For the case displayed in Fig. 3, the spins initially polarized inthe xy-plane the relaxation has a larger effect on the calculated trajectories and there are significant differences between the two alternatives (i) and (ii). When the relaxation is negligible the spin dynamics is completely determined by the Larmor precession, there is no mechanism to induce polarization in the z-direction for central trajectories, y E 0. For these trajectories the net force on the particles is negligible and there is a negligible deviation from zero in the detected z-coordinate. However, when (by)2/ {(B0 + bz)2 +(by)2}r1, there can be a net polarization along the z-direction.
The magnitude and sign of this polarization depend on the initial phase angle of the xy-polarization. A random distribution of this angle results in a pattern observed in Fig. 3A.