Vortex Expulsion Research Articles

Vortex matter and critical magnetic fields in mesoscopic superconducting strips

As compared with bulk materials, superconducting strips with lateral dimensions limited to the mesoscopic region exhibit non-trivial properties, among which the critical magnetic fields related to both vortex penetration and full vortex expulsion still remain elusive. By using low-temperature scanning Hall probe microscope, the critical magnetic fields are studied experimentally in a series of superconducting Pb strips with different widths. It is found that the penetration magnetic field follows a power law dependence with strip width, and vortices can only penetrate the strips when the energy barrier at the edges is completely suppressed. In the field-cooling process, vortices are fully expelled from the strips below , above which the number of trapped vortices linearly increases with magnetic field. Compared with various theoretical predictions, we have found that the experimentally observed corresponds to the field at which the Gibbs free energy in the strip center is minimized. Our study provides important implications for designing nanostructured devices with superconducting strips.

Ultrahigh detection sensitivity exceeding 105 V/W in spin-torque diode

Microwave detection has a huge number of applications in physics and engineering. It has already been shown that biased spin torque diodes have performance overcoming the CMOS counterpart in terms of sensitivity. In this regard, the spin torque diodes are promising candidates for the next generation of microwave detectors. Here, we show that the optimization of the rectification process based on the injection locking mechanism gives an ultrahigh sensitivity exceeding 200 kV/W with an output resistance below 1 kΩ while maintaining the advantages over other mechanisms such as vortex expulsion or non-linear resonance, to work without a bias magnetic field.

Spin transfer driven resonant expulsion of a magnetic vortex core for efficient rf detector

Spin transfer magnetization dynamics have led to considerable advances in Spintronics, including opportunities for new nanoscale radiofrequency devices. Among the new functionalities is the radiofrequency (rf) detection using the spin diode rectification effect in spin torque nano-oscillators (STNOs). In this study, we focus on a new phenomenon, the resonant expulsion of a magnetic vortex in STNOs. This effect is observed when the excitation vortex radius, due to spin torques associated to rf currents, becomes larger than the actual radius of the STNO. This vortex expulsion is leading to a sharp variation of the voltage at the resonant frequency. Here we show that the detected frequency can be tuned by different parameters; furthermore, a simultaneous detection of different rf signals can be achieved by real time measurements with several STNOs having different diameters. This result constitutes a first proof-of-principle towards the development of a new kind of nanoscale rf threshold detector.

Controlling the chirality and polarity of vortices in magnetic tunnel junctions

Static and dynamic control of the chirality and polarity of a magnetic vortex confined in a magnetic tunnel junction is demonstrated. The modes associated with the four chirality/polarity vortex configurations are first explored by resonant excitation with a low power rf current. When the rf power is increased, both the chirality and polarity of the vortex can be resonantly switched, which—as shown by micromagnetic simulations—involves vortex expulsion and renucleation. This tunable resonant switching of the vortex parameters are an exciting step forward for the viability of magnetic vortex-based applications.

Local field loop measurements by magnetic force microscopy

Magnetic force microscopy (MFM) is a valuable technique to investigate the reversal mechanisms of the magnetization in micrometric and sub-micrometric-patterned thin films that cannot be studied by means of magneto-optical methods because of their limited resolution. However, acquiring tens or hundreds of images consecutively at different applied magnetic fields is often impossible or impractical. Therefore, a field-dependent MFM-derived technique is discussed and applied on square and circular dots of different materials (Ni80Fe20, Co67Fe4Si14.5B14.5, Fe78Si9B13) having sizes ranging from 800 nm to 20 µm. Experimental local hysteresis loops are obtained by properly analysing the phase signal of the MFM along a selected profile of the studied patterned structure, as a function of the applied magnetic field. Characteristic features of the magnetization process, such as vortex nucleation and expulsion, transition from C-state to saturated state or domain wall motion in Landau-like domain configuration are identified, and their evolution with the applied field is followed. The necessity to combine experimental and theoretical analyses is addressed by micromagnetic simulations on a model system (a Ni80Fe20 square dot with a lateral size of 800 nm), comparable to one of the studied samples. The agreement between experimental and simulated MFM maps, at different applied fields, and hysteresis loops provides the necessary validation for the technique. Additionally, the simulations have been proven to be necessary to understand the magnetization reversal processes occurring in the studied sub-micrometric structures and to associate them with characteristic features of the hysteresis loops measured with the proposed technique.

