  Binary mixtures of Bose-Einstein condensates trapped in deep optical lattices
and subjected to equal contributions of Rashba and Dresselhaus spin-orbit
coupling (SOC), are investigated in the presence of a periodic time modulation
of the Zeeman field. SOC tunability is explicitly demonstrated by adopting a
mean-field tight-binding model for the BEC mixture and by performing an
averaging approach in the strong modulation limit. In this case, the system can
be reduced to an unmodulated vector discrete nonlinear Schr\"odinger equation
with a rescaled SOC tunning parameter $\alpha$, which depends only on the ratio
between amplitude and frequency of the applied Zeeman field. The dependence of
the spectrum of the linear system on $\alpha$ has been analytically
characterized. In particular, we show that extremal curves (ground and highest
excited states) of the linear spectrum are continuous piecewise functions
(together with their derivatives) of $\alpha$, which consist of a finite number
of decreasing band lobes joined by constant lines. This structure also remains
in presence of not too large nonlinearities. Most important, the interactions
introduce a number of localized states in the band-gaps that undergo change of
properties as they collide with band lobes. The stability of ground states in
the presence of the modulating field has been demonstrated by real time
evolutions of the original (un-averaged) system. Localization properties of the
ground state induced by the SOC tuning, and a parameter design for possible
experimental observation have also been discussed.
