Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli-limit heavy-electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to the muon spin rotation (??SR) experiment. Based on the Ginzburg-Landau expansion for the superconductor free energy, we study the evolution with respect to the external field of the static linewidth both in the limit of independent vortices (low magnetic field) with a variational expression for the order parameter and in the near H _c2 ^P (T) regime with an extension of the Abrikosov analysis to Pauli-limit superconductors. We conclude that in the Ginzburg-Landau regime in the Pauli-limit, anomalous variations of the static linewidth with the applied field are predicted as a result of the superconductor spin response around a vortex core that dominates the usual charge-response screening supercurrents. We propose the effect as a benchmark for studying new puzzling vortex lattice properties recently observed in CeCoIn₅.     

Possible Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconducting state in CeCoIn5

We present specific heat and thermal conductivity of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical fieldH _c2, measured with magnetic field in the plane of this quasi-2D compound and at temperatures down to 50 mK. The superconducting phase diagram and the first order nature of the superconducting phase transition at high fields close to a critical fieldH _c2 indicate the importance of the Pauli limiting effect in CeCoIn₅. In the same range of magnetic field we observe a second specific heat anomaly within the superconducting state, and interpret it as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. In addition, the thermal conductivity data as a function of field display a kink at a fieldH _k below the superconducting critical field, which closely coincides with the low temperature anomaly in specific heat tentatively identified with the appearance of the FFLO superconducting state. The enhancement of thermal conductivity within the FFLO state calls for further theoretical investigations of the real space structure of the order parameter (and in particular, the structure of vortices) and of the thermal transport within the inhomogeneous FFLO state.     

Courants critiques d'alliages supraconducteurs de concentration modulee spatialement I — Effet de la periode

We discuss the effect of the period of the sinusoidal variations of concentration of superconducting $\text{Pb}$Bi films, on the critical current densities J_c as a function of an applied magnetic field H, perpendicular to J and parallel to the film plane. The existence of peaks on the J_c(H) curves suggests a matching effect between the vortex lattice and the modulation of concentration.     

Magnetism and superconductivity in ErNi2B2C

We have performed a series of neutron diffraction experiments from the magnetic order and the vortex lattice in single crystal ErNi₂B₂C. The incommensurate magnetic structure develops additional even harmonics below the ‘ferromagnetic’ ordering temperature, T _F of 2.3 K. This feature and the existence of rods of diffuse scattering suggest the development of ferromagnetic microdomain walls. The magnetic structure is very sensitive to the application of a magnetic field with changes in modulation vector and harmonic content. Studies of the vortex lattice show the presence of a 45° reorientation transition and a distorted hexagonal to square transition as a function of applied field. Further distortions of the vortex lattice occur at T _N, but no changes are seen at T _F.     

Vortex glass phase and flux creep in YBa2Cu3O y epitaxial film

Nonlinear I–V characteristics of YBa₂Cu₃O _y epitaxial film at different temperatures in a magnetic field of up to 5T and angles between the direction of the field and the a–b plane of 0°, 30°, 45°, 60°, and 90° were measured. We find that there are the vortex glass phase and vortex liquid phase in the mixed state. The flux creep exists in the vortex glass phase, and it obviously appears in the area around the boundary between the vortex glass phase and the vortex liquid phase.     

Vortex lattices in type-II superconductors studied by small-angle neutron scattering

Here we review recent small-angle scattering studies of the vortex lattice in a range of type-II superconductors carried out by our group. Emphasis is placed on providing examples of the kind of information which can be obtained by such measurements, focusing in particular on studies of the vortex lattice structure and form factor in LuNi₂B₂C, TmNi₂B₂C, CeCoIn₅ and Ba(Fe_0.93Co_0.07)₂As₂.     

Helical magnetic structure in a quasi-one-dimensional LiCu<Subscript>2</Subscript>O<Subscript>2</Subscript> multiferroic crystal according to <Superscript>63,65</Superscript>Cu NMR studies

The NMR spectra of ⁶³Cu and ⁶⁵Cu natural copper isotopes in a LiCu₂O₂ multiferroic single crystal compound have been measured above and below the temperature of magnetic phase transition (T _c = 23 K) in zero magnetic field and in applied magnetic field H ₀ = 94 kOe parallel to the c axis of the crystal. In LiCu₂O₂ below T _c, a complicated helical magnetic structure with the magnetic moment of copper ions Cu²⁺ varying along the chain according to the harmonic law with the wave vector being incommensurate to the crystal lattice constants has been revealed. The experimental results have been successfully interpreted using the model based on the planar helical magnetic structure. It has been found that the plane of rotation for Cu²⁺ magnetic moments in LiCu₂O₂ does not coincide at H ₀ = 0 with the ab plane. The high magnetic field (H ₀ = 94 kOe) applied along the c axis of the single crystal does not affect the spatial orientation of the plane of rotation.     