Magnetodynamical response of large-area close-packed arrays of circular dots fabricated by nanosphere lithography

We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic excitations in large-area arrays of NiFe nanodisks forming a hexagonal lattice with the lattice constant of 390 nm. Arrays were fabricated by patterning a 20-nm-thick NiFe film using the etched nanosphere lithography. We have studied a close-packed (edge-to-edge separation between disks dcp = 65 nm) and an ultraclosed packed (ducp = 20 nm) array. Hysteresis loops for both arrays were qualitatively similar and nearly isotropic, i.e., independent on the in-plane external field orientation. The shape of these loops revealed that magnetization reversal is governed by the formation and expulsion of vortices inside the nanodisks. When we assumed that the nanodisks’ magnetization significantly decreases near their edges, micromagnetic simulations with material parameters deter-mined independently from continuous film measu-rements could satisfactorily reproduce the hysteresis. Despite the isotropic hysteresis, significant in-plane anisotropy of the dynamic response of the ultraclose-packed array was found experimentally by the all-electrical spin-wave spectroscopy and Brillouin light scattering. Dynamical simulations could successfully reproduce the difference between excitation spectra for fields directed along the two main symmetry axes of the hexagonal lattice. Simulations revealed that this difference is caused by the magnetodipolar interaction between nanodisks, which leads to a strong variation of the spatial distribution of the oscillation power both for bulk and edge modes as a function of the bias field orientation. Comparison of simulated and measured frequencies enabled the unambiguous identification of experimentally observed modes. Results of this systematic research are relevant both for fundamental studies of spin-wave modes in patterned magnetic structures and for the design of magnonic crystals for potential applications as, e.g., spin-wave guides and filters.

Effect of strain on the evolution of magnetic multi-vortices in ferromagnetic nano-platelets

The effect of external strain on the evolution of magnetic multi-vortices in nanoscale ferromagnetic platelets is investigated by a phase field model that explicitly includes the coupling between the magnetization and deformation. Phase field simulations show that a compressive strain makes the magnetic vortex–antivortex pair stable in rectangular ferromagnetic platelets, which is unstable in the absence of an external magnetic field and strain. The magnetic clockwise (CW) and counterclockwise (CCW) vortex pairs disappear in ferromagnetic platelets under an external magnetic field through the annihilation of the vortex and antivortex, or through expulsion when external strain is absent. In the presence of tensile strain, the expulsion of CW and CCW vortices is suppressed in ferromagnetic platelets. However, external strain has less effect on the annihilation of CW and CCW vortices. For ferromagnetic platelets with triple vortices, both tensile strain and a magnetic field induce the annihilation and expulsion of vortices. The effect of strain on the evolution of magnetic vortices suggests a new way to control them by strain engineering.

Switching current modulations induced by vortices rearrangement in mesoscopic superconducting loops

Periodic modulations in the switching current of niobium mesoscopic thin loops have been observed as a function of a perpendicular magnetic field. These modulations reflect the formation of specific vortices configurations in the arms and in the contacts of the loops. The voltage measured just before the current-driven transition to the normal state takes either zero or nonzero values depending on whether the vortices are efficiently pinned or move under the action of the applied current. This switching voltage varies sharply in the vicinity of the regularly spaced matching fields at which the switching current is minimum. This reflects the rearrangement of the vortices pattern from an unstable configuration into a more stable one. In addition, multimodal switching current distributions obtained at a constant field highlight that the few vortices involved in the field-cooling process freeze into a limited number of configurations. Finally, the spacing between the matching fields allows us to extract the critical field for complete vortex expulsion of the samples. Electrical transport measurements appear to be an efficient tool to determine the superheating field of submicrometer-wide structures, which is not obvious when measured by scanning probe microscopy.

