Penetration Depth Λab Research Articles

Oxygen isotope effect on the superfluid density within the [formula omitted]-wave and [formula omitted]-wave pairing channels of YBa[formula omitted]Cu[formula omitted]O[formula omitted

We report on measurements of the oxygen isotope (16O/18O) effect (OIE) on the transition temperature Tc and the zero-temperature in-plane magnetic penetration depth λab(0) in the stoichiometric cuprate superconductor YBa2Cu4O8 by means of muon-spin rotation/relaxation. An analysis of the temperature evolution of λab−2 in terms of coexisting isotropic s-wave and anisotropic d-wave order parameters (s+d-wave) reveals that the OIE on the superfluid density ρs(0)∝λab−2(0) stems predominantly from the d-wave component while the contribution of the s-wave one is almost zero. The OIE on the transition temperature Tc is found to be rather small: δTc/Tc=−0.32(7)%, compared to the total OIE on the superfluid density ρs(0): δρs(0)/ρs(0)=−2.8(1.0)%. The partial OIE’s on the corresponding d-wave and s-wave components of ρs(0) are δρs,d(0)/ρs(0)=−3.0(1.2)%, and δρs,s(0)/ρs(0)=0.2(1.2)%, respectively. Our results demonstrate that polaron formation in the CuO2 planes is the origin of the observed OIE in the d-wave channel. In the much weaker s-wave channel, fermionic quasiparticles are present, which do not contribute to the OIE on ρs(0). Our results support the original idea of K. Alex Müller on the polaronic nature of the supercarriers in high-temperature cuprate superconductors.

Equilibrium magnetic properties of the Fe-doped HTSC YBaCuO

For the polycrystalline high-temperature superconductor Y1 –xFexBa2Cu3Oy (0 ≤ x ≤ 0.05), where a significant increase in the intragrain critical current density has recently been found, the effect of iron doping on the equilibrium magnetic characteristics is studied. The field dependences of the magnetization are measured in the temperature range of 40–85 K and in the field range up to 60 kOe with increasing and decreasing fields. The temperature dependences of the London penetration depth λab, the superconducting carrier density ns, and the thermodynamic critical field Hc are determined from an analysis of the middle lines of the magnetic hysteresis loop. It is shown that the thermodynamic properties of Fe substituted samples do not change at x ≤ 0.03. At a higher Fe content, a slight decrease in Hc and the superconducting transition temperature is observed. However, changes in the condensation energy turn out to be much smaller than values expected due to an increase in the density of effective pinning centres created by substitutional atoms in both the yttrium and copper sublattices. It is concluded that the pinning regions in chain CuO planes near substituted Cu sites are two-dimensional in nature and do not affect the superconducting pairing in CuO2 planes. Another possible pinning mechanism, which does not affect Hc, is the interaction of vortices with the magnetic moments of Fe3+ ions.

In-plane magnetic penetration depth in FeSe1-xSx (x = 0, 0.04, 0.09) and FeTe1-xSex (x = 0.40) single crystals

ABSTRACTThe magnetization anomaly of FeSe1–xSx(x = 0, 0.04, 0.09) and FeTe1–xSex(x = 0.40) single crystals are examined through our Modified Phenomenological Ginzburg–Landau (MPGL) theory applicable to two-band superconducting systems. The theory in the London limit calculates the values of λab(0) as 445.695, 372.058 and 432.957 nm of FeSe1–xSx for x = 0, 0.04, 0.09 which are very close to the experimental values reported by Hafiez et al. [Superconducting properties of sulfur-doped iron selenide. Phys Rev B. 2015;91(16):165109–165120] and as 534 nm for FeTe1–xSex(x = 0.40) single crystal, which is close to the experimental value reported by Yadav and Paulose [Upper critical field, lower critical field and critical current density of FeTe0.60Se0.40 single crystals. New J Phys 2009;11:103046]. In addition, the variation of temperature-dependent in-plane magnetic penetration depth λab(T) with the temperature (T) has been presented, which agrees well as reported by Hafiez et al. [Superconducting properties of sulfur-doped iron selenide. Phys Rev B. 2015;91(16):165109–165120] and Yadav and Paulose [Upper critical field, lower critical field and critical current density of FeTe0.60Se0.40 single crystals. New J Phys. 2009;11:103046].

Superconducting properties in heavily overdoped Ba(Fe0.86Co0.14)2As2 single crystals

We report the intrinsic superconducting parameters in a heavily overdoped Ba(Fe1−xCox)2As2 (x=0.14) single crystal and their influence in the resulting vortex dynamics. We find a bulk superconducting critical temperature of 9.8K, magnetic penetration depth λab (0)=660±50nm, coherence length ξab (0)=6.4±0.2nm, and the upper critical field anisotropy γT→Tc≈3.7. The vortex phase diagram, in comparison with the optimally doped compound, presents a narrow collective creep regime. The intrinsic pinning energy plays an important role in the resulting vortex dynamics as compared with similar pinning landscape and comparable intrinsic thermal fluctuations.

