Penetration Depth Anisotropy Research Articles

Superconductivity and Field-Induced Magnetism inSrFe1.75Co0.25As2

Using muon-spin rotation, we studied the in-plane (lambda_{ab}) and the out of plane (lambda_{c}) magnetic field penetration depth in SrFe_{1.75}Co_{0.25}As_{2} (T_{c} approximately 13.3 K). The penetration depth anisotropy gamma_{lambda} = lambda_{c}/lambda_{ab} increases from gamma_{lambda} approximately 2.1 at T_{c} to 2.7 at 1.6 K. The mean internal field in the superconducting state increases with decreasing temperature, just opposite to the diamagnetic response seen in magnetization experiments. This unusual behavior suggests that the external field induces a magnetic order which is maintained throughout the whole sample volume.

Nonexponential London Penetration Depth of FeAs-Based SuperconductingRFeAsO0.9F0.1(R=La, Nd) Single Crystals

The superconducting penetration depth, $\lambda(T)$, has been measured in RFeAsO$_{0.9}$F$_{0.1}$ (R=La,Nd) single crystals (R-1111). In Nd-1111, we find an upturn in $\lambda(T)$ upon cooling and attribute it to the paramagnetism of the Nd ions, similar to the case of the electron-doped cuprate Nd-Ce-Cu-O. After the correction for paramagnetism, the London penetration depth variation is found to follow a power-law behavior, $\Delta \lambda_L(T)\propto T^{2}$ at low temperatures. The same $T^2$ variation of $\lambda(T)$ was found in non-magnetic La-1111 crystals. Analysis of the superfluid density and of penetration depth anisotropy over the full temperature range is consistent with two-gap superconductivity. Based on this and on our previous work, we conclude that both the RFeAsO (1111) and BaFe$_2$As$_2$ (122) families of pnictide superconductors exhibit unconventional two-gap superconductivity.

Two-Gap Superconductivity inBa1−xKxFe2As2: A Complementary Study of the Magnetic Penetration Depth by Muon-Spin Rotation and Angle-Resolved Photoemission

We investigate the magnetic penetration depth lambda in superconducting Ba1-xKxFe2As2 (Tc approximately 32 K) with muon-spin rotation (microSR) and angle-resolved photoemission (ARPES). Using microSR, we find the penetration-depth anisotropy gamma lambda=lambda c/lambda ab and the second-critical-field anisotropy gammaHc2 to show an opposite T evolution below Tc. This dichotomy resembles the situation in the two-gap superconductor MgB2. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth lambda ab around 7 K. The complementarity of microSR and ARPES allows us to pinpoint the values of the two gaps and to arrive to a remarkable agreement between the two techniques concerning the full T evolution of lambdaab. This provides further support for the described scenario and establishes ARPES as a tool to assess macroscopic properties of the superconducting condensate.

Single crystals of LnFeAsO 1−xF x (Ln = La, Pr, Nd, Sm, Gd) and Ba 1−xRb xFe 2As 2: Growth, structure and superconducting properties

A review of our investigations on single crystals of LnFeAsO 1− x F x (Ln = La, Pr, Nd, Sm, Gd) and Ba 1− x Rb x Fe 2As 2 is presented. A high-pressure technique has been applied for the growth of LnFeAsO 1− x F x crystals, while Ba 1− x Rb x Fe 2As 2 crystals were grown using a quartz ampoule method. Single crystals were used for electrical transport, structure, magnetic torque and spectroscopic studies. Investigations of the crystal structure confirmed high structural perfection and show incomplete occupation of the (O, F) position in superconducting LnFeAsO 1− x F x crystals. Resistivity measurements on LnFeAsO 1− x F x crystals show a significant broadening of the transition in high magnetic fields, whereas the resistive transition in Ba 1− x Rb x Fe 2As 2 simply shifts to lower temperature. The critical current density for both compounds is relatively high and exceeds 2 × 10 9 A/m 2 at 15 K in 7 T. The anisotropy of magnetic penetration depth, measured on LnFeAsO 1− x F x crystals by torque magnetometry is temperature dependent and apparently larger than the anisotropy of the upper critical field. Ba 1− x Rb x Fe 2As 2 crystals are electronically significantly less anisotropic. Point-Contact Andreev-Reflection spectroscopy indicates the existence of two energy gaps in LnFeAsO 1− x F x . Scanning Tunneling Spectroscopy reveals in addition to a superconducting gap, also some feature at high energy (∼20 meV).

