Penetration depth measurement in high quality YBa2Cu3O7−x thin films

The parallel plate resonator method has been used for measuring high quality YBa2Cu3O7−x (YBCO) thin films, which have low temperature residual losses comparable to those previously obtained in single crystals. The surface resistance and the real part of the conductivity show a non-monotonic behaviour with a broad peak around 45 K. The penetration depth and the real part of the conductivity vary linearly at low temperatures. The lowest penetration depth linear fitting has a slope value of 2.2 Å/K to 2.5 Å/K up to 20 K which is lower than previous measurements on YBCO single crystals. An interpretation of this smaller slope in terms of the generally accepted d-wave order parameter symmetry presents difficulties. PACS. 74.25.Nf Response to electromagnetic fields (nuclear magnetic resonance, surface impedance, etc.) – 74.72.Bk Y-based cuprates – 74.76.Bz High-Tc films Determining the symmetry of the superconducting order parameter is one of the main issues in understanding the mechanism that causes superconductivity in the high Tc cuprates. For a d-wave superconductor the energy gap vanishes along four lines in the kz direction located at the position |kx| = |ky | on a cylindrical Fermi surface . These node lines lead to a change in the penetration depth as a function of temperature that varies linearly with temperature, i.e. λ(T ) ∝ T [1,2]. In contrast, for an s-wave superconductor one has an exponential monotonic behaviour of the superconducting properties [3,4]. In the case of YBCO single crystals, the linear variation of the penetration depth at low temperatures is accompanied by a non-monotonic variation of the surface resistance Rs(T ) and of the real part of the conductivity σ1(T ). By introducing Zn impurities into a YBa2Cu3O7−x (YBCO) single crystal, Bonnet et al. [6] were able to show the suppression of that nonmonotonic behavior and did get a change of ∆λ(T ) from a linear to a quadratic temperature dependence, as predicted by d-wave theory. More generally, the microwave surface impedance Zs = Rs + iωμ0λ yields important information regarding the superconducting carrier density ns(T ) and the quasiparticles scattering rate 1/τ(T ), whose low temperature limit can give us precious indication about the quality of the high Tc material. In low quality films, τ(T ) reaches very fast its maximum value close to Tc [7]. a e-mail: [email protected] There are two contributions to losses in YBCO thin films at microwave frequencies regime, one which has an intrinsic origin and the other one an extrinsic one. One of the long standing problems is the residual surface resistance [5] which has presumably an extrinsic origin such as twins, grain boundaries and other defects. These extrinsic losses can smear out the non-monotonic behaviour of Rs(T ) in YBCO single crystals [6], and they can influence in the same manner YBCO thin film properties. It was shown that this non-monotonic behavior manifests itself as a broad peak in Rs(T ) around 40 K which is more conspicuous in σ1(T ) [7]. This broad peak can be an indication for a low defect density sample, where the scattering time τ(T ) attains a higher value at low temperatures. It can be understood in the framework of the two fluid model by using the Drude formula σ1 ∝ nqpτ in the limit ωτ 1, where nqp is the quasiparticles density. A non monotonic behaviour of σ1(T ) was reported by Ma et al. [8] in YBCO thin films, but it was accompanied by ∆λ(T ) ∝ T 2 in the low temperature range. On the other hand, Hardy et al. reported a linear behaviour ∆λ(T )of for a high quality YBCO single crystal [2], showing the non-monotonic behaviour of σ1(T ). In our experiment we measured high quality YBCO thin films on LaAlO3 substrates. These films where grown by pulsed laser deposition at 785 ◦C and 300 mtorr of molecular oxygen [9]. The thickness of these films is about 3000 Å, their Tc is ∼ 91.5 K and a transition width of 0.3 K is obtained by four point resistive measurement. The best pair of such films used in our parallel plate 160 The European Physical Journal B resonator gave a small residual loss of about 50 μΩ at 10 GHz. These residual losses are intermediate between two values reported for YBCO single crystals (200 μΩ [10], 10 μΩ [11] at 10 GHz). They are approximately lower by a factor 2 than the residual losses reported by Ma et al. [8] for their lower Rres post annealed YBCO thin films. The parallel plate resonator technique [12] (PPR) has two major advantages in comparison to other resonant cavities. The surface resistance can be calculated directly from the measured Q-value without any corrections. It is a highly sensitive method for measuring small changes in the penetration depth, although it does not lend its absolute value. In our measurements we used two 1× 1 cm YBCO thin films with a Teflon spacer 25 μm thick in between them. We rely on a weak coupling transmission mode signal. The PPR was measured using the HP-8510C vector network analyzer. The change of the penetration depth and of the real part of the conductivity can be calculated from the phase velocity of the electromagnetic field in the PPR and is given by [13,14]