 20 nm we also measured a doubled perpendicular critical magnetic field compared to its saturation value for d>33 nm, indicating shortening of the correlation length and the formation of small Cooper pairs in the condensate. Our data analysis evidences an exciting interplay between quantum-size and proximity effects together with strong-coupling effects and importance of disorder in the thinnest films, locating the ones with optimally enhanced critical properties close to the BCS-BEC crossover regime.

Recent experiments show that an atomic step on the surface of atomically thin metallic films can strongly affect electronic transport. Here we reveal multiple and versatile effects that such a surface step can have on superconductivity in ultrathin films. By solving the Bogoliubov-de Gennes equations self-consistently in this regime, where quantum confinement dominates the emergent physics, we show that the electronic structure is profoundly modified on the two sides of the step, as is the spatial distribution of the superconducting order parameter and its dependence on temperature and electronic gating. Furthermore, the surface step changes non-trivially the transport properties both in the proximity-induced superconducting order parameter and the Josephson effect, depending on the step height. These results offer a new route to tailor superconducting circuits and design atomically thin hetero-junctions made of one same material., Comment: 7 pages, 4 figures

Two-dimensional materials are known to harbour properties very different from those of their bulk counterparts. Recent years have seen the rise of atomically thin superconductors, with a caveat that superconductivity is strongly depleted unless enhanced by specific substrates, intercalants or adatoms. Surprisingly, the role in superconductivity of electronic states originating from simple free surfaces of two-dimensional materials has remained elusive to date. Here, based on first-principles calculations, anisotropic Eliashberg theory, and angle-resolved photoemission spectroscopy (ARPES), we show that surface states in few-monolayer MgB2 make a major contribution to the superconducting gap spectrum and density of states, clearly distinct from the widely known, bulk-like σ- and π-gaps. As a proof of principle, we predict and measure the gap opening on the magnesium-based surface band up to a critical temperature as high as ~30 K for merely six monolayers thick MgB2. These findings establish free surfaces as an unavoidable ingredient in understanding and further tailoring of superconductivity in atomically thin materials.

© 2017 American Physical Society. To unravel the effects of phonon confinement, the influence of size and morphology on the atomic vibrations is investigated in Sn nanoislands and cluster-assembled films. Nuclear resonant inelastic x-ray scattering is used to probe the phonon densities of states of the Sn nanostructures which show significant broadening of the features compared to bulk phonon behavior. Supported by ab initio calculations, the broadening is attributed to phonon scattering and can be described within the damped harmonic oscillator model. Contrary to the expectations based on previous research, the appearance of high-energy modes above the cutoff energy is not observed. From the thermodynamic properties extracted from the phonon densities of states, it was found that grain boundary Sn atoms are bound by weaker forces than bulk Sn atoms. ispartof: Physical Review B vol:95 issue:15 status: published

The Dzyaloshinskii-Moriya interaction (DMI) is a chiral interaction that favors formation of domain walls. Recent experiments and ab initio calculations show that there are multiple ways to modify the strength of the interfacially induced DMI in thin ferromagnetic films with perpendicular magnetic anisotropy. In this paper we reveal theoretically the effects of spatially varied DMI on the magnetic state in thin films. In such heterochiral 2D structures we report several emergent phenomena, ranging from the equilibrium spin canting at the interface between regions with different DMI, over particularly strong confinement of domain walls and skyrmions within high-DMI tracks, to advanced applications such as domain tailoring nearly at will, design of magnonic waveguides, and much improved skyrmion racetrack memory.

Magnetic skyrmions are topological spin configurations in materials with chiral Dzyaloshinskii-Moriya interaction (DMI), that are potentially useful for storing or processing information. To date, DMI has been found in few bulk materials, but can also be induced in atomically thin magnetic films in contact with surfaces with large spin-orbit interactions. Recent experiments have reported that isolated magnetic skyrmions can be stabilized even near room temperature in few-atom-thick magnetic layers sandwiched between materials that provide asymmetric spin-orbit coupling. Here we present the minimum-energy path analysis of three distinct mechanisms for the skyrmion collapse, based on ab initio input and the performed atomic-spin simulations. We focus on the stability of a skyrmion in three atomic layers of Co, either epitaxial on the Pt(111) surface or within a hybrid multilayer where DMI nontrivially varies per monolayer due to competition between different symmetry breaking from two sides of the Co film. In laterally finite systems, their constrained geometry causes poor thermal stability of the skyrmion toward collapse at the boundary, which we show to be resolved by designing the high-DMI structure within an extended film with lower or no DMI.

