s-Wave Symmetry Along the c-Axis and s+d In-plane Superconductivity in Bulk YBa2Cu4O8

Abstract

To clarify the order parameter symmetry of cuprates, the magnetic penetration depth λ was measured along the crystallographic directions a, b, and c in single crystals of YBa 2 Cu 4 O 8 via muon spin rotation. This method is direct, bulk sensitive, and unambiguous. The temperature dependences of λ −2 a and λ −2 b exhibit an inflection point at low temperatures as is typical for two-gap superconductivity (TGS) with s + d-wave character in the planes. Perpendicular to the planes a pure s-wave gap is observed thereby highlighting the important role of c-axis effects. We conclude that these are generic and universal features in the bulk of cuprates. Recently, new muon spin rotation (μSR) investigations of single crystal La 1.83 Sr 0.17 CuO 4 detected an inflection point in the temperature dependence of the inverse-squared in-plane magnetic penetration depth λ −2 ab , which is a direct consequence of two superconducting gaps with largely different zero temperature gap values [14]. Since it is unclear whether these observations are a material specific property or generic and intrinsic to HTS, the previous μSR studies were extended to single crystal YBa 2 Cu 4 O 8 and were performed by applying a magnetic field along the crystallographic directions a, b, and c. Thereby we obtain the three principle components of the second moments of the local magnetic field distribution P (B) in the mixed state, which are related to the superfluid density, and reflect directly the corresponding penetration depths λ a , λ b , and λ c . While λ −2 a and λ −2 b vary almost linearly with temperature for 20 < T < 50 K, as is expected for a d-wave order parameter, the c-axis response (λ −2 c ) saturates below 30 K, as expected for a s-wave order parameter. In addition, λ −2 a and PACS

Concerning the superconducting gap symmetry in YBa2Cu3O7 − δ, YBa2Cu4O8, and La2 −xSrxCuO4determined from muon spin rotation in mixed states of crystals and powders

“…Indeed, the sample preparation described all but guarantees a sample filled with dislocations and cracks; flux penetration into the cracks and the formation of Josephson vortices could mimic pinning effects of the mixed state even for H < H c1 , easily explaining the anomalous magnetization results. Such a sample is obviously not a random sintered powder [49,52], and measurements of diamagnetic screening at surfaces are not equivalent to the bulk probe provided by  + SR [40]. Such presumed equivalences in sample morphologies as well as measured physical properties serve only to obviate the approach of [40] to meaningful data comparison.…”

“…Approximating the lineshape of the mixed state by fitting multiple Gaussians to μ + SR time series data, as was done for the crystal data [37,40,41], allows one to extract a second-moment parameter σ 2 associated with the formation and characteristics of the fluxon lattice. We recognize the potential for systematic improvement in determination of the second moment of P(B) by such techniques as Fourier transformation or, with improved signal-to-noise, by maximum entropy methodology [46].…”

“…In the data refinement method of [37] and [40] individual a-, b-and c-axis components of σ(T,H) were then mathematically extracted according to the equations,…”

“…where i, j, and k represent a, b, or c. For both YBa 2 Cu 3 O 7-δ [37] and YBa 2 Cu 4 O 8 (nonoptimal at zero applied pressure) [40] the results for σ a (T) and σ b (T) show an inflection as a function of T in the range 10-15 K, while σ c (T) exhibits no such feature (discussed in section 4.2.). To prove that the lowtemperature inflection is unrelated to the superconducting hole condensate gap function, we construct the root-mean-square average of the three planar  ij components measured for an oriented crystal sample [47],…”

“…To understand the implication, we decompose the pinning factor in equation (1) The temperature dependent c-axis components for both YBa 2 Cu 3 O 7-δ [37] and YBa 2 Cu 4 O 8 [40] are given in figure 7; the curves shown are fits of the generalized two-fluid model [equation (12)], yielding α = 3.30 (17) and σ c (T→0) = 0.1845 (22) [40]). Since the YBa 2 Cu 4 O 8 sample is nonoptimal, the significance of the actual value of α is unclear.…”