  We show that a Spin Field Effect Transistor, realized with a semiconductor
quantum wire channel sandwiched between half-metallic ferromagnetic contacts,
can have Fano resonances in the transmission spectrum. These resonances appear
because the ferromagnets are half-metallic, so that the Fermi level can be
placed above the majority but below the minority spin band. In that case, the
majority spins will be propagating, but the minority spins will be evanescent.
At low temperatures, the Fano resonances can be exploited to implement a
digital binary switch that can be turned on or off with a very small gate
voltage swing of few tens of microvolts, leading to extremely small dynamic
power dissipation during switching. An array of 500,000 x 500,000 such
transistors can detect ultrasmall changes in a magnetic field with a
sensitivity of 1 femto-Tesla/sqrt{Hz}, if each transistor is biased near a Fano
resonance.