Transverse anisotropy field and lattice plane anisotropy of stress annealed Fe–Cu–Nb–Si–B ribbons

The transverse magnetic anisotropy and lattice plane anisotropy of stress-annealed Fe–Cu–Nb–Si–B amorphous ribbons have been studied. The GMI effect or impedance ratio decreased gradually with increasing applied tensile stress. The transverse anisotropy field (H_k) corresponded to the full width at half maximum (FWHM) of the GMI curves. A linear response was found between the applied tensile stress (σ) and the transverse anisotropy field (H_k), and it was seen from the linear expression that annealing without stress resulted in a very small H_k of ～200 A/m. We also calculated the strains from the elongations obtained during the stress annealing process, the results showed that the strain and applied stress were linearly related and for a zero-tensile stress, the elastic strain was negative (?0.0219) showing that contraction dominates during annealing without tensile stresses. The lattice plane anisotropy (Δd) calculated from XRD peaks was also linearly related to the applied tensile stress. The lattice spacing in the direction parallel to the tensile stress was elongated while the lattice spacing in the direction perpendicular to the tensile stress was compressed.     

Phase separation effects in charge-ordered Pr<Subscript>0.5</Subscript>Ca<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> thin film

Compressed Pr_0.5Ca_0.5MnO₃ films (250 nm) deposited on LaAlO₃ have been studied by Electron Spin Resonance technique under high frequency and high magnetic field. We show evidences for the presence of a ferromagnetic phase (FM) embedded in the charge-order phase (CO), in form of thin layers which size depends on the strength and orientation of the magnetic field (parallel or perpendicular to the substrate plane). This FM phase presents an easy plane magnetic anisotropy with an anisotropy constant 100 times bigger than typical bulk values. When the magnetic field is applied perpendicular to the substrate plane, the FM phase is strongly coupled to the CO phase whereas for the parallel orientation it keeps an independent ferromagnetic resonance even when the CO phase becomes antiferromagnetic.     

Deposition of superconducting CeCoIn5 thin films by co-sputtering and evaporation

Thin superconducting films of CeCoIn₅ were prepared in situ by simultaneous thermal evaporation of indium and dc magnetic field assisted sputtering of planar metallic Ce and Co targets. To achieve an effective sputtering of the magnetic Co target a special geometry with two facing planar targets (Ce and Co) and magnetic field perpendicular to the targets was used. The stoichiometric (0 0 1)-oriented CeCoIn₅ films were grown on r-cut sapphire substrates with a high-rate of 100 nm/min. The temperature dependence of the electrical resistivity revealed the characteristic heavy-fermion behavior and a superconducting transition at about 2 K in agreement with the literature data for CeCoIn₅ bulk material and thin films.     

Pinning by twin boundaries and peak effect in YBaCuO high-T c superconductors

Measurements of the imaginary part of the ac magnetic susceptibility of single crystals and melt-textured samples of YBa₂Cu₃O_x (YBCO) at T=77 K in a magnetic field ranging between 1 and 20 kOe are reported. If the dc magnetic field H _dc is rotated in the ab plane of the sample, the magnetic susceptibility and critical current density j _c have peaks corresponding to the magnetic field aligned with twin boundaries. Peaks in the curve of j _c versus magnetic field are observed at angles corresponding to these peaks, where AH _dc in a wide range of magnetic fields. The results have been interpreted in terms of the theory describing twin boundaries as a system of quasi-planar pinning sites. The pinning is strong if the elastic displacements of flux lines are of the order of the vortex lattice constant d _f. These displacements decrease with the magnetic field because of the decrease in d _f, and the contribution of the elastic energy to the Gibbs potential is reduced accordingly, which is the cause of the peak effect. Zh. éksp. Teor. Fiz. 111, 2158–2174 (June 1997)     

Doping dependence of the vortex glass and sublimation transitions in the high-T<Subscript>c</Subscript> superconductor La<Subscript>2-x</Subscript>Sr<Subscript>x</Subscript>CuO<Subscript>4</Subscript> as determined from macroscopic measurements

Magnetization and ac-susceptibility measurements are used to characterize the mixed phase of the high-temperature cuprate superconductor La_2-xSr_xCuO₄ over a large range of doping (0.075 0.20). The first order vortex lattice phase transition line H_FOT(T), the upper critical field H_c2(T) and the second peak H_sp(T) have been investigated up to high magnetic fields (8 Tesla applied perpendicular to the CuO₂ planes). Our results reveal a strong doping dependence of the magnetic phase diagram, which can mainly be explained by the increasing anisotropy with underdoping. Within our interpretation, the first order vortex lattice phase transition is due to the sublimation (rather than melting) of the vortex lattice into a gas of pancake vortices, whereas the second peak is related to the transition to a more disordered vortex glass state.     

Vortex phase diagram studies in the weakly pinned single crystals of YNi2B2C and LuNi2B2C

We present a study of magnetization measurements performed on the single crystals of YNi₂B₂C and LuNi₂B₂C. For both the compounds, we find flux jumps in magnetisation values in the respective field regions, where the structural transitions in the flux line lattice symmetry have been reported in these systems via the small angle neutron scattering experiments. The magnetisation hysteresis loops and the AC susceptibility measurements show pronounced peak effect as well as second magnetisation peak anomaly for both YNi₂B₂C and LuNi₂B₂C. Based on these results, a vortex phase diagram has been constructed for YNi₂B₂C forH∥c depicting different glassy phases of the vortex matter.     

