Thickness-modulated tungsten-carbon superconducting nanostructures grown by focused ion beam induced deposition for vortex pinning up to high magnetic fields

Abstract

We report efficient vortex pinning in thickness-modulated tungsten-carbon-based (W-C) nanostructures grown by focused ion beam induced deposition (FIBID). By using FIBID, W-C superconducting films have been created with thickness modulation properties exhibiting periodicity from 60 to 140 nm, leading to a strong pinning potential for the vortex lattice. This produces local minima in the resistivity up to high magnetic fields (2.2 T) in a broad temperature range due to commensurability effects between the pinning potential and the vortex lattice. The results show that the combination of single-step FIBID fabrication of superconducting nanostructures with built-in artificial pinning landscapes and the small intrinsic random pinning potential of this material produces strong periodic pinning potentials, maximizing the opportunities for the investigation of fundamental aspects in vortex science under changing external stimuli (e.g., temperature, magnetic field, electrical current).

Keywords: focused ion beam induced deposition; magnetotransport; superconductivity; vortex lattice.

Figure 1

(a) Scheme of the experiment performed to measure the electrical resistance under perpendicular magnetic field. Due to the Lorentz force, the vortex lattice tends to move transversally to the low-thickness zones, which act as vortex pinning lines. (b) SEM false-colored micrograph showing the Ti pads (green), the buried contacts of Pt (red), the Pt connection to the Ti pads (brown) and the W–C deposit (blue) with the pinning grooves along the x direction.

Figure 2

Cross-sectional SEM micrographs of a sample with 60 nm pitch (a), a sample with 100 nm pitch (b) and the flat sample (c). The y and z axes correspond to the short sides of the film and the thickness direction, respectively.

Figure 3

Scanning transmission electron microscopy (STEM) study of the sample with pitch 100 nm. (a) STEM-HAADF image of the sample, including a red arrow signaling the full linear beam scan performed for the compositional analysis shown in (c). (b) Compositional data obtained from EDX spectroscopy measurements performed at the red cross and red square shown in (a) after analyzing all the observed peaks. (c) STEM-HAADF intensity along the red arrow shown in (a). The intensity modulation is related to the slight changes in composition caused by the thickness modulation. The overall slope is a result of the small thickness variation of the lamella where the STEM experiment is carried out. (d) Modulation in the W composition along the red arrow line extracted from the EDX intensity at energy 1774 eV, which corresponds to the W M-edge peak.

Figure 4

(a) Magnetoresistance curves of the sample with 100 nm pitch at 1.9 K (0.43T_c), 2.2 K (0.49T_c), 2.5 K (0.56T_c), 3 K (0.67T_c), 3.5 K (0.78T_c), 3.8 K (0.85T_c), 4 K (0.9T_c), and 4.2 K (0.94T_c). The measurements were performed with a cureent of 20 μA. Vertical dashed lines in red and blue color indicate, respectively, the theoretical magnetic fields in which Equation 2 (mode A) and Equation 2 (mode B) are satisfied for the sample with 100 nm pitch. (b) Sketch with selected pinning modes.

Figure 5

Magnetoresistance curves at 2.5 K of the flat sample, and samples with 60, 80, 100, 120 and 140 nm pitch. The measurements have been carried out using 20 µA, which corresponds to the following current densities: 8.33 kA/cm² (flat), 10.53 kA/cm² (60 nm), 8.70 kA/cm² (80 nm), 8.70 kA/cm² (100 nm), 9.52 kA/cm² (120 nm) and 8.33 kA/cm² (140 nm).

Figure 6

Dependence of the magnetic fields where local minima in the resistance are experimentally observed, as a function of n²/pitch². The theoretical (linear) dependence expressed by Equation 2 is also displayed for modes A (red) and B (blue).

Figure 7

Comparison of the critical current density and the resistance versus magnetic field of the sample with pitch 100 nm at 1.9 K. The matching field corresponding to mode A, n = 4 is not observed in the resistance measurement at 1.9 K due to the low value of the resistance but becomes observable at 3 K as displayed in Figure 4a.

Figure 8

Magnetoresistance measurements for the sample with pitch 60 nm and values of T₀ obtained from the fit to Equation 4 of the descending part of the local minima. The two sets of black lines indicate regions of the fits, given in greater detail below the upper graph.