  The question whether the Anderson-Mott localisation enhances or reduces
magnetic correlations is central to the physics of magnetic alloys.
Particularly intriguing is the case of (Ga,Mn)As and related magnetic
semiconductors, for which diverging theoretical scenarios have been proposed.
Here, by direct magnetisation measurements we demonstrate how magnetism evolves
when the density of carriers mediating the spin-spin coupling is diminished by
the gate electric field in metal/insulator/semiconductor structures of
(Ga,Mn)As. Our findings show that the channel depletion results in a monotonic
decrease of the Curie temperature, with no evidence for the maximum expected
within the impurity-band models. We find that the transition from the
ferromagnetic to the paramagnetic state proceeds via the emergence of a
superparamagnetic-like spin arrangement. This implies that carrier localisation
leads to a phase separation into ferromagnetic and nonmagnetic regions, which
we attribute to critical fluctuations in the local density of states, specific
to the Anderson-Mott quantum transition.
