Properties of inductance and magnetic penetration depth in (103)-oriented ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ thin films

Properties of inductance and magnetic penetration depth in (103)-oriented ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ thin films

J. Johansson, K. Cedergren, T. Bauch, and F. Lombardi

Phys. Rev. B 79, 214513 – Published 12 June 2009

Abstract

We present a study of the anisotropy of the inductance in (103) ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ (YBCO) films. YBCO superconducting quantum interference devices (SQUIDs) were fabricated by the biepitaxial technique. SQUIDs with (001)- and (103)-oriented YBCO electrodes characterized by different grain-boundary angles were realized on the same chip. Two extrainjection lines were attached to the (103) YBCO electrode. These devices, when operated in current injection mode, allow us to measure the inductance of the (103) YBCO electrode. We have found that the inductance $L$ of the (103) YBCO can differ by a factor of 20 in the two extreme cases: $L$ determined by current transport parallel to the $a b$ planes and $L$ dominated by the transport in the $c$ -axis direction. The full in-plane angular dependence of the inductance has been obtained by considering geometrically identical SQUIDs oriented with different angles with respect to the [100] direction of the (103) film. From these measurements, we have determined the London penetration depths in the $a b$ direction $λ_{a b}$ and the $c$ direction $λ_{c}$ and their temperature dependence.

Received 30 October 2008

DOI:https://doi.org/10.1103/PhysRevB.79.214513

Authors & Affiliations

J. Johansson¹, K. Cedergren^1,2, T. Bauch¹, and F. Lombardi¹

¹Department of Microtechnology and Nanoscience, Quantum Device Physics Laboratory, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
²Dipartimento Scienze Fisiche, CNR-INFM Coherentia, Università di Napoli, 81031 Aversa (CE), Italy

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Vol. 79, Iss. 21 — 1 June 2009

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Figure 1
(Color online) (a) Sketch of YBCO GB structure with different interface orientation. In the (001) YBCO electrode, which is grown on the ${CeO}_{2}$ seed layer, the CuO planes are parallel to the (110) substrate surface with a $45 °$ rotation around the $c$ axis. In the (103) electrode, which is grown on the (110) STO substrate, the CuO planes are slanted by $45 °$ with respect to the substrate surface. The big arrows indicate the current path in the (103) electrode parallel to the grain boundary. (b) Normalized current components in the CuO planes $i_{a b}^{103}$ and in the $c$ -axis direction $i_{c}^{103}$ for the charge transport parallel to the GB in the (103) electrode as a function of angle $θ$ .Reuse & Permissions
Figure 2
(Color online) (a) Optical micrograph of a SQUID with rotation angle $θ = 30 °$ . The grain boundary is indicated by a dashed line. The lower part is (103)-oriented YBCO grown on (110) STO and the upper part is (001) oriented YBCO grown on a seed layer of CeO. The distance between the JJs is $l = 24 μ m$ and the width of the (103) electrode is $w = 11 μ m$ . (b) Schematic sketch of the measurement setup. The JJs are indicated by the crosses. (c) Schematic sketch of the orientation of the CuO planes ( $a b$ planes) in the (103) and (001) electrodes for this SQUID geometry. In the (001) electrode, the CuO planes are parallel to the substrate surface; whereas in the (103) electrode the CuO planes are slanted by $45 °$ with respect to the substrate surface. For $θ = 0 °$ , the control current flows in the $a b$ planes, while for $θ = 90 °$ it has equal components in $c$ and $a$ directions of the (103) electrode. Depending on the current path, the kinetic inductance of the (103) electrode changes.Reuse & Permissions
Figure 3
Magnetic diffraction pattern as a function of control current $I_{ctrl}$ for two SQUIDs with rotation angles $θ = 40 °$ and $90 °$ at $T = 280 mK$ . The inductance of the bottom electrode can be extracted from the modulation period $Δ I_{ctrl}$ .Reuse & Permissions
Figure 4
(Color online) Measured inductance of the lower (103) electrode of the SQUIDs $L_{103} = L_{geo} + L_{k}$ as a function of the angle $θ$ at $T = 280 mK$ (closed circles). The measurements were done by operating the SQUIDs in current injection mode. For $θ = 0 °$ , $L_{103} = 13 p H$ ; whereas for $θ = 90 °$ the inductance increases by a factor of $20 - 265 p H$ . The solid line is a fit of the inductance with respect to the angle $θ$ which is obtained by numerically calculating the current distribution in the (103) electrode. From the fit, one obtains $λ_{a b} = 270 nm$ and $λ_{c} = 4.4 μ m$ . The dashed line is the inductance calculated from the analytical expression [Eq. (2)]. The inset shows the extracted values of the effective penetration depth $λ_{eff}$ from the experimental data of $L_{103}$ as a function of angle $θ$ for $θ \geq 40 °$ (solid circles). The solid line is the analytical expression of the effective penetration depth [Eq. (1)].Reuse & Permissions
Figure 5
Normalized temperature dependence of $λ_{eff} (T) / λ_{eff} (T = 0)$ for $θ = 0 °$ , $40 °$ , and $50 °$ . The data (open symbols) follow the Gorter-Casimir two fluid dependence (solid line) with exponent $n_{c}$ equal to $2.15 \pm 0.5$ for $λ_{c}$ ( $θ = 40 °$ and $50 °$ ) and $n_{a b} = 1.5 \pm 0.2$ for $λ_{a b} (θ = 0 °)$ (see text for details). (Inset) ${log}_{10} {1 - {[λ_{eff} (0) / λ_{eff} (T)]}^{2}}$ is plotted versus ${log}_{10} (T / T_{c})$ for $θ = 0 °$ , $40 °$ , and $50 °$ . From the slope of the curves, the exponents $n_{a b}$ and $n_{c}$ are determined.Reuse & Permissions
Figure 6
Circuit diagram of a current-biased SQUID operated in the current injection mode (see text for details).Reuse & Permissions

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Properties of inductance and magnetic penetration depth in (103)-oriented ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ thin films

J. Johansson, K. Cedergren, T. Bauch, and F. Lombardi

Phys. Rev. B 79, 214513 – Published 12 June 2009

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Properties of inductance and magnetic penetration depth in (103)-oriented YBa2Cu3O7−δ thin films

J. Johansson, K. Cedergren, T. Bauch, and F. Lombardi

Phys. Rev. B 79, 214513 – Published 12 June 2009

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Properties of inductance and magnetic penetration depth in (103)-oriented ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ thin films