We present a microscopic study of superconductivity in OsB2, and discuss the origin and characteristic length scales of the superconducting state. From first-principles we show that OsB2 is characterized by three different Fermi sheets, and we prove that this fermiology complies with recent quantum-oscillation experiments. Using the found microscopic properties, and experimental data from the literature, we employ Ginzburg-Landau relations to reveal that OsB2 is a distinctly type-I superconductor with a very low Ginzburg-Landau parameter κa rare property among compound materials. We show that the found coherence length and penetration depth corroborate the measured thermodynamic critical field. Moreover, our calculation of the superconducting gap structure using anisotropic Eliashberg theory and ab initio calculated electron-phonon interaction as input reveals a single but anisotropic gap. The calculated gap spectrum is shown to give an excellent account for the unconventional behavior of the superfluid density of OsB2 measured in experiments as a function of temperature. This reveals that gap anisotropy can explain such behavior, observed in several compounds, which was previously attributed solely to a two-gap nature of superconductivity.

In the nearest vicinity of the critical temperature, types I and II of conventional single-band superconductors interchange at the Ginzburg-Landau parameter $\ensuremath{\kappa}=1/\sqrt{2}$. At lower temperatures this point unfolds into a narrow but finite interval of $\ensuremath{\kappa}$'s, shaping an intertype (transitional) domain in the $(\ensuremath{\kappa},T)$ plane. In the present work, based on the extended Ginzburg-Landau formalism, we show that the same picture of the two standard types with the transitional domain in between applies also to multiband superconductors. However, the intertype domain notably widens in the presence of multiple bands and can become extremely large when the system has a significant disparity between the band parameters. It is concluded that many multiband superconductors, such as recently discovered borides and iron-based materials, can belong to the intertype regime.

We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system., 13 pages, 16 color figures; v2 is identical in content to the published article

We study the vortex profiles in two-gap superconductors using the extended Ginzburg-Landau theory. The results shed more light on the disparity between the effective length scales in two bands. We compare the behavior expected from the standard Ginzburg-Landau theory with this new approach, and find good qualitative agreement in the case of LiFeAs. (C) 2011 Elsevier B.V. All rights reserved.

We performed a molecular dynamics study of vortex-antivortex motion in a superconducting disk with a magnetic dot on top, in the Corbino disk geometry. In this system, vortices and antivortices are forced to move in opposite azimuthal directions by a radially applied current. The dot is magnetized out of plane in order to stabilize composite vortex-antivortex configurations, with vortices closer to the center of the disk and antivortices near to the disk edge. We observe that the interplay between the spatially inhomogeneous current distribution, the screening currents induced by the dipole, and the attractive vortex-antivortex (v-av) interaction result in different dynamical phases. At low current values, antivortices which are distributed at outer rings - remain bounded to vortices at inner rings and the whole configuration rotates rigidly. Above a threshold current, vortices and antivortices unbind and move at different angular velocities in a highly correlated way. Finally, at very strong drive, vortex-antivortex attraction is overhelmed by the external current Lorentz force, causing them to move in opposite directions. (C) 2011 Elsevier B.V. All rights reserved.

We solve analytically the linearized Ginzburg-Landau (GL) equation in the presence of an uniform magnetic field with cylindrical boundary conditions. The solution of the non-linear GL equation is provided as an expansion in the basis of linearized solutions. We present examples of the resulting vortex structure for a solid and perforated superconducting cylinder. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.

A thorough understanding of the skyrmion motion through nanotracks is a prerequisite to realize the full potential of spintronic applications like the skyrmion racetrack memory. One of the challenges is to place the data, i.e. skyrmions, on discrete fixed positions, e.g. below a read or write head. In the domain-wall racetrack memory, one proposed solution to this problem was patterning the nanotrack with notches. Following this approach, this paper reports on the skyrmion mobility through a nanotrack with periodic notches (constrictions) made using variations in the chiral Dzyaloshinskii-Moriya interaction. We observe that such notches induce a coupling between the mobility and the skyrmion breathing mode, which manifests itself as velocity-dependent oscillations of the skyrmion diameter and plateaus in which the velocity is independent of the driving force. Despite the fact that domain walls are far more rigid objects than skyrmions, we were able to perform an analogous study and, surprisingly, found even larger plateaus of constant velocity. For both systems it is straightforward to tune the velocity at these plateaus by changing the design of the notched nanotrack geometry, e.g. by varying the distance between the notches. Therefore, the notch-induced coupling between the excited modes and the mobility could offer a strategy to stabilize the velocity against unwanted perturbations in racetrack-like applications. In the last part of the paper we focus on the low-current mobility regimes, whose very rich dynamics at nonzero temperatures are very similar to the operating principle of recently developed probabilistic logic devices. This proves that the mobility of nanomagnetic structures through a periodically modulated track is not only interesting from a fundamental point of view, but has a future in many spintronic applications.

