Effect of the microwave signal power on the controllability of a ferroelectric phase shifter

We consider a microwave phase shifter based on thin-film ferroelectric parallel-plate capacitors operating as a part of a phased array at an elevated microwave power level and for a limited power in the control circuits. To eliminate capacitance modulation in parallel-plate capacitors by an ac field, we propose the separation of the effects of the dc control voltage and the ac voltage based on the symmetry of the capacitance-voltage characteristic of the unit including two capacitors parallel-connected in the ac voltage U _ac and series-connected in dc voltage U _dc. The experiment shows that for U _dc > U _ac, the phase of the wave passing through the phase shifter weakly depends on the microwave signal power. The reflection phase shifter is tested for a pulsed power of the microwave signal up to 6 W and a power in the control circuit on the order of 10 μW.     

Surface impedance of a superconducting slab in the mixed state: Effect of the surface barrier

The effect of the surface barrier on the surface impedance Z of a type-II superconductor slab with a finite thickness is investigated in dc magnetic fields H ₀, which are aligned parallel or perpendicular to the slab plane. It is demonstrated that, in a perpendicular geometry, the surface resistivity ρ_s=ReZ has a maximum when the depth of penetration of the ac magnetic field is of the order of the slab thickness (size effect). For a parallel orientation of the magnetic field H ₀, the effect of the Bean-Livingston surface barrier manifests itself as a decrease in the dissipative loss and a change in the field dependence of the surface resistivity characterized by a magnetic hysteresis. It is shown for the first time that, under the conditions of persistent trapped magnetic flux, the dependence ρ_s(H ₀) is a decreasing function, which is associated, in particular, with a nontrivial suppression of the size effect.     

The anomalous anisotropy in the ac susceptibility of La1.45Nd0.4Sr0.15CuO4 single crystal

The dependencies of ac susceptibility on the superimposed dc magnetic fields for the stripe-ordered La_1.45Nd_0.4Sr_0.15CuO₄ single crystal with two superconducting transitions have been studied in the 3D and 2D superconducting ranges for the fields along different orientations of the crystal. The results show that with increasing fields the interlayer Josephson coupling and the in-plane superconductivity are suppressed orderly for the fields perpendicular to CuO₂ planes. The influences of the field parallel to CuO₂ planes on the 3D and 2D superconductivity are much weaker than those of the field parallel to the c-axis. The irreversibility lines for the 3D and 2D superconducting states are also studied.     

Vortex oscillations in TFA-grown YBCO thin-films with BZO nanoparticles

An ac susceptibility methodology has been applied to investigate the vortex dynamics of YBa₂Cu₃O_7−x–BaZrO₃ nanocomposites grown by the chemical solution deposition TFA route, close to the irreversibility line. By analysing the linear, non-dissipative Campbell regime at low ac fields, we determined the temperature and field dependence of the restoring pinning constant, α_L(H_dc, T), characterising the harmonic oscillation of vortices inside their potential wells. Different than standard TFA–YBCO films, BZO nanocomposites displayed increasing α_L(H_dc) curves in the whole studied (H_dc, T) phase diagram, a behavior not predicted by the standard collective theory. We suggest results may be explained by the softening of the vortex-lattice, owed to the microstrain induced by the nanoparticles in the YBCO matrix.     

Quantum oscillations of rectified dc voltage as a function of magnetic field in an “almost” symmetric superconducting ring

Periodic oscillations in the dependence V _dc(B) of rectified dc voltage on the perpendicular magnetic field have been experimentally observed near the critical temperature in a single superconducting aluminum ring with slight geometric inhomogeneities (without specially formed circular asymmetry), biased by an external ac current (without a dc component). With a change in the external current and temperature, the voltage V _dc(B) behaves like the corresponding voltage on a circularly asymmetric ring but has a much smaller amplitude. The Fourier spectrum of the function V _dc(B) contains the fundamental frequency, corresponding to the ring area, and its highest harmonics. “Satellite” frequencies, dependent on the structure geometry and external parameters, were unexpectedly found in the spectrum.     

