Test of Bell's inequality using the spin filter effect in ferromagnetic semiconductor microstructures

A theoretical proposal for testing Bell's inequality in mesoscopic systems is presented. We show that the entanglement of two electron spins can be detected in the spin filter effect in the mesoscopic semiconductor / ferromagnetic semiconductor / semiconductor junction. In particular, we show how to test Bell's inequality via the measurement of the current-current correlation function in this setup. We also discuss the influence of an imperfect spin filter and derive the condition to examine the violation of Bell's inequality experimentally.