Authors: Linek, M Wyszynski, B Müller, D Korinski, M V Milošević, R Kleiner
and D Koelle
Supercond. Sci. Technol. 37 (2024) 025010
Abstract: We investigate the coupling factor φµ that quantifies the magnetic flux Φ per magnetic moment µ of a point-like magnetic dipole that couples to a superconducting quantum interference device (SQUID). Representing the dipole by a tiny current-carrying (Amperian) loop, the reciprocity of mutual inductances of SQUID and Amperian loop provides an elegant way of calculating ϕμ(r,e^μ) vs. position r and orientation e^μ of the dipole anywhere in space from the magnetic field BJ(r) produced by a supercurrent circulating in the SQUID loop. We use numerical simulations based on London and Ginzburg–Landau theory to calculate φµ from the supercurrent density distributions in various superconducting loop geometries. We treat the far-field regime (r≳a= inner size of the SQUID loop) with the dipole placed on (oriented along) the symmetry axis of circular or square shaped loops. We compare expressions for φµ from simple filamentary loop models with simulation results for loops with finite width w (outer size A > a), thickness d and London penetration depth λL and show that for thin (d≪a) and narrow (w < a) loops the introduction of an effective loop size aeff in the filamentary loop-model expressions results in good agreement with simulations. For a dipole placed right in the center of the loop, simulations provide an expression ϕμ(a,A,d,λL) that covers a wide parameter range. In the near-field regime (dipole centered at small distance z above one SQUID arm) only coupling to a single strip representing the SQUID arm has to be considered. For this case, we compare simulations with an analytical expression derived for a homogeneous current density distribution, which yields excellent agreement for λL>w,d. Moreover, we analyze the improvement of φµ provided by the introduction of a narrow constriction in the SQUID arm below the magnetic dipole.