Influence of temperature on critical fields in ZnCr2Se4

The complex ac dynamic magnetic susceptibility was used to study the influence of temperature on critical fields in polycrystalline ZnCr₂Se₄ spinel. An antiferromagnetic order with a Néel temperature T_N=20.7 K and a strong ferromagnetic exchange evidenced by a positive Curie-Weiss temperature θ_CW=55.1 K were established. An increasing static magnetic field shifts T_N to lower temperatures while a susceptibility peak at T_m in the paramagnetic region—to higher temperatures. The non-zero and negative values both of the second and third harmonics of susceptibility suggest only a parallel spin coupling in ferromagnetic clusters in the range between the Néel and Curie-Weiss temperatures. Below T_N the magnetic field dependence of susceptibility, χ_ac(H), shows two peaks at critical fields H_c1 and H_c2. The values of H_c1 decrease slightly with temperature while the values of H_c2 drop rapidly with temperature. The strong changes of H_c2 temperature induced are mainly responsible for a spin frustration of the re-entrant type in the spinel under study.     

Formation of a quasi-uniform sequence of vortices in a periodically modulated finite-length Josephson contact

The configurations of currents and the profile of a magnetic field penetrating into a finite-length contact at I < I _C are calculated. The computational method is based on analyzing the continuous variation of the current structure leading to a decrease in the Gibbs potential. Such an approach makes it possible to find a configuration that sets in when an external field slightly exceeds H _max and trace the evolution of this configuration with increasing field. It is shown that at H > H _max boundary structures turn into quasi-uniform sequences of vortices the spacing between which oscillates about a mean value decreasing with increasing H. At some values of H, vortices with a number of fluxoids Φ₀ larger by unity start penetrating into the contact in the form of boundary sequences. As the field grows, they produce quasi-uniform sequences, etc. Vortices with the number of fluxoids Φ₀ differing by more than unity can fall into the contact at no field. The penetration of vortices with (k + 1)Φ₀ into a contact each cell of which contains kΦ₀ is fully identical to the penetration of vortices with one Φ₀ into the Meissner configuration. This statement is supported by the almost strict periodicity of mean induction b in the contact versus external field h dependence with a period of 1 along both axes and also by the form of the dependences of the magnetic field in the cells on the cell-boundary distance.     

Superconducting slab in contact with thin superconducting layer at higher critical temperature

Within the framework of nonlinear time dependent Ginzburg–Landau equations (TDGL) we study the properties of a mesoscopic superconducting film with both surfaces in contact with a thin superconducting layer at a higher critical temperature. The properties of the layer are taken into account by the de Gennes boundary conditions via the extrapolation length b. We assume that the magnetic field is parallel to the multilayer interfaces. We obtain magnetization curves and calculate the spatial distribution of the superconducting electron density using a numerical method based on the technique of gauge invariant variables. This work tests both the rectangular cross-section size and b limit for the occurrence of vortices in a mesoscopic sample of area d_xxd_y where d_y = 80ξ(0) and dx varies discretely from 20ξ(0) to 3ξ(0). Our data also show a linear behavior of the magnetization curve and a power-law of order parameter modulus in limit b → 0_-.     

Application of nano-scale Josephson junction as phase sensitive detector for analysis of vortex states in mesoscopic superconductors

We study phase shifts in a Josephson junction induced by vortices in superconducting mesoscopic electrodes. The position of the vortices are controlled by suitable geometry of a nano-scale Nb–Pt_1−xNi_x–Nb junction of the overlap type made by Focused Ion Beam (FIB) sculpturing. The vortex is kept outside the junction, parallel to the junction plane. From the measured Fraunhofer characteristics the entrance and exit of vortices are detected. By changing the bias current through the junction at constant magnetic field the vortices can be manipulated and the system can be switched between two consecutive vortex states which are characterized by different critical currents of the junction. A mesoscopic superconductor thus acts as a non-volatile memory cell in which the junction is used both for reading and writing information (vortex). Furthermore, we observe that the critical current density of Nb–Pt_1−xNi_x–Nb junctions decreases non-monotonously with increasing Ni concentration. It exhibits a minimum at ∼40 at.% Ni, which is an indication of switching into the π state.     

