Phase transitions in uniaxial ferromagnetic film covered by superconducting layers

The phase diagram and the single-domain uniform state for a uniaxial ferromagnetic film with the superconducting layers covering one or both sides of a ferromagnet are investigated. The superconductor is supposed to be a second-order one and the interaction between the magnetic sub-system and with the conductivity electrons in a superconductor is purely electromagnetic and the vortices in a superconductor are pinned. The critical thickness of the magnetic film for which the uniform state becomes absolutely stable is calculated when the external magnetic field is supposed to be in-plane of the film. It is shown that the critical thickness of the film from the magnetic material with the quality factor Q>1 monotonically decreases as the magnetic field increases in the range from zero value to the value of the transition field where the collinear phase transforms into the angular (canted) phase. Further the critical thickness increases with the increase of the field. The quasi-single-domain magnetic film states were considered when the film thickness was close to the critical one. It is shown that for a thin isolated magnetic film the domain period exponentially increases with the decrease of the film thickness. Such dependence, however for the film with double-side superconducting cover and close to the transition into the single domain state becomes logarithmic and for the film covered by superconductor only on the one side varies as the power series. The single-domain state existence and the asymptotic behaviour of the domain structure is explained by the features of the asymptotic behaviour of the domain walls within the system. As for isolated magnetic film and for a film with the superconductor cover layers the transition from the collinear phase to the inhomogeneous state is the second-order phase transition and the transition from the uniform angular phase to the inhomogeneous phase is the first-order transition.     

Ferromagnet–superconductor hybrids

The new class of phenomena described in this review is based on the interaction between spatially separated, but closely located ferromagnets and superconductors, the so-called ferromagnet–superconductor hybrids (FSH). Typical FSH are: coupled uniform and textured ferromagnetic and superconducting films, magnetic dots over a superconducting film, magnetic nanowires in a superconducting matrix, etc. The interaction is provided by the magnetic field generated by magnetic textures and supercurrents. The magnetic flux from magnetic structures or topological defects can pin vortices or create them, changing the transport properties and transition temperature of the superconductor. On the other hand, the magnetic field from supercurrents (vortices) strongly interacts with the magnetic subsystem, leading to formation of coupled magnetic–superconducting topological defects.

The proximity of ferromagnetic layer dramatically changes the properties of the superconducting film. The exchange field in ferromagnets not only suppresses the Cooper-pair wavefunction, but also leads to its oscillations, which in turn leads to oscillations of observable values: the transition temperature and Josephson current. In particular, in the ground state of the Josephson junction the relative phase of two superconductors separated by a layer of ferromagnetic metal is equal to?π?instead of the usual zero (the so-called π-junction). Such a junction carries a spontaneous supercurrent and possesses other unusual properties. Theory predicts that rotation of magnetization transforms s-pairing into p-pairing. The latter is not suppressed by the exchange field and serves as a carrier of long-range interaction between superconductors.     

Features of magnetization reversal in LCMO/YBCO heterostructures

The change in the magnetic domain structure due to the proximity of a superconductor has been experimentally investigated for the first time. The complex character of magnetization reversal at temperatures below critical, caused by the mutual long-range effect of a superconductor and a magnet, has been shown. In particular, it is found that even magnetization reversal of the heterostructure by an in-plane field leads to the formation of Abrikosov vortices in the superconductor, carrying a flux perpendicularly to the film plane. It is shown that this is a consequence of the transformation of narrow domain walls into wide stripes due to the interaction with scattering fields from the superconductor. In turn, after penetration of the magnetic flux into the superconductor at some depth, the scattering fields cause backward magnetization reversal of the external film edge, as a result of which vortices with oppositely directed fluxes enter the crystal and propagate in the superconductor bulk in the form of chains along twins, as in the case of magnetization by a perpendicular magnetic field. Thus, at longitudinal magnetization, the flux enters the superconducting film in the form of wide stripes with alternating perpendicular induction, which is explained by the long-range interaction of the scattering fields of the superconductor with the manganite magnetization.     

Structural phase transition in the mixed state of superconducting films in a parallel magnetic field

A thin film of a second-kind superconductor in a magnetic field parallel to the surface of the film is considered in the London approximation. It has been shown that if bulk pinning is absent and the suppression of super-conductivity by the magnetic field is negligible, the splitting of a vortex chain in the film occurs as a structural phase transition either of the first or second order, depending on the ratio of the thickness of the film d to the penetration depth of the magnetic field λ. The ratio d/λ, and thereby the character of the transition in the vortex lattice, can be changed by varying the temperature. The corresponding critical thicknesses of films and field ranges in which this effect can be observed experimentally have been calculated.     