Direct measurement of the temperature dependence of the magnetic penetration depth in Ba(Fe1−xNix)2As2 superconductors

The temperature dependence of the in-plane magnetic penetration depth λab of Ba(Fe1−xNix)2As2 single crystals is determined directly from the shielding magnetic susceptibility, measured in the Meissner region with the field parallel to the ab layers. The doping levels studied cover the underdoped, optimally doped and overdoped regimes. At temperatures below 0.5Tc a well-defined power-law behavior λab(T) − λab(0) = ATn (with n ≈ 2.5) is observed. At lower temperatures (T < 0.3Tc) the data are still consistent with n = 2 and , as predicted by the strong pair-breaking scenario proposed by Gordon et al (2010 Phys. Rev. B 81, 180501(R)). The temperature dependence of the superfluid density presents a marked positive curvature just below Tc, which is a sign of two-gap superconductivity. The analysis of ρs(T) in terms of a two-gap model allowed estimation of parameters like the in-band and inter-band couplings, the relative weight of each band, and their dependence on the doping level. A comparison with ρs(T) data obtained by using other techniques in compounds with a similar composition is also presented.

Two energy gaps in superconducting Lu2Fe3Si5 single crystal derived from the temperature dependence of lower critical field Hc1(T)

We report a detailed study of in-plane lower critical field Hc1(T) and penetration depth λab(T) of the Lu2Fe3Si5 superconductor. Two pronounced changes of the Hc1 curvature are observed on the Hc1(T) curve around 0.4Tc and 0.65Tc, respectively, which are attributed to the two-band nature of superconductivity in Lu2Fe3Si5. The penetration depth of λab(T) follows a power law (∼Tn) below 0.4Tc, with n=2.5 close to the values reported for the FeAs-pnictides, suggesting possible s±-wave pairing in Lu2Fe3Si5. Temperature dependence of Hc1 can be well fitted by the two-gap BCS model in the full temperature region using two superconducting gaps Δ1=0.19±0.1meV and Δ2=1.02±0.1meV.

Muon Spin Rotation Study of the Intercalated Graphite Superconductor CaC6 at Low Temperatures

Muon spin rotation (μSR) experiments were performed on the intercalated graphite CaC6 in the normal and superconducting state down to 20 mK. In addition, AC magnetization measurements were carried out resulting in an anisotropic upper critical field \(H_{\text{c2}}\), from which the coherence lengths ξab(0)=36.3(1.5) nm and ξc(0)=4.3(7) nm were estimated. The anisotropy parameter \(\gamma _{H}=H_{\text{c2}}^{ab}/H_{\text{c2}}^{c}\) increases monotonically with decreasing temperature. A single isotropic s-wave description of superconductivity cannot account for this behavior. From magnetic field dependent μSR experiments, the absolute value of the in-plane magnetic penetration depth λab(0)=78(3) nm was determined. The temperature dependence of the superfluid density ρs(T) is slightly better described by a two-gap than a single-gap model.

Effect of point-like disorder on the vortex phase diagram in Bi2Sr2CaCu2O8−δ in oblique field

The phase diagram of vortex matter in the layered superconductor Bi2Sr2CaCu2O8−δ exposed to a magnetic field oblique to the crystalline c-axis contains two first order transition (FOT) lines [1]. The first, HFOTm, separates the vortex solid from the vortex liquid, the second, HFOTct, separates the combined lattice state in the vortex solid from a tilted lattice state. The angular dependence of HFOTm in the tilted lattice region follows the anisotropic Ginzburg–Landau model [2], allowing for the determination of the anisotropy factor γeff and the contribution of magnetic coupling to the mutual interaction of “pancake” vortices in the crossed lattice limit. The later parameter is directly related to the in-plane penetration depth λab. We investigate the evolution of the phase diagram of Bi2Sr2CaCu2O8−δ in oblique fields with point-like disorder, introduced by irradiation with 2.3MeV electrons. Apart from the depression of Tc, point-like disorder induces an increase of γeff and a depression of the superfluid density.