Bipolar cycling effects in BiFeO3–BaTiO3 piezoelectric ceramics

BiFeO₃–BaTiO₃ (BF-BT) lead-free piezoelectric system has been paid much attention due to good piezoelectric properties and high Curie temperature. Poling is a process to align ferroelectric domains and increase the piezoelectric coefficients. During the poling process, unipolar direct current (dc) electric fields were applied conventionally, but recently bipolar alternating current (ac) cycling was reported to improve piezoelectric properties in rhombohedral structure piezoelectric materials. We investigated the effects of dc-poling and ac-cycling in BF-BT ceramics. The d₃₃ increased from 210 pC/N with dc-poling to 240 pC/N with ac-cycling in the morphotropic phase boundary region of BF-BT with domain engineering. This improvement of piezoelectric properties with ac-cycling was consistent with the structural evolution related to ferroelectric domains.     

Pinning efficiency of splayed columnar defects in Bi-2212 single crystal: Evidence of a cage pinning effect

A three-directional configuration of columnar defects has been induced in a Bi₂Sr₂CaCu₂O₈ single crystal by irradiation with heavy ions of high energy. Persistent current densities have been extracted, using the Bean model, from hysteresis loops recorded in the orientation H||c. We have shown that improvements in pinning properties are larger in this three-directional splayed configuration than in the one obtained with columnar defects parallel to the c-axis. This effect exists only for H larger than H_Φ, where H_Φ is the matching field, and disappears as temperature is increased and vortices become less stiff. This is the first time that such a beneficial effect is reported for a compound of such a high electronic anisotropy.     

Two regimes of vortex penetration into platelet-shaped type-II superconductors

Vortex penetration into a thin superconducting strip of a rectangular cross section is considered at an increasing applied magnetic field H _a , taking an interplay between the Bean-Livingston and the geometric barriers in the sample into account. We calculate the magnetic field H _p at which the penetration begins and show that two regimes of vortex penetration are possible. In the first regime, vortices appearing at the corners of the strip at H _a = H _p immediately move to its center, where a vortex dome starts to develop. In the second regime, the penetration occurs in two stages. In the first stage, at H _a < H _p , tilted vortices penetrate into the edge regions of the strip, where novel domes are shown to be formed at the top, bottom, and lateral surfaces. In the second stage, at H _a = H _p , the vortex propagation to the center becomes possible. The difference between the regimes manifests itself in slightly different dependences of the magnetic moment of the strip on H _a .     

Magnetic field penetration into a 3D ordered Josephson medium and applicability of the bean model

The results of calculation of penetration of an external magnetic field into a 3D ordered Josephson medium, based on analysis of modification of the configuration in the direction of the decrease in its Gibbs potential, are reported. When the external field slightly exceeds the stability threshold, the Meissner configuration is transformed into a periodic sequence of linear vortices, which are parallel to the boundary of the medium and are located at a certain distance from it. There exists a critical value I _C separating two possible regimes of penetration of the external magnetic field into the medium. For I > I _C , for any value of the external field, a finite-length boundary current configuration appears, which completely compensates the external field in the bulk of the sample. At the sample boundary, the field decreases with increasing depth almost linearly. The values of the slope of the magnetic field dependence are rational fractions, which remain constant in finite intervals of I. When the value of I exceeds the upper boundary of such an interval, the slope increases and assumes the value of another rational fraction. If, however, I < I _C , such a situation takes place only up to a certain value of external field H _max. For higher values, the field penetrates into the medium to an infinite depth. These results lead to the conclusion that the Bean assumptions are violated and that Bean’s model is inapplicable for analyzing the processes considered here.     

Transport and magnetic properties of disordered LixVyO2 (x=0.8 and y=0.8)

The magnetic and electron transport properties of rhombohedral Li_xV_yO₂ (x=0.8 and y=0.8) are studied. The dc susceptibility of Li_xV_yO₂ can be well fitted to the modified Curie-Weiss law, which verified the paramagnetic ground state. The magnetic hysteresis and ac susceptibility also confirm this paramagnetism. The Li_xV_yO₂ exhibits semiconducting behavior, which is explained by thermal activated process at high temperature and variable-range hopping mechanism at low temperature. Anderson localization plays an important role in both the electron transport behavior and the magnetic behavior due to the site disorder between the Li⁺ ion and V⁴⁺ ion.     