Anisotropy of Critical Fields in MgB2: Two–Band Ginzburg–Landau Theory for Layered Superconductors

The temperature dependence of the anisotropy parameter of upper critical field γHc2 (T) = H⊥c2 (T)/H⊥c2 (T) and London penetration depth γλ(T) = λ⊥(T)/λ⊥ (T) are calculated using two-band Ginzburg–Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 (T) is increased, while the London penetration depth anisotropy γλ(T) reveals an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations. Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.

Evidence for Two Distinct Anisotropies in the Oxypnictide Superconductors SmFeAsO0.8F0.2 and NdFeAsO0.8F0.2

Single crystals of the oxypnictide superconductors SmFeAsO0.8F0.2 and NdFeAsO0.8F0.2 with T c in the range of 44 to 48 K were investigated by torque magnetometry. An analysis of the data in terms of a recently proposed model for the anisotropic magnetization in the superconducting state, treating the magnetic penetration depth anisotropy γ λ differently than the upper critical field anisotropy γ H , provides evidence that in the oxypnictide superconductors two distinct anisotropies are present. As a result γ λ differs significantly in magnitude and in temperature dependence from γ H , analogous to MgB2 but with a reversed sign of slope. This scenario strongly suggests a new multi-band mechanism in the novel class of oxypnictide high-temperature superconductors.

Penetration depth anisotropy in cuprates with pseudogap

AbstractWe study the penetration depths along the a (λa), b (λb) and c (λc)‐axes in the presence of the pseudogap and d superconducting phases (DSC) in a simple model for cuprates. The pseudogap phase is addressed within the framework of the ordered d ‐density wave (DDW). The above scenario is considered using a mean‐field calculation of the tight binding model which incorporates two layers – a CuO2 plane and a CuO chain per unit cell. The CuO chains become superconducting due to the proximity to the planes below the critical temperature. Moreover our model includes a momentum dependent chain‐plane coupling. We observe distinct behaviors for the penetration depth results along the three directions which is consistent with the anisotropy observed in the experimental results. The temperature dependence of λc is ex‐ actly the same as that of the recent experimental results as demonstrated for Tc = 18 K in the underdoped region. We observe a qualititave difference in the temperature dependence of λa and λb when compared to our previous studies. However the phase diagram due to the inclusion of the momentum dependence of the coupling suffers no significant variation. The main result of our work then is that a simple proximity DDW model in which the pairing interaction is localized to the planes and the planes are coupled to the chains through a momentum dependent term can account for many observed experimental properties. The inclusion of the pseudogap and also the value of the chain‐plane coupling modifies the general trend of our results when compared to the simple DSC model without the coupling. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Small-angle neutron scattering measurements of the vortex lattice inCaC6

Small-angle neutron scattering has been applied to study the vortex lattice in the intercalated graphite superconductor CaC6 (T-c=11.3 K). Scattering from the vortex lattice is in the form of a ring, most likely reflecting the absence of in-plane orientational order of the pyrolitic graphene planes. The temperature and field dependence of the scattered intensity allows the in-plane zero temperature value of the coherence length [xi=350(25) angstrom] and the London penetration depth [lambda=500(30) angstrom] to be estimated. Measurements with the applied field at 70 degrees to the c axis directly reveal the penetration depth anisotropy, gamma(lambda)=5.1(4), which, unlike MgB2, is equal to the anisotropy of the coherence length deduced from magnetization measurements. The orientation of the vortex lattice is fixed relative to the rotation axis of the crystal as predicted by anisotropic London theory.

