  We have studied the magnetization process of the new insulating ferromagnetic
semiconductor (Al,Fe)Sb by means of x-ray magnetic circular dichroism. For an
optimally doped sample with 10% Fe, a magnetization was found to rapidly
increase at low magnetic fields and to saturate at high magnetic fields at room
temperature, well above the Curie temperature of 40 K. We attribute this
behavior to the existence of nanoscale Fe-rich ferromagnetic domains acting as
superparamagnets. By fitting the magnetization curves using the Langevin
function representing superparamagnetism plus the paramagnetic linear function,
we estimated the average magnetic moment of the nanoscale ferromagnetic domain
to be 300-400 $\mu_{B}$, and the fraction of Fe atoms participating in the
nano-scale ferromagnetism to be $\sim$50%. Such behavior was also reported for
(In,Fe)As:Be and Ge:Fe, and seems to be a universal characteristic of the
Fe-doped ferromagnetic semiconductors. Further Fe doping up to 14% led to the
weakening of the ferromagnetism probably because antiferromagnetic
superexchange interaction between nearest-neighbor Fe-Fe pairs becomes
dominant.
