Highly transparent superconducting-normal junctions induced by local fields of magnetic domains in a homogeneous superconductor

Using the highly inhomogeneous fields of a magnetic substrate, tunable junctions between superconducting and normal-state regions were created inside a thin-film superconductor. The investigation of these junctions, created in the same material, gave evidence for the occurrence of Andreev reflection, indicating the high transparency of interfaces between superconducting and normal-state regions. For the realization of this study, a ferromagnet with magnetic-stripe domains was used as a substrate, on top of which a superconducting transport bridge was prepared perpendicular to the underlying domains. The particular choice of materials allowed to restrict the nucleation of superconductivity to regions above either reverse domains or domain walls. Moreover, due to the specific design of the sample, transport currents in the superconductor passed through a sequence of normal and superconducting regions.

Figure 1

(Color online) (a) Photograph of the as-grown barium hexaferrite single crystal. (b) Sketch of the crystal after slicing under a cut angle $\phi$ with respect to its $c$ axis. (c) Magnetic-force microscopical image of the magnetic domains at the cut surface of a slice of the ${\text{BaFe}}_{12}{\text{O}}_{19}$ single crystal. (d) Sketch of a transport bridge processed perpendicular to the $c$ axis on the cut surface of a slice of the crystal.

Figure 2

(Color online) The magnetization $M$ of a slice of the ${\text{BaFe}}_{12}{\text{O}}_{19}$ single crystal at 5 K as a function of the external magnetic field ${\vec{H}}_{\text{ext}}$ normal to the cut surface. The insert shows a magnification of the curve for $\left|H_{\text{ext}}\right|\le 150\text{mT}$.

Figure 3

(Color online) The increase in the width $w$ of a parallel domain (the bright areas in the inserts) in the ferromagnetic substrate as a function of $H_{\text{ext}}$. The shown data is the average of the results obtained for an increasing and a decreasing external magnetic field. The inserts show two examples of the position of the same domain wall at 0 and 150 mT, respectively.

Figure 4

(Color online) (a) AFM images of two transport bridges with their underlying magnetic domains (MFM images). The MFM images are vertically extended to illustrate the domains. Arrows indicate the $z$ component $M_{\text{z}}$ of the magnetization of the template. (b) The normalized resistance of the two bridges, measured at 340 mK with a bias current of $10\mu \text{A}$ as a function of $H_{\text{ext}}$. The insert shows the superconducting transition of a reference Al film on a Si substrate as a function of temperature (critical current density $j_{\text{c}}\sim 1.2\times {10}^8\text{A}/{\text{m}}^2$ at 340 mK).

Figure 5

(Color online) (a) The transport bridge (optical image shown in three dimensions) with its underlying magnetic domains (MFM image). The MFM image is vertically extended to illustrate the domains. Arrows indicate the $z$ component $M_{\text{z}}$ of the magnetization of the template. (b) A detailed MFM image of a typical domain wall in the substrate.

Figure 6

(Color online) The normalized resistance of the transport bridge of Fig. 5a at 340 mK, as a function of bias current $I$ and external field $H_{\text{ext}}$ $\left(R_{\text{N}}=3.62\Omega \right)$. Regions where RDS and DWS occur are indicated. The insert shows the resistive transitions $\left(I=10\mu \text{A}\right)$ from the normal state to the states of DWS (blue curve with diamonds) and RDS (red curve with circles). The points corresponding to $T=340\text{mK}$ are indicated in the main panel.

Figure 7

(Color online) Differential conductance spectra of the transport bridge of Fig. 5a at 53 mT in the state of RDS. Arrows mark two minima whose positions can be traced. In the left panel, curves are shifted for clarity and the vertical scale corresponds to the top curve.

Figure 8

The positions of characteristic minima in the conductance spectra of Fig. 7, 9 (markers) are compared with $\Delta \left(T\right)$ (solid lines). For clarity, the results obtained at 0 mT are shifted by $-0.2$.

Figure 9

(Color online) Differential conductance spectra of the transport bridge of Fig. 5a at 0 mT (DWS). Arrows mark two minima whose positions can be traced. In the left panel, curves are shifted for clarity and the vertical scale corresponds to the top curve.