Figure 3: Magnetoelectric effects.

(a) Spin precession in magnetic field along θ=10° (c.f. inset), from initial state
. Oscillation in
is tunable by the electric field
as shown by the contour plot. The dashed curves on the contour image denote the time when the spin precessions at K and –K acquire a phase difference of (2n+1)π. A horizontal cut of the contour image at Ez=0.2B0 is shown as the black solid curve atop, while the red and blue curves denote
sz
at K and –K, respectively. (b) Oscillation of the layer polarization
σz
in a magnetic field, with a pattern tunable by Ez. The initial state is
. (c) Finite spin polarization can evolve out of the initial state
of zero spin polarization. Magnetic field is along the direction θ=10°. In all calculations, we assumed the doublet has a spin relaxation rate of 0.01B0. The unit of time is
.