  We explore the bistability effect in a dimensionally scaled semiconductor
nanostruncture consisting of a diluted magnetic semiconductor quantum dot (QD)
and a reservoir of itinerant holes separated by a barrier. The bistability
stems from the magnetic phase transition in the QD mediated by the changes in
the hole population. Our calculation shows that when properly designed, the
thermodynamic equilibrium of the scaled structure can be achieved at two
different configurations; i.e., the one with the QD in a ferromagnetic state
with a sufficient number of holes and the other with the depopulated QD in a
paramagnetic state. Subsequently, the parameter window suitable for this
bistability formation is discussed along with the the conditions for the
maximum robustness/non-volatility. To examine the issue of scaling, an
estimation of the bistabiity lifetime is made by considering the thermal
fluctuation in the QD hole population via the spontaneous transitions. A
numerical evaluation is carried out for a typical carrier-mediated magnetic
semiconductor (e.g., GaMnAs) as well as for a hypothetical case of high Curie
temperature for potential room temperature operation.