The influence of static-stripes on superfluid density in La1.84−yEuySu0.16CuO4

To clarify how superfluid density ns changes with the emergence of the static-stripe ordering, the in-plane penetration depth λab (∝ns-1/2) is evaluated from detailed magnetization measurements in La1.84−yEuySr0.16CuO4 single crystals, in which the degree of static-stripe fluctuations is controlled by the Eu content without changing the carrier concentration. A significant suppression of ns is found when static-stripes are stabilized, indicating that carriers forming static-stripes do not turn into Cooper pairs. Whereas Tc-suppression is clearly associated with this ns-reduction, Tc remains high at ns→0, suggesting that a real space phase separation occurs in this extreme region.

Probing the order parameter of magnetically grain-aligned NCCO electron-doped cuprate

The c-axis alignment of Nd1.85Ce0.15CuO4.105 superconducting powder was achieved by applying an external magnetic field of 1T perpendicular to the axis of rotation of powder/epoxy tetragonal holder. The temperature dependencies of the in-plane penetration depth λab and out-of-plane penetration depth λc were obtained by measuring the zero-filed-cooled ac diamagnetic susceptibility χd(T) in a low applied field (Ba=10Oe). An observed Nd paramagnetic background was subtracted. The relative change temperature dependence penetration depth Δλ(T)=λ(T)−λ(0) for both c-axis parallel and perpendicular to the applied field can be fitted to a quadratic d-wave rather than an exponential s-wave like function up to 0.5Tc. This result is in agreement with recent experiments suggest the unconventional nature for electron-doped RCCO (R=Pr, Nd, La, Eu, Sm) cuprates.

Pressure effect on the in-plane magnetic penetration depth inYBa2Cu4O8

We report a study of the pressure effect (PE) on the in-plane magnetic field penetration depthλab inYBa2Cu4O8 by means of Meissner fraction measurements. A pronounced PE onλab−2(0) was observed with a maximum relative shift ofΔλab−2/λab−2 = 44(3)% ata pressure of 10.2 kbar. It arises from the pressure dependence of the effective in-plane charge carriermass and pressure-induced charge carrier transfer from the CuO chains to the superconductingCuO2 planes. The present results imply that the charge carriers inYBa2Cu4O8 are coupled to the lattice.

The oxygen isotope effect on the in-plane penetration depth in cuprate superconductors

Muon spin rotation (μSR) studiesof the oxygen isotope (16O/18O) effect (OIE) on the in-plane magnetic field penetration depthλab in cuprate high-temperature superconductors (HTS) are presented.First, the doping dependence of the OIE on the transition temperatureTc in various HTS is briefly discussed. It is observed that differentcuprate families show similar doping dependences of the OIE onTc. Then,bulk μSR,low-energy μSR, and magnetization studies of the total and site-selective OIE onλab are described in some detail. A substantial OIE onλab was observed in various cuprate families at all doping levels, suggesting that cuprate HTS arenon-adiabatic superconductors. The experiments clearly demonstrate that the total OIE onTc and λab arise from the oxygen sites within the superconductingCuO2 planes, demonstrating that the phonon modes involving the movement of planar oxygen aredominantly coupled to the supercarriers. Finally, it is shown that the OIE onTc and λab exhibit a relation that appears to be generic for different families of cuprate HTS. Theobservation of these unusual isotope effects implies that lattice effects play an essential rolein cuprate HTS and have to be considered in any realistic model of high-temperaturesuperconductivity.

Metal–insulator transition, Cu K-edge x-ray absorption near-edge structures and pairing symmetry for electron-doped Pr1.85Ce0.15CuO4+δ superconductors

A metal–insulator transition near oxygen content parameter δ∼0.018(5) was observed for the Ce-optimal-doped (x=0.15) Pr1.85Ce0.15CuO4+δ (−0.003⩽δ⩽0.03) electron superconductors. Cu K-edge x-ray absorption near-edge structure reflects the 3dn character where low-energy peak A1 reflects the 3d10 configuration of Cu(I) oxidation state and A2 peak reflects the 3d10L (L for oxygen ligand hole) for Cu(II) state. The abrupt increase of A1 peak intensity and energy separation ΔE(A2−A1) near δ=0.018 coincide with the metal–insulator transition due to the formation of a broader 3d conduction band. The basal-plane penetration depth λab(T) for c-axis aligned powders show a d-wave power-law behavior with a linear-T temperature dependence for the 17.5 K underdoped superconductor [δ=0.011(5)], while a quadratic-T2 temperature dependence was observed for the 21 K optimal-doped superconductor (δ=−0.002–0.003). The superfluid density ns∼λab−2 increases from the underdoped to the optimal-doped region.