AC response of vortices subjected to pinning by columnar defects in Tl2Ba2CaCu2O8 epitaxial films

A micro-Hall-probe-based ac susceptometer is used to study the dynamics of vortices in Tl₂Ba₂CaCu₂O₈ (Tl-2212) epitaxial films with and without correlated disorder in a low field (<6 kG) and high temperature (T>60 K) regime. The Bean critical state model for a thin superconducting disc in perpendicular magnetic field is used to extract the critical current density of the films. The temperature and frequency dependence of the irreversibility field (B_irr) is compared for samples with and without the linear defects. The B_irr(T) curve shows a distinct discontinuity at B≈B_φ. The frequency dependence of the screening current density J(ω), extracted from the inphase component (T^′_H) of the fundamental transmittivity, has been analyzed in the framework of Bose glass dynamics. This analysis shows that the vortex depinning temperature is ≈24 K for this Tl-2212 film and the depinning process starts via excitations of half-loops. The angle dependent studies of the susceptibility further suggest that these half-loops consist of many pancake vortices.     

Influence of crystal defects on the irreversibility line of YBa2Cu3O7-x single crystals

High quality flux grown and defect enriched peritectically grown YBa₂Cu₃O_7–x single crystals have been investigated by an ac-susceptibility technique. This method allows to determine an irreversibility line from the temperature and field dependence of the peaked imaginary part of the susceptibility, which is due to magnetic losses. For magnetic fieldsH _ac perpendicular to thec-axis of the crystal, the irreversibility line of the defect enriched crystal shows a shift to higher field values as compared to the perfect crystal, a sign that crystal defects like Y₂BaCuO₅(211)-precipitates and microcracks act as strong pinning centers. ForH _ac parallel to thec-axis no clear evidence for a stronger pinning is found. From these results we conclude that different pinning mechanisms are dominating at different field orientations.     

Vortex lattice symmetry in hexagonal superconductor CaAlSi probed by small angle neutron scattering

The small angle neutron scattering diffraction patterns from the flux line lattice state in the layered hexagonal superconductor CaAlSi are observed. Under an applied magnetic field (H) parallel to the crystalline c-axis, a hexagonal vortex structure is observed over the entire temperature/field regions. On the other hand, the vortex configuration under H∥a shows an ellipsoidal arrangement of the first-order Bragg peaks due to the anisotropic penetration depth. It was inferred from these results that the vortex state characterized by penetration depth and coherence length in CaAlSi may be described by that of anisotropic uniaxial superconductor using London theory.     

Harmonic generation studies in laser ablated YBCO thin film grown on 〈100〉 MgO

The generation of harmonics in a laser ablated YBCO film deposited on a 〈100〉 MgO substrate is reported. Higher odd harmonics appeared when the film was subjected to an ac field. The presence of a dc field induces only the second harmonic with a small value of slope ofV ₂−H _dc curve (δV ₂/δH _dc) compared to bulk YBCO. The variation of the amplitude of third harmonic (V ₃) withH _ac and temperature was studied. These results are explained in terms of a critical state model. The observation of only a small amplitude of second harmonic (V ₂) with a smallδV ₂/δH _dc is explained in terms of a special kind of clean grain boundary present in YBCO laser ablated films on 〈100〉 MgO.     

Microwave absorption in high-T c superconductors at high magnetic fields

In the mixed state of superconductors (H _c1?H?H _c2) the penetration of microwaves is governed by both, complex conductivity σ(T) and driven oscillation of vortices. In this paper, we show that an effective microwave conductivity can be derived and used to fit the field dependences of the surface resistanceR _s. The fit parameter is the upper critical field. Measurements on single crystals YBa₂Cu₃O_7-δ were made in magnetic fields (H∥c) up to 2.25 T, and in the temperature range from 70–100 K. The critical temperature for mean field superconductivity appears to be 89.3 K, while the apparent onset in the curve ofR _s(T) appears at about 92 K. The magnetic dependences ofR _s clearly demonstrate that one can separate the regions of mean field superconductivity from the region of fluctuations.     

Microstructure and spin wave scattering in polycrystalline yttrium iron garnet

Polycrystalline ceramic YIG has been synthesized with submicron microstructure. The log-log plot of FMR linewidth versus average grain size gives a power law dependence α^-1₀ where α₀ is the average grain size. The instability threshold h_crit for increasing magnetic field vector of the microwave parallel pump shows a linear log-log dependence with average grain size.