Sheet-current distribution in a dc SQUID washer probed by vortices

Abstract

We present a novel method, based on vortex imaging by low-temperature scanning electron microscopy (LTSEM), to directly image the sheet-current distribution in YBa2Cu3O7 dc SQUID washers. We show that the LTSEM vortex signals are simply related to the scalar stream function describing the vortex-free circulating sheet-current distribution J . Unlike previous inversion methods that infer the current distribution from the measured magnetic field, our method uses pinned vortices as local detectors for J . Our experimental results are in very good agreement with numerical calculations of J .PACS numbers: 68.37. Hk, 74.25.Op, 85.25.Dq Spatially resolved techniques can provide important insight into current flow, arrangement of vortices, flux pinning, and noise in superconductors and their mutual interactions. So far there has been only one method of imaging the current distribution in superconductors: The magnetic field distribution on top of a superconducting thin film is measured, e.g. by magneto-optics, from which the current distribution can then be calculated by inverting the Biot-Savart law [1].In this paper we present a novel method to directly image the sheet-current distribution in a YBa 2 Cu 3 O 7 thin film. We use low-temperature scanning electron microscopy (LTSEM) [2,3,4,5] to image vortices in dc SQUID washers [6,7]. Most techniques for vortex imaging, such as Lorentz microscopy [8], scanning SQUID microscopy [9,10], scanning Hall microscopy [11] or magneto-optics[12] rely on the detection of the stray magnetic field produced in close proximity to a vortex. In contrast, vortex imaging by LTSEM is different from those techniques, as it is based on the electron-beaminduced apparent displacement of a vortex, pinned at position r in the (x, y)-plane of a SQUID washer, which is detected as a change of stray magnetic flux Φ(r) coupled to the SQUID. Hence, the contrast of the LTSEM vortex signals directly senses ∇Φ(r). Recently, Clem and Brandt [13] have shown that Φ(r) is proportional to the scalar stream function G(r) that describes the circulating sheet-current density J(r) flowing in the vortex-free case at position r in the SQUID washer. In this paper we show that this relationship allows us to use the vortices as local detectors for J(r): At each position a vortex has been imaged, we can directly determine J(r) without complicated calculations.In our experiments, we investigated several dc SQUID washers [see Fig. 1(a)] fabricated from epitaxially grown d=80 nm thick c-axis oriented YBa 2 Cu 3 O 7 (YBCO) thin * Electronic address: koelle@uni-tuebingen.de films. We will present an analysis of LTSEM data obtained from one representative device with washer size 120 µm × 305 µm, with a 100 µm long and 4 µm wide slit. The 1 µm wide Josephson junctions are formed by a 24 • symmetric grain boundary in the underlying SrTiO 3 substrate. For imaging by LTSEM, the YBCO SQUIDs are mounted on a magnetically shielded, liquid nitrogen cooled cryostage of an SEM [14] and read out by a standard flux-locked loop (FLL) w...

Electron-beam-induced shift in the apparent position of a pinned vortex in a thin superconducting film

“…24, where the authors estimated that R Ϸ ⌳ 0 Ϸ 0.5 m. Figure 6 strongly resembles the vortex images displayed in Ref. 24.…”

“…29, Doenitz et al 24 estimated that R = 0.53 m at E 0 = 10 keV. Assuming that this rangeenergy relation holds for all energies, one finds the results given in Table I would provide a stringent test of the four models.…”

“…Assume that the incident electron energy is E 0 = 10 keV and the beam current is I b = 7 nA, as in Ref. 24, and that the fraction of the incident electron energy that is converted into heat 29 is f = 0.6, such that P 0 =42 W. With a SrTiO 3 thermal conductivity =18 W/Km at 77 K ͑Ref. 33͒ and an electron range R = 0.53 m ͑Ref.…”

“…24, in which a well-collimated electron beam of energy E 0 = 10 keV, beam current I b = 7 nA, and radius a Ϸ 5 nm was normally incident upon an epitaxial c-axis-oriented superconducting YBa 2 Cu 3 O 7 ͑YBCO͒ thin film of thickness d = 80 nm on a thick SrTiO 3 substrate at 77 K. The range R-i.e., the maximum distance from the point of incidence the electron travels until it thermalizes-was estimated to be R Ϸ 0.53 m. Each incident electron undergoes numerous elastic and inelastic scattering processes as it loses energy along its diffusion path s, and some of this energy emerges from the top surface of the sample as back scattered electrons, secondary electrons, x rays, and electromagnetic radiation. 29 The thermal power delivered to the sample is P 0 = fI b E 0 / e, where the fraction of energy that is ultimately converted into heat is of the order of f = 40% -80%.…”

Response of thin-film SQUIDs to applied fields and vortex fields: Linear SQUIDs

“…Roughly speaking, when Λ is small, I c is most strongly dependent upon the vortex position when the vortex is close to the edges of the film, but when Λ is large, I c is equally sensitive to the vortex position wherever the vortex is. Recent experiments 49 have used the relationship Φ v = φ 0 G d to determine the vortex-free sheet-current density J d (x, y) from vortex images obtained via low-temperature scanning electron microscopy. 6,9 The experimental data obtained in magnetic fields up to 40 µT are in excellent agreement with numerical calculations of J d (x, y), confirming the validity of the above relationship, even in the presence of many (up to 200) vortices in the SQUID washer.…”