In the last twenty years, numerical modeling has become an indispensable part of magnetism research. It has become a standard tool for both the exploration of new systems and for the interpretation of experimental data. In the last five years, the capabilities of micromagnetic modeling have dramatically increased due to the deployment of graphical processing units (GPU), which have sped up calculations to a factor of 200. This has enabled many studies which were previously unfeasible. In this topical review, we give an overview of this modeling approach and show how it has contributed to the forefront of current magnetism research.

A mesoscopic superconductor with a magnetic moment in its center exhibits confined vortex loops with threefold symmetry in its center. Here, we show how the boundaries can affect this symmetry by considering a superconducting cube and sphere.

Hybrid structures composed of superconducting films deposited on ordered arrays of magnetic ‘dots’ have attracted enormous interest in recent years. Dots with sufficiently large magnetic moments may generate one or more spontaneous vortex–antivortex (V–AV) pairs in the superconducting film which can either remain associated with individual nanomagnets as V–AV “molecules” in dilute arrays or organise themselves into an ‘ionic’ crystal in dense arrays. Exactly how V–AV molecules transform into lattices and how they interact with (anti)fluxons induced by external magnetic fields remain challenging questions for both theory and experiment. We have used high resolution scanning Hall probe microscopy to image V–AV “molecules” induced in superconducting Pb films by the stray fields from square arrays of ferromagnetic Co/Pt dots. We have directly observed spontaneous V–AV pairs and studied how they interact with added “free” (anti)fluxons in an applied magnetic field. We observe a rich variety of subtle phenomena arising from competing symmetries in our system which can either drive added antivortices to join AV shells around nanomagnets or stabilise the translationally symmetric AV lattice between the dots. Added vortices annihilate AV shells, leading eventually to a stable ‘nulling state’ with no free fluxons, which should exhibit a strongly field-enhanced critical current. At higher densities we actually observe vortex shells around the magnets, stabilised by the asymmetric anti-pinning potential. Our experimental findings are in good agreement with Ginzburg–Landau calculations.

We examine theoretically the dynamics of two vortex shells in pinning-free superconducting thin disks in the Corbino geometry. In the first considered case, the inner shell is composed of vortices and the outer one of antivortices, corresponding to a state induced by the stray field of an off-plane magnetic dipole placed on top of the superconductor. In the second considered case, both shells comprise vortices induced by a homogeneous external field. We derive the equation of motion for each shell within the Bardeen-Stephen model and study the dynamics analytically by assuming both shells are rigid and commensurate. In both cases, two distinct regimes for vortex shell motion are identified: For low applied currents the entire configuration rotates rigidly, while above a threshold current the shells decouple from each other and rotate at different angular velocities. Analytical expressions for the decoupling current, the recombination time in the decoupled phases, as well as the voltage-current characteristics are presented. Our analytical results are in excellent agreement with numerical molecular dynamics simulations of the full many-vortex problem.

An experimental determination of the mean vortex velocity in superconductors mostly relies on the measurement of flux-flow resistance with magnetic field, temperature, or driving current. In the present work we introduce a method combining conventional transport measurements and a frequency-tuned flashing pinning potential to obtain reliable estimates of the vortex velocity. The proposed device is characterized using the time-dependent Ginzburg-Landau formalism, where the velocimetry method exploits the resonances in mean vortex dissipation when temporal commensuration occurs between the vortex crossings and the flashing potential. We discuss the sensitivity of the proposed technique on applied current, temperature and heat diffusion, as well as the vortex core deformations during fast motion.

