A nonconductive ferromagnetic core is inserted into the pickup coil of a superconducting flux transformer which is matched to a 19 MHz rf‐superconducting quantum interference device (SQUID). We demonstrate that the flux sensitivity of the SQUID is enhanced by a factor of 2–2.7 with respect to a comparable air core flux transformer for signals up to 80 kHz. The equivalent flux noise of 2×10−3&Fgr;0/&sqrt;Hz is of the same magnitude as for a conventional transformer and associated with external fluctuations from vibrations and from the superconducting shields. We take as a source a very thin spin sheet like that which is formed by spin‐polarized electrons excited in thin semiconducting epitaxial layers in a photomagnetization experiment. Under experimental conditions (changes of the irradiated area, absorption depth, beam deflections) one expects distinct distributions of spins in the sheet and corresponding variations of the flux depicted by the flux transformer. To detect the magnetic moment of a certain number (≳1010) of spins the proportionality between the detected flux &Fgr; and the excited total magnetic momentmof the spins is checked. We compare various configurations of spin sheets of distinct size and locations beginning with an air core flux transformer. The flux threading the pickup loop is then more efficiently coupled by employing a ferromagnetic shell‐shaped core with an axial hole (for the entrance of the light beam in photomagnetization studies). Thus flux line patterns are simulated for various sizes of cores, different permeabilities, and different air slits (where the sample is located). Due to additional degrees of freedom of design parameters a simultaneous increase of sensitivity is achieved together with a response &Fgr;∝m. Simulations and measurements are compared. The ultimate resolution of the magnetic moment is &Dgr;m=10−13A m2/&sqrt;Hz.