  Ballistic spin resonance was experimentally observed in a
quasi-one-dimensional wire by Frolov et al. [Nature (London) 458, 868 (2009)].
The spin resonance was generated by a combination of an external static
magnetic field and the oscillating effective spin-orbit magnetic field due to
periodic bouncings of the electrons off the boundaries of a narrow channel. An
increase of the D'yakonov-Perel spin relaxation rate was observed when the
frequency of the spin-orbit field matched that of the Larmor precession
frequency around the external magnetic field. Here we develop a model to
account for the D'yakonov-Perel mechanism in multisubband quantum wires with
both the Rashba and Dresselhaus spin-orbit interactions. Considering elastic
spin-conserving impurity scatterings in the time-evolution operator (Heisenberg
representation), we extract the spin relaxation time by evaluating the
time-dependent average of the spin operators. The magnetic field dependence of
the nonlocal voltage, which is related to the spin relaxation time behavior,
shows a wide plateau, in agreement with the experimental observation. This
plateau arises due to injection in higher subbands and small-angle scattering.
In this quantum mechanical approach, the spin resonance occurs near the
spin-orbit induced energy anticrossings of the quantum wire subbands with
opposite spins. We also predict anomalous dips in the spin relaxation time as a
function of the magnetic field in systems with strong spin-orbit couplings.