When subjected to the interfacially induced Dzyaloshinskii-Moriya interaction, the ground state in thin ferromagnetic films with high perpendicular anisotropy is cycloidal. The period of this cycloidal state depends on the strength of the Dzyaloshinskii-Moriya interaction. In this work, we have studied the effect of confinement on the magnetic ground state and excited states, and we determined the phase diagram of thin strips and thin square platelets by means of micromagnetic calculations. We show that multiple cycloidal states with different periods can be stable in laterally confined films, where the period of the cycloids does not depend solely on the Dzyaloshinskii-Moriya interaction strength but also on the dimensions of the film. The more complex states comprising skyrmions are also found to be stable, though with higher energy., Comment: 8 pages, 10 figures

Using advanced Ginzburg-Landau simulations, we study the superconducting state of a thin superconducting film under a ferromagnetic layer, separated by an insulating oxide, in applied external magnetic field and electric current. The taken uniaxial ferromagnet is organized into a series of parallel domains with alternating polarization of out-of-plane magnetization, sufficiently strong to induce vortex-antivortex pairs in the underlying superconductor in absence of other magnetic field. We show the organization of such vortex-antivortex matter into rich configurations, some of which are not matching the periodicity of the ferromagnetic film. The variety of possible configurations is enhanced by applied homogeneous magnetic field, where additional vortices in the superconductor may lower the energy of the system by either annihilating the present antivortices under negative ferromagnetic domains or by lowering their own energy after positioning under positive ferromagnetic domains. As a consequence, both the vortex-antivortex reordering in increasing external field and the evolution of the energy of the system are highly nontrivial. Finally, we reveal the very interesting effects of applied dc electric current on the vortex-antivortex configurations, since resulting Lorentzian force has opposite direction for vortices and antivortices, while direction of the applied current with respect to ferromagnetic domains is of crucial importance for the interaction of the applied and the Meissner current, as well as the consequent vortex-antivortex dynamics-both of which are reflected in the anisotropic critical current of the system. (C) 2016 AIP Publishing LLC.

Vortices and vortex arrays have been used as a hallmark of superfluidity in rotated, ultracold Fermi gases. These superfluids can be described in terms of an effective field theory for a macroscopic wave function representing the field of condensed pairs, analogous to the Ginzburg-Landau theory for superconductors. Here, we have established how rotation modifies this effective field theory, by rederiving it starting from the action of Fermi gas in the rotating frame of reference. The rotation leads to the appearance of an effective vector potential, and the coupling strength of this vector potential to the macroscopic wave function depends on the interaction strength between the fermions, due to a renormalization of the pair effective mass in the effective field theory. The mass renormalization derived here is in agreement with results of functional renormalization group theory. In the extreme BEC regime, the pair effective mass tends to twice the fermion mass, in agreement with the physical picture of a weakly interacting Bose gas of molecular pairs. Then, we use our macroscopic wave function description to study vortices and the critical rotation frequencies to form them. Equilibrium vortex state diagrams are derived, and they are in good agreement with available results of the Bogoliubov - De Gennes theory and with experimental data., 32 pages, 6 figures, accepted in Phys. Rev. A (2016)

We reveal the emergence of metallicKondo clouds in an atomistic carbon quantum dot, realized as a single-atom junction in a suitably patterned graphene nanoflake. Using density functional dynamical mean-field theory (DFDMFT) we show how correlation effects lead to striking features in the electronic structure of our device, and how those are enhanced by the electron-electron interactions when graphene is patterned at the atomistic scale. Our setup provides a well-controlled environment to understand the principles behind the orbital-selective Kondo physics and the interplay between orbital and spin degrees of freedom in carbon-based nanomaterials, which indicate new pathways for spintronics in atomically patterned graphene.

Conventional superconductivity is inevitably suppressed in ultra-small metallic grains for characteristic sizes smaller than the Anderson limit. Experiments have shown that above the Anderson limit the critical temperature may be either enhanced or reduced when decreasing the particle size, depending on the superconducting material. In addition, there is experimental evidence that whether an enhancement or a reduction is found depends on the strength of the electron-phonon interaction in the bulk. We reveal how the strength of the e-ph interaction interplays with the quantum-size effect and theoretically obtain the critical temperature of the superconducting nanograins in excellent agreement with experimental data. We demonstrate that strong e-ph scattering smears the peak structure in the electronic density-of-states of a metallic grain and enhances the electron mass and thereby limits the highest Tc achievable by quantum confinement.