Measuring the penetration depth anisotropy inMgB2using small-angle neutron scattering

Using small-angle neutron scattering, we have measured the misalignment between an applied field of $4\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ and the flux-line lattice in $\mathrm{Mg}{\mathrm{B}}_{2}$, as the field is rotated away from the $c$ axis by an angle $\ensuremath{\theta}$. The measurements, performed at $4.9\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, showed the vortices canting towards the $c$ axis for all field orientations. Using a two-band/two-gap model to calculate the magnetization, we are able to fit our results yielding a penetration depth anisotropy, ${\ensuremath{\gamma}}_{\ensuremath{\lambda}}=1.1\ifmmode\pm\else\textpm\fi{}0.1$.

Penetration depth anisotropy in MgB2 single crystals and powders

Abstract We present small-angle neutron scattering (SANS) measurements of the vortex lattice in single crystal and powder samples of MgB 2 —a two band superconductor. SANS is a powerful method allowing us to measure directly the distribution of vortex separations and hence the anisotropy of the penetration depth, γ λ . Single crystal results show the expected rise of γ λ with applied field as the weaker, almost isotropic, π-band is suppressed. Results from the powder samples do not show as significant a rise in γ λ with field. We believe this originates from ‘averaged’ properties of the penetration depth experienced by vortices in each multi-crystallite powder grain.

Effect of two bands on the scaling of critical current density inMgB2thin films

The dependence of critical current density $({J}_{c})$ on applied magnetic field $(B)$ and angle $(\ensuremath{\theta})$ between $B$ and the $c$ axis has been investigated to determine the anisotropy of ${\text{MgB}}_{2}$ thin films at different temperatures. The results have been compared with upper critical field $({H}_{c2})$ anisotropy $({\ensuremath{\gamma}}_{H})$ determined by measuring ${H}_{c2}$ for fields applied parallel to the $ab$ plane and the $c$ axis. Contrary to the case of ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\mathrm{O}}_{8}$ and ${\text{YBa}}_{2}{\text{Cu}}_{3}{\mathrm{O}}_{x}$, where ${J}_{c}(\ensuremath{\theta},H)$ scales with $H∕{H}_{c2}(\ensuremath{\theta})$, ${J}_{c}(\ensuremath{\theta},H)$ for ${\text{MgB}}_{2}$ did not follow this scaling. Surprisingly, the temperature dependence of anisotropy determined from ${J}_{c}(\ensuremath{\theta},H)$ is similar to the predictions for penetration depth anisotropy of ${\text{MgB}}_{2}$. These results have been understood as a combined effect of a two-band theory and the collective pinning model, in which ${J}_{c}$ strongly depends on the elastic properties of a vortex lattice.

Vortex lattice reorientation and anisotropy in MgB 2––effects of two-band superconductivity

We present small-angle neutron scattering (SANS) measurements of the vortex lattice (VL) in single crystal MgB 2––a two-band superconductor. Bragg diffraction of neutrons visualizes the structure and orientation of the VL while the scattered intensity probes the super-carrier density. Superconductivity in the π-band is rapidly suppressed with increasing field with a corresponding decrease in scattered intensity and a re-orientation of the VL between 0.5 and 0.9 T. Both these observations are consistent with superconductivity in the π-band being weaker than in the σ-band ( Δ π< Δ σ), and a changing influence of different parts of the Fermi surface determining the VL orientation. SANS measurements of the VL for fields applied at an angle to the c-axis allow the penetration depth anisotropy, γ λ , to be estimated.

Penetration depth and Hc2 anisotropy of MgB 2 by [formula omitted]B NMR

11 B nuclear magnetic resonance (NMR) measurements have been performed to investigate vortex states of polycrystalline MgB 2. The spectrum below T c shows a composite structure with a narrow symmetric peak at an unshifted position and a broad asymmetric peak with a large diamagnetic shift. We identify that the broad peak originates from the vortex state whereas the narrow peak comes from crystallites in the normal state. This behavior can be understood as the NMR powder spectrum with significant anisotropy of an upper critical field H c2. From temperature dependence of the broad fraction, we find the anisotropy of H c2 is ∼4.7. We also determine the temperature-dependent penetration depth from the linewidth of the broad peak.