Ferromagnet/superconducting YBa2Cu3O7−δ bilayer devices

A magnetic fringe-field effect has been investigated for a simple bilayer device structure consisting of a Co_0.9Fe_0.1 film and an epitaxial YBa₂Cu₃O_7−δ (YBCO) film patterned as a microbridge. The resistance of the bridge is measured with a four-probe technique and is found to depend on the orientation of a magnetic field, which is externally applied in the device plane. A maximum (minimum) of the resistance occurs when the magnetic field is applied in parallel (perpendicular) to the bridge axis. The difference between the maximum and the minimum is very large for a small range of temperature below the critical temperature of the YBCO film. The observed features in the resistance are qualitatively explained by vortex motion in the YBCO bridge under the influence of the magnetic fringe-field of the Co_0.9Fe_0.1 film.     

Effect of natural and magnetic convections on the structure of electrodeposited zinc-nickel alloy

The effects of a magnetic field applied in a direction parallel or perpendicular to the cathode substrate plane, during electrodeposition process of Zn-Ni alloy have been investigated by means of chronoamperometric measurements, X-ray diffraction and EDX analysis. The modification of crystal orientation of the alloy by the superimposition of a high magnetic field is discussed for alloys with a content of nickel range 6-13 at%. Whatever the phase composition obtained without magnetic field, either γ-Ni₅Zn₂₁ or a mixture of the γ and zinc phases, which depends on the concentration of Ni²⁺ in the electrolyte bath, the preferential orientation (1 0 1) of the zinc phase is always favoured with perpendicular and parallel magnetic field. There is no saturation of this effect with amplitude of B up to 8 T. A study of different geometric configurations of the cathode, which induce more or less natural convection, consolidates these results. The structural modifications of Zn-Ni alloy electrodeposits are thus probably due to a magnetohydrodynamic effect. An additional phenomenon is observed in presence of a perpendicular applied magnetic field since the (3 3 0) preferential orientation of the γ-Ni₅Zn₂₁ disappears with high values of B.     

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.     

Anomalous losses in a Bi 2212 vortex lattice in magnetic fields of 1–3 kOe

The results of an experimental investigation of the dependence of the dissipation in a vortex lattice on the magnetic field strength and orientation of a Bi 2212 crystal at a temperature of ~15 K are presented. A sharp peak, whose width depends on the orientation of the superconductor relative to the field, is observed in the dissipation. The results can be explained qualitatively by the appearance of a geometrical barrier that leads to a substantial redistribution of the magnetic field in the bulk of the sample. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 331–335 (10 March 1996)     

Characteristics of CeCoIn5/Al/AlOx/Nb and CeCoIn5/Al/AlOx/Al tunnel junctions

We report characteristics of CeCoIn₅/Al/AlO_x/Nb and CeCoIn₅/Al/AlO_x/Al tunnel junctions fabricated on the (0 0 1) surface of CeCoIn₅ crystal platelets. The main result of this work is the observation of a low Josephson current (as compared with that expected from the Ambegaokar–Baratoff formula), which is consistent with idea that the order parameter in the heavy-fermion superconductor CeCoIn₅ has unconventional pairing symmetry.     

Dynamics of the magnetic flux component normal to the layers of Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>8</Subscript> in a tilted field

High-frequency losses in the strongly anisotropic layered superconductor Bi₂Sr₂CaCu₂O₈ are measured at 600 MHz under a magnetic field rocking about the ab plane. Anomalies in losses and hysteretic phenomena are found while performing periodic rocking, i.e., cycling the magnetic field component normal to the sample surface. Based on these observations, conclusions are drawn about the nature of magnetic-flux penetration into the superconductor. It is found that, in the range between 60 K and T _c , the dynamics of magnetic-flux vortex lines normal to the ab plane in the presence of a constant magnetic field applied parallel to this plane is governed by the critical penetration field H _c ^⊥* and the surface barrier in the presence of thermally activated vortex motion (giant flux creep). The dependences of H _c1 ^⊥* and the characteristic field of the surface barrier on the magnitude of the parallel magnetic field are measured.     

Distorted vortex lattice in a tetrahedral superconductor

The equilibrium shape and the orientation of the vortex lattice are studied for an s-wave tetrahedral superconductor in the vicinity of the upper critical field. The phase diagram, which includes transitions between rhombic and rectangular lattices, is constructed in the parameter space of the Ginzburg-Landau functional. The developed theory is applied to the heavy-fermion superconductor PrOs₄Sb₁₂. In a wide range of parameters, the shape of the vortex lattice is only weakly dependent on the temperature. The neutron scattering measurements of the vortex lattice in PrOs₄Sb₁₂ can be explained by particularities of the tetrahedral symmetry group and are further supported by analysis of the appropriate band structure calculations. The text was submitted by the authors in English.