Spin- and valley-dependent transport through arrays of ferromagnetic silicene junctions

We study ballistic transport of Dirac fermions in silicene through arrays of barriers, of width $d$, in the presence of an exchange field $M$ and a tunable potential of height $U$ or depth $-U$. The spin- and valley-resolved conductances as functions of $U$ or $M$, exhibit resonances away from the Dirac point (DP) and close to it a pronounced dip that becomes a gap when a critical electric field $E_z$ is applied. This gap widens by increasing the number of barriers and can be used to realize electric field-controlled switching of the current. The spin $p_s$ and valley $p_v$ polarizations of the current near the DP increase with $E_z$ or $M$ and can reach 100\% for certain of their values. These field ranges widen significantