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.
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