Vortex imaging in magnesium diboride withH⊥c

We have performed scanning tunneling spectroscopy imaging of vortices in ${\mathrm{MgB}}_{2}$ with both the tunneling current and the applied field perpendicular to the crystalline c axis. This revealed a well ordered vortex lattice with a relatively low anisotropy of $1.19\ifmmode\pm\else\textpm\fi{}0.04.$ This is significantly below the upper-critical-field anisotropy, but in good agreement with theoretical predictions for the penetration depth anisotropy, which at low fields is expected to be dominated by the $\ensuremath{\pi}$ band. The value of the anisotropy is smaller than estimated from small-angle neutron-scattering measurement.

Effects of two-band superconductivity on the flux-line lattice in magnesium diboride.

We present neutron scattering from the flux line lattice (FLL) in MgB2. Between 0.5 and 0.9 T the FLL undergoes a 30 degrees reorientation, and simultaneously the scattered intensity falls sharply consistent with the weaker superconducting pi band being suppressed with increasing field. We speculate that the pi and sigma bands favor different FLL orientations, and that the reorientation is driven by the suppression of the pi band. When the c axis of the crystal is rotated 45 degrees to the applied field the penetration depth anisotropy could be measured, and rises both as a function of applied field and temperature.

Vortex lattice anisotropy in the conducting plane of organic superconductors

Vortex structure in organic superconductors κ-(BEDT-TTF) 2Cu(NCS) 2 and κ-(BEDT-TTF) 2CuN(CN) 2Br has been studied by use of the decoration technique at magnetic fields up to 23 Oe directed perpendicular to the two-dimensional superconducting bc-plane. A quantitative analysis of high quality vortex lattice (VL) images reveals an anisotropy of the VL which can be interpreted as a penetration depth anisotropy.

Anisotropic penetration depth and optical sum rule violation in La 2−xSr xCuO 4

We calculate the doping dependence of the penetration depths and optical sum rule violation in La 2−xSr xCuO 4 within the model of hole superconductivity. In the clean limit the predicted in-plane sum rule violation is larger than the c-axis one, however in the presence of disorder the latter one becomes very substantially enhanced.

Pairing symmetry of Tl-2201 from measurements of temperature and magnetic field dependencies of the anisotropic penetration depth

We report a complete set of measurements of the anisotropic penetration depth of single crystals of Tl-2201 at varying doping levels (and corresponding critical temperatures). Using low field (below H c1 ) dc magnetization data, we solve the London equation for the anisotropic specimen geometry and obtain both λ ab and λ c as a function of temperature and magnetic field. Values of the penetration depth were calculated by a self-consistent condition, and we have found that both temperature and field dependences are linear for samples with 20 K≦ T c≦70 K. These dependencies give strong evidence for d-wave pairing with nodes in the superconducting gap, a not-surprising finding for this simplest of HTSC tetragonal cuprates. The data for optimally doped crystals with T c=90 K show, however, a quadratic temperature dependence. This latter feature is difficult to reconcile with known theories of s- or d-wave pairing, and this issue poses a central question yet to be answered.

In-plane and out-of-plane superfluid density of the layered organic superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br

The anisotropic magnetic penetration depth λ b (t) and λ ac (t), where t = T/T c , in the layered organic superconductor κ-(BEDT-TTF) 2 Cu[N(CN) 2 ]Br (abbreviated as κ-ET-Br) are obtained from AC susceptibility data. We find λ b (0) = 133 μm, consistent with earlier results and Δλ b (t) = λ b (t) - λ b (0) t 2 , which is new. Also, assuming λ ac (0) 1 μm, we obtain Δλ ac (t) oc t. The observed power laws are consistent with the ones expected in d-wave superconductivity.