外场中超导结的直流约瑟夫逊电流的计算

外加磁场对超导体/半导体/超导体结的临界电流有一定影响。超导结的临界电流与磁场的曲线非常类似于单色光在单狭缝衍射的夫琅和费图样。该文在未考虑外加磁场的超导体/半导体/超导体结的临界电流的基础上,进一步对外加磁场的情形进行了研究,并对其结果借助M athem atica软件做了进一步的讨论。     

The upper critical magnetic field of lead as a function of the mean free path of the electrons

The transition curves of quenched lead films are measured in a perpendicular magnetic field as a function of the field strength. We vary the mean free path of the electrons by different condensation temperatures and by the annealing of the films. An influence of the edge of the film on the resistance measurement is suppressed by the superposition of iron onto the lead film. We will show, that the measured critical fieldB _{c ⊥} of the film is the upper critical fieldB _c2 of a bulk superconductor with the sameeffective mean free path. As a result of the measurements we obtain ?B _c2/?T as a function of the degree of disorder (the mean free path of the electrons) of the films. The results are compared with the theory of Gor'kov for the weak coupling superconductor and the theory of Eilenberger and Ambegaokar for the strong coupling superconductor. They disagree with both theories. From the magnetic measurement we can determine the coherence length of lead. An independent determination at the same film is given by the proximity effect of the system Pb/Fe. The results of both methods are compared.     

Explicit calculation of a tricritical point in a Pauli paramagnetically limited superconductor

We extend the Maki-Tsuneto Green's function formulation for the critical magnetic field vs temperature of a Pauli paramagnetically limited thin film superconductor to include the field conjugate to the order parameter and show the system displays a tricritical point. We present numerical calculations within the mean field theory in the neighborhood of the tricritical point and describe an explicit experimental arrangement for producing an adjustable staggered field.     

The spontaneous formation of a vortex structure in a type II superconductor-ferromagnet bilayer

The conditions for the formation of a vortex structure in a thin superconducting film under the action of a stray field of stripe domain structure of a uniaxial ferromagnet are determined. The critical magnetization of the magnetic material is calculated, above which the mixed state of the superconductor becomes energetically favored over the Meissner phase. It is shown that the critical magnetization decreases monotonically with decreasing thickness of the superconducting film and is of the order of ten gauss in typical actual situations. The critical-current anisotropy in a superconducting film with an induced vortex structure is discussed qualitatively.     

Vortex Pinning due to Dynamic Spin-Vortex Interaction in aSuperconductor/Ferromagnet Multilayer

We investigate the mutual interaction between superconductivity and ferromagnetism in a Nb/Ni81 Ee19 multilayer by ac susceptibility measurements. Compared with a pure superconducting Nb film, the critical current density of the multilayer is apparently enhanced in a low magnetic field region but remains nearly the same in high magnetic fields, which indicates that a continuous ferromagnetic layer with in-plane magnetization can produce strong vortex pinning in a low field region. We interpret this unusual vortex-pinning phenomenon as a consequence of dynamic spin vortex interaction which induces a spin rotation following vortex movement. In addition, we propose that this dynamic interaction could be used for spin manipulation via a superconductor.     

Enhancement of the Josephson current by an exchange field in superconductor-ferromagnet structures

We calculate the dc Josephson current for two superconductor/ferromagnet (S/F) bilayers separated by a thin insulating film. It is demonstrated that the critical Josephson current I(c) in the junction strongly depends on the relative orientation of the effective exchange field h of the bilayers. We found that in the case of an antiparallel orientation I(c) increases at low temperatures with increasing h and at zero temperature has a singularity when h equals the superconducting gap Delta. This striking behavior contrasts with the suppression of the critical current by the magnetic moments aligned in parallel and is an interesting new effect of the interplay between superconductors and ferromagnets.     

A very simple explanation of the effects of a.c. fields on the critical currents in type II superconductors

The electric field induced in a type II superconductor foil by an a.c. magnetic field is rectified by the non-linear static voltage current characteristic of the superconductor when there is a static current, so that the static critical current seems to decrease.     

Vortex-rectification effects in films with periodic asymmetric pinning

We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field, and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very different from standard overdamped models. Rather, the repinning force, necessary to stop vortex motion, is considerably smaller than the depinning force, resembling the behavior of the so-called inertia ratchets. Calculations based on an underdamped ratchet model provide a very good fit to the experimental data.     