Non-s-wave behavior of c-axis aligned Pr1.85Ce0.15CuO3.97 superconducting powder

The tetragonal c-axis alignment of Tc=23 K Pr1.85Ce0.15CuO3.97 superconducting powder was achieved in a 1 T alignment field with rotating powder/epoxy holder perpendicular to the alignment field. The in-plane penetration depth λab for this electron-doped superconductor was derived using zero-field-cooled Meissner diamagnetic data with low applied field (Ba&amp;lt;Hc1ab) parallel to the c-axis aligned powder. A small Pr paramagnetic contribution was subtracted. The temperature dependence of Δλab(T)=λab(T)−λab(0) [with λab(0)∼133 nm] up to ∼0.5 Tc can be fitted well with a non-s-wave or d-wave-like power law Δλab(T)=AT2+CT4, where the T2 law is dominated at low temperature. The present result agrees with recent phase-sensitive experiment, which indicates d-wave nature for these electron-doped 214 cuprates.

Variable sample temperature scanning superconducting quantum interference device microscope

We demonstrate a design for a scanning superconducting quantum interference device (SQUID) microscope in which the sample temperature can be varied over a large range. In this design, both sample and SQUID are in the same vacuum space, separated by a few microns. By firmly anchoring the SQUID to a low-temperature bath, the sample temperature can be changed while the SQUID remains superconducting. This allows magnetic imaging at varying sample temperatures with micron-scale spatial resolution and the sensitivity of a low-Tc SQUID. We demonstrate this approach by imaging the temperature dependence of Abrikosov vortices in thin films of the high-temperature superconductor YBa2Cu3O7−δ. We extract the in-plane penetration depth λab(T) in our samples from these measurements.

Vortex fluctuation in HgBa2Ca3Cu4O10+δ

Reversible magnetization with the external magnetic fields of 1 T ≤ H ≤ 5 T parallel to the c-axis has been measured for the grain aligned HgBa2Ca3Cu4O10+δ. A strong vortex fluctuation effect was clearly observed and the magnetization is well described by the vortex fluctuation model. From this analysis, the penetration depth λab(0) = 1583 Å and the effective interlayer spacing s = 44.6 Å were estimated. However, the value of s is significantly larger than the lattice parameter c = 19 Å, which is different from the prediction of the vortex fluctuation model. From the model on superconducting fluctuations proposed by Koshelev, in which not only the critical fluctuations at the lowest Landau level but also the Gaussian fluctuations at higher Landau levels were considered, the different value of s = 15.4 Å was obtained.

Thermodynamic properties of YBa2Cu4O8 crystal near upper critical fields Hc2(T)

High-field magnetization with external magnetic fields parallel to the c-axis has been measured in high-quality YBa2Cu4O8 single crystal. The fluctuation-induced magnetization above Tc and a crossover of magnetization curves M(T) at T*=77.4 K were clearly observed for various magnetic fields, and analyzed by the high-field scaling law and the vortex fluctuation theory for three-dimensional systems. In the reversible temperature region, the magnetization is well described by the model of Hao et al. [Phys. Rev. B 43, 2884 (1991)]. From this analysis, the thermodynamic parameters such as upper critical field slope −dHc2/dT=1.2 T/K near Tc, penetration depth λab(0)=1943 Å, and coherence length ξab(0)=21.7 Å were extracted.

Magnetic anisotropy in Hg1201 and Hg1223 superconducting single crystals

We report dc magnetization measurements on the first available HgBa2CuO4+δ and HgBa2Ca2Cu3O8+δ (respectively Hg1201 and Hg1223) superconducting single crystals, for fields applied both perpendicular and parallel to the CuO2 planes. In the regime where the magnetization is reversible and linear in logarithm of the applied field, we have used the 3D London theory to determine the penetration depth λab for in-plane currents (λab(0)≃1300±100A, for Hg1201 and ≈1500±100A for Hg1223). Using a relation derived from the anisotropic Ginzburg-Landau approach, we have made an estimate of the anisotropy factor (γ≈30 for Hg1201 and γ≈50 for Hg1223). The results are in agreement with recent torque experiments on Hg1223.

Epitaxial growth of superconducting YBa2Cu3O7−x on Si(100) with CaF2 as intermediate buffer

Epitaxial superconducting YBa2Cu3O7−x (YBCO) thin films have been grown on Si(100) using CaF2 as an intermediate buffer layer. The CaF2(100) layers were grown by molecular beam epitaxy while for the YBCO layers a laser ablation process was used. Electron channeling patterns of the YBCO surface show the characteristic four-fold symmetry for c-axis orientation. The epitaxial relationship is (001)YBCO//(001)Si and [010]YBCO//[110]Si. This corresponds to a lattice mismatch of only 1% in the a-b-YBCO interface plane. The 60-nm-thick layers are crack free. Magnetic shielding properties of the epitaxial YBCO layers have been studied by measuring the zero temperature penetration depth λab(0) and the power law dependence of the transition temperature versus magnetic field.