Experimental distinction between giant vortex and multivortex states in mesoscopic superconducting squares

We study the distinction between giant vortex states and multivortex states in a thin mesoscopic superconducting square by using the temperature dependence of the vortex expulsion fields. We find that the results agree well with those obtained from the multiple-small-tunnel-junction method, indicating that the distinction by the temperature dependence of the vortex expulsion fields is applicable to superconducting squares.

Thermal suppression of surface barrier in ultrasmall superconducting structures

In the recent experiment by Cren \textit{et al.} [Phys. Rev. Lett. \textbf{102}, 127005 (2009)], no hysteresis for vortex penetration and expulsion from the nano-island of Pb was observed. In the present paper, we argue that this effect can be associated with the thermoactivated surmounting of the surface barrier by a vortex. The typical entrance (exit) time is found analytically from the Fokker-Planck equation, written in the form suitable for the extreme vortex confinement. We show that this time is several orders of magnitude smaller than 1 second under the conditions of the experiment considered. Our results thus demonstrate a possibility for the thermal suppression of the surface barrier in nanosized low-$T_{c}$ superconductors. We also briefly discuss other recent experiments on vortices in related structures.

Switching behavior of superconducting current injected from quasi-one-dimensional leads into mesoscopic samples

We have investigated the distribution of external current injected from superconducting leads into mesoscopic samples using time dependent Ginzburg-Landau theory. In particular, we have taken account of the current and field variation in the thickness direction. We have performed numerical simulations for the sample composed of two rectangular solids connected by two bridges. We have observed “switching” like behavior in the current distribution at the bridges, which corresponds to the change between vortex penetration and expulsion. This switching like behavior, as well as the magnitude of the currents, depends on the sample thickness in the direction of the external field.

Meissner effect and vortex expulsion in color-superconducting quark stars, and its role for reheating of magnetars

Compact stars made of quark matter rather than confined hadronic matter, are expected to form a color superconductor. This superconductor ought to be threaded with rotational vortex lines, within which the star's interior magnetic field is at least partially confined. The vortices (and thus magnetic flux) would be expelled from the star during stellar spin-down, leading to magnetic reconnection at the surface of the star and the prolific production of thermal energy. In this paper, we show that this energy release can re-heat quark stars to exceptionally high temperatures, such as observed for Soft Gamma Repeaters (SGRs), Anomalous X-Ray pulsars (AXPs), and X-ray dim isolated neutron stars (XDINs). Moreover, our numerical investigations of the temperature evolution, spin-down rate, and magnetic field behavior of such superconducting quark stars suggest that SGRs, AXPs, and XDINs may be linked ancestrally. Finally, we discuss the possibility of a time delay before the star enters the color superconducting phase, which can be used to estimate the density at which quarks deconfine. From observations, we find this density to be of the order of five times that of nuclear saturation.

Vortex Trapping and Expulsion in Thin-Film Type-II Superconducting Strips

Vortex trapping is investigated in thin-film strips of superconducting material. We present a model for the critical field above which vortex trapping occurs in these strips. This model includes the pairing energy of vortex-antivortex pairs in addition to the energy of single vortices. Experimental verification of the model with a scanning SQUID microscope shows very good agreement between the model and experiments on YBa2Cu3O7-delta and Nb strips. Statistical analysis of the vortex distribution in the strips above the critical field has been performed and a comparison has been made between Nb and YBa2Cu3O7-delta for the distributions in the lateral and longitudinal directions.

Effect of supercurrent injection on vortex penetration and expulsion fields in mesoscopic superconducting squares

We report an experimental study on the effect of supercurrent injection on vortex states in mesoscopic superconductors. The sample consists of an Al square with side of 1.1 μm, which is directly connected to Al leads for current injection. The vortex penetration/expulsion is detected by the voltage change across a small tunnel junction attached to the square. We find that the vortex penetration/expulsion fields are significantly influenced by the external current of the order of 10 μA. The shift of the vortex penetration/expulsion fields is interpreted in terms of the forces exerted by the external current.