Shape of the magnetic resonance line in a thin film on the surface of an anisotropic superconductor

The shape of the EPR line in a thin (=λ/2, where λ is the London penetration depth of the magnetic field in the superconductor) paramagnetic film deposited on the surface of an anisotropic superconductor is calculated in an oblique magnetic field with allowance for the inhomogeneity of the local magnetic field of the Abrikosov vortex lattice. It is shown that, as the tilt angle of the external magnetic field is varied, the shape of the EPR line changes noticeably. This fact can give additional information about the superconductor parameters (the symmetry type of the vortex lattice and the anisotropy parameter of the superconductor). Fiz. Tverd. Tela (St. Petersburg) 41, 386–388 (March 1999)     

Autowave dynamics of the magnetic flux in nonideal type-II superconductors with different current-voltage characteristics

An analysis was performed of the processes of penetration of a macroscopic electromagnetic field into superconducting media with different current-voltage characteristics induced by a variable external magnetic field or by carrier transport. It has been shown that even if a finite electrical voltage arises in the superconductor before the critical current is reached, the magnetic flux, as in the critical state model, penetrates into the superconductor at a finite rate as a characteristic electromagnetic wave. At its front, a special condition is fulfilled; namely, a smooth transition to the nonperturbed value of the strength of the electric field induced by an external perturbation. Formulas are given for the calculation of the penetration rate of the electromagnetic field into a superconductor. For corroboration of the formulated relationships, the study was compared with corresponding numerical calculations.     

Inverted satellites of a solitary oscillating pearl vortex in a thin magnetic superconductor film

An electrodynamic equation is derived for the magnetic field of an isolated Pearl vortex moving along an arbitrary trajectory in an ultrathin film of a magnetic superconductor. This equation is valid for any type of magnetic order in the magnetic subsystem. The magnetic structure of an isolated oscillating Pearl vortex is investigated in a thin magnetic superconductor film. Oscillations of the vortex and the presence of the magnetic subsystem are shown to lead to a significant renormalization of the vortex field in comparison with the Pearl solution. New phenomena of inverted satellites are predicted in which an inverted precursor appears in front of the vortex and an inverted wake is formed behind the latter at a distance of the order of 10λ_eff from the vortex center. These phenomena can be observed in magnetooptical experiments.     

Thin film arrays of weakly coupled superconducting particles

Thin film, macroscopic arrays of superconducting particles 100–10,000 Å in diameter can be produced by evaporating the superconductor in a gas at low pressure. The arrays have a critical supercurrent, I_c, which is a sensitive, multiply periodic function of the applied magnetic field. A simple model of multiple current paths through the array is proposed to explain both this observation and the general shape of the current-voltage characteristics.     

Micromagnetic properties and magnetization switching of single domain Co dots studied by magnetic force microscopy

Magnetic force microscopy was applied to study the magnetic properties of Co dot microstructures. The high density magnetic dot arrays were fabricated using nanolithographic techniques on GaAs substrates. The ferromagnetic Co dots were found to be in a single domain state for Co film thicknesses of 7 nm and 17 nm. The magnetization of the as-prepared Co dot array was found to be in a non-uniform state. After applying a magnetic field the Co dots are in a uniform magnetization state. Induced switching of the magnetization of single Co dots by the stray field of the probing tip using an additionally applied in-situ magnetic field has been demonstrated.     

Terahertz transmission of NbN superconductor thin film

Transmission of terahertz waves through a thin layer of the NbN superconductor deposited on a sapphire substrate was studied as a function of temperature in zero field as well as in magnetic field perpendicular to the sample. For photon energies lower than optical gap, detailed temperature measurements in zero field provide BCS-like curves with a pronounced peak below the critical temperature. In accordance with the BCS model, the temperature peak disappears as the energy of incident radiation is increased above the gap. In non-zero field, the temperature behavior of transmission is modified because the gap is suppressed and vanishes at upper critical field. In addition, the presence of quantized vortices in the superconducting film substantially changes shape of the temperature curves.     

Non-isothermal adiabatic critical state stability of a hard superconductor

A basic feature of a hard superconductor is that dissipative processes occur in them because of a thermally activated motion of vortices. The resulting dissipation of the energy stored may be accompanied by a disruption of the critical state. This instability leads to an increase in the temperature of the superconductor. Most of the carried out investigations have been based on a study of the initial stage of the magnetic flux penetration and ignore permissible heating of the superconductor. The main purpose of this work is to analyze the conditions for the onset of the thermomagnetic instability in a hard superconductor with allowance for a non-zero initial temperature heating. Conditions for adiabatic stability of the screening currents induced by an external magnetic field are formulated. It is shown that the adiabatic criteria for stability of the critical state depend strongly on the initial temperature of the superconductor.     

Granular high-temperature superconductor film in a steady magnetic field

An electrodynamic model is constructed for a granular Josephson high-temperature superconductor film in a steady magnetic field. The field induces anisotropy and spatial inhomogeneity for a high-frequency field. The data can be used in boundary-value treatments for layered structures that include high-temperature superconductor films, and also in research on acoustoelectronic and magnetostatic interactions of surface acoustoelectronic and magnetostatic waves with the high-temperature superconductor medium.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 91–94, August, 1995.