On the coupling of magnetic moments to superconducting quantum interference devices

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,ê μ ) vs.~position r and orientation ê μ of the dipole anywhere in space from the magnetic field B( 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 SQUID 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 λ L and show that for thin (d << a) and narrow (w < a) loops the introduction of an effective loop size a eff 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,λ L) 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 λ L > 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.