We present a microscopic analysis of electron spin dynamics in the presence
of an external magnetic field for non-centrosymmetric semiconductors in which
the D'yakonov-Perel' spin-orbit interaction is the dominant spin relaxation
mechanism. We implement a fully microscopic two-step calculation, in which the
relaxation of orbital motion due to electron-bath coupling is the first step
and spin relaxation due to spin-orbit coupling is the second step. On this
basis, we derive a set of Bloch equations for spin with the relaxation times
T_1 and T_2 obtained microscopically. We show that in bulk semiconductors
without magnetic field, T_1 = T_2, whereas for a quantum well with a magnetic
field applied along the growth direction T_1 = T_2/2 for any magnetic field
strength.Comment: to appear in Proceedings of Mesoscopic Superconductivity and
Spintronics (MS+S2002