Abstract
A Josephson junction can be subjected to a local, strongly inhomogeneous magnetic field in various experimental situations. Here this problem is analyzed analytically and numerically. A modified sine-Gordon type equation in the presence of time-dependent local field is derived and solved numerically in static and dynamic cases. Two specific examples of local fields are considered: induced either by an Abrikosov vortex, or by a tip of a magnetic force microscope (MFM). It is demonstrated that time-dependent local field can induce a dynamic flux-flow state in the junction with shuttling, or unidirectional ratchet-like Josephson vortex motion. This provides a mechanism of detection and manipulation of Josephson vortices by an oscillating MFM tip. In a static case local field leads to a distortion of the critical current versus magnetic field, $I_c(H)$, modulation pattern. The distortion is sensitive to both the shape and the amplitude of the local field. Therefore, the $I_c(H)$ pattern carries information about the local field distribution within the junction. This opens a possibility for employing a single Josephson junction as a scanning probe sensor with spatial resolution not limited by its geometrical size, thus obviating a known problem of a trade-off between field sensitivity and spatial resolution of a sensor.
Highlights
Properties of Josephson junctions (JJs) with spatially uniform parameters in a homogenous magnetic field are well studied [1]
In many experimental situations, JJs are subjected to a local, strongly inhomogeneous magnetic field. It can originate from a self-induced flux in JJs with a sign-reversal order parameter [10,11,12]; appear in JJs containing ferromagnetic interlayers with spatially inhomogeneous thicknesses [13,14,15,16], nanoparticles, or domain walls [17,18,19,20,21,22]; in JJs with a local current injection [23,24]; and can be induced by a nearby Abrikosov vortex [25,26,27,28], by a sharp tip of a magnetic force microscope (MFM) [29,30], etc
Such a situation has been considered previously, often this has been done without proper substantiation
Summary
Properties of Josephson junctions (JJs) with spatially uniform parameters in a homogenous magnetic field are well studied [1]. The Ic(H ) pattern carries detailed information about the local field and it should be possible to extract field distribution within the junction using proper mathematical treatment This would open the possibility for making a scanning probe sensor based on a single planar JJ with spatial resolution not limited by its geometrical size, obviating the trade-off problem between sensitivity and resolution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
