  By measuring the critical current versus the applied magnetic field
$I_c(\Phi)$ of an Al superconducting loop enclosing a soft Permalloy magnetic
dot, we demonstrate that it is feasible to design a linear magnetic flux
amplifier for applications in superconducting quantum interference devices. The
selected dimensions of a single-domain Permalloy dot provide that the
preferential orientation of the magnetization is rotated from the perpendicular
direction. By increasing an applied magnetic field, the magnetization of the
dot coherently rotates towards the out-of-plane direction, thus providing a
flux gain and an enhancement of the sensitivity. As a result of a pronounced
shape anisotropy, the flux gain generated by the dot can be tuned by adjusting
the dimensions of the dot.