Experimental determination of vortex configuration in a mesoscopic superconducting square with artificial pinning centers

We study the response of a mesoscopic superconducting square with 2×2 artificial pinning centers (antidots) to perpendicular magnetic field. In the sample, two current-biased tunnel junctions are placed near adjacent antidots. The junction voltages are measured as a function of the magnetic field (multiple small tunnel junction technique). From the magnitude of the voltage jumps which correspond to the vortex penetration (expulsion), we determine the position of the penetrating (expelled) vortex in increasing (decreasing) magnetic field. We find that the order of the vortex penetration is the same as that of vortex expulsion. We also discuss the stability of the vortex states in a square with antidots in comparison with that of a square without antidots.

Superconducting Pb Island Nanostructures Studied by Scanning Tunneling Microscopy and Spectroscopy

Superconductivity of nanosized Pb-island structures whose radius is 0.8 to 2.5 times their coherence length was studied under magnetic fields using low-temperature scanning tunneling microscopy and spectroscopy. Spatial profiles of superconductivity were obtained by conductance measurements at zero-bias voltage. Critical magnetic fields for vortex penetration and expulsion and for superconductivity breaking were measured for each island. The critical fields depending on the lateral size of the islands and existence of the minimum lateral size for vortex formation were observed.

Phase diagram of a mesoscopic superconducting Pb square: Ballistic Hall magnetometry

Ballistic Hall magnetometry is used to investigate the magnetization of a mesoscopic superconducting Pb square as a function of magnetic field $(H)$ and temperature $(T)$. Vortex penetration and expulsion fields are determined from magnetization curves at different temperatures below ${T}_{c}$ and are combined in an experimental $T\text{\ensuremath{-}}H$ phase diagram. Enhanced stability of the symmetry-matching vorticities $L=1$ and $L=4$ is observed. The experimental results are compared with theoretical calculations using the nonlinear Ginzburg-Landau theory for a thin square.

Fine frequency shift of single vortex entrance and exit in superconducting loops

The heat capacity C p of an array of independent aluminum rings has been measured under an external magnetic field H → using highly sensitive ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex entrance induces a phase transition and a heat capacity jump and hence C p oscillates with H → . This oscillatory and non-stationary behavior measured versus the magnetic field has been studied using the Wigner–Ville distribution (a time–frequency representation). It is found that the periodicity of the heat capacity oscillations varies significantly with the magnetic field; the evolution of the period also depends on the sweeping direction of the field. This can be attributed to a different behavior between expulsion and penetration of vortices into the rings. A variation of more than 15% of the periodicity of the heat capacity jumps is observed as the magnetic field is varied. A description of this phenomenon is given using an analytical solution of the Ginzburg–Landau equations of superconductivity.

Observation of vortex expulsion in mesoscopic superconducting disks

We have studied vortex expulsion processes in a superconducting disk with a multi-terminal Hall sensor. Various combinations of these terminals enabled us to obtain an angular dependence of magnetization in the disk. The resolution of π/4 allowed us to identify three vortices. With a decrease in magnetic fields, vortices were expelled one by one from the different edges. After each expulsion the residual vortices were reconfigured in a complicated way. Their equilibrium positions changed with lowering temperatures. These results are interpreted in terms of repulsively interacting particles in the confinement and the pinning potential. The latter potential is found to be important at low temperatures.

Critical fields for vortex expulsion from narrow superconducting strips

We calculate the critical magnetic fields for vortex expulsion for an infinitely long superconducting strip, using the Ginzburg-Landau formalism. Two critical fields can be defined associated with the disappearance of either the energetic stability or metastability of vortices in the center of the strip for decreasing magnetic fields. We compare the theoretical predictions for the critical fields in the London formalism with ours and with recently published experimental results. As expected, for narrow strips our results reproduce better the experimental findings.