Scanning Hall probe microscopy (SHPM) has been used to study vortex structures in thin epitaxial films of the superconductor MgB[subscript 2]. Unusual vortex patterns observed in MgB[subscript 2] single crystals have previously been attributed to a competition between short-range repulsive and long-range attractive vortex-vortex interactions in this two band superconductor; the type 1.5 superconductivity scenario. Our films have much higher levels of disorder than bulk single crystals and therefore both superconducting condensates are expected to be pushed deep into the type 2 regime with purely repulsive vortex interactions. We observe broken symmetry vortex patterns at low fields in all samples after field-cooling from above T[subscript c]. These are consistent with those seen in systems with competing repulsions on disparate length scales, and remarkably similar structures are reproduced in dirty two band Ginzburg-Landau calculations, where the simulation parameters have been defined by experimental observations. This suggests that in our dirty MgB[subscript 2] films, the symmetry of the vortex structures is broken by the presence of vortex repulsions with two different lengthscales, originating from the two distinct superconducting condensates. This represents an entirely new mechanism for spontaneous symmetry breaking in systems of superconducting vortices, with important implications for pinning phenomena and high current density applications., United States. Office of Naval Research (Grant N00014-06-01-0235)

Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux. In the absence of pinning such paramagnetic response is weak, and ceases with increasing sample thickness. Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field. We link the appearance of this giant paramagnetic response to the broad crossover between conventional Type-I and Type-II superconductors, where Abrikosov vortices interact non-monotonically and multibody effects become important, causing unique flux configurations and their locking in the presence of surfaces., Comment: 9 pages, 6 figures

The vortex matter and related phenomena in superconducting films with periodic arrays of microholes (antidots) are studied within the nonlinear Ginzburg–Landau (GL) theory. By varying the GL parameter κ , the vortex–vortex interaction is fine tuned, from repulsive to attractive behavior. This interaction is of crucial importance for equilibrium vortex structures, the saturation number of the antidots, and the related quantities, such as critical current. Due to vortex attraction in effectively type-I samples, the giant-vortex state becomes energetically favorable (contrary to the type-II behavior). For the same reason, the number of vortices which can be captured by antidots, increases with decreasing κ . As a result, for given magnetic field, the critical current is larger for effectively type-I superconductors than in conventional type-II cases.

Using the phenomenological Ginzburg–Landau (GL) theory, we investigate the superconducting (SC) state of a thin SC film under a square array of rectangular ferromagnets (FM) with in-plane magnetization. The equilibrium vortex states consist of vortex–antivortex (VAV) pairs formed under the poles of each magnet due to their specific inhomogeneous magnetic field which makes the total flux penetrating the SC equal zero. Even for a weakly magnetized FM, the nucleation of VAV structures can be stimulated by applying electric current perpendicular to the FM-moment. When the sample is exposed to an additional homogeneous magnetic field H , the presence of VAV pairs results in an even j c ( H ) characteristic, with maximal critical current achieved at H = ± H max ≠ 0, where H max can be temperature dependent.

Within the phenomenological Ginzburg–Landau (GL) theory, we investigate the vortex structure of a thin superconducting film (SC) with a regular matrix of ferromagnetic dots (FD) deposited on top of it. The vortex pinning properties of such a magnetic lattice are studied, and the field polarity dependent votex pinning is observed. The exact vortex configuration depends on the size of the magnetic dots, their polarity, periodicity of the FD-rooster and the properties of the SC expressed through the effective Ginzburg–Landau parameter κ * .

Mesoscopic superconducting disks are versatile systems to study different aspects of phase transitions. In such systems one finds giant to multivortex transitions and different vortex configurations for the same vorticity. The system exhibits metastable states which can lead to paramagnetic response, non-quantized flux entry and even negative flux entry. Vortex-antivortices can be nucleated by positioning a ferromagnetic disk on top of a superconducting film.

The interaction between a vortex in a superconducting film and a magnetic dipole with in- or out-of-plane magnetization is studied within the London approximation. We investigate the magnetic pinning properties of such magnetic dipoles. The dependence of the interaction energy on the parameters of the system is investigated and analytical results are obtained in limiting cases.

Within the non-linear Ginzburg-Landau (GL) theory, we investigate the vortex structure of a thin type II superconductor with a ferromagnetic dot on top of it. Spontaneous creation of vortex-antivortex pairs as well as specific arrangements of vortices are found. We show that the equilibrium vortex phase diagram depends on the size of the magnetic dot and its magnetization, and we discuss the shell structure of the multivortex states with “magic” numbers which are size and magnetization dependent.

Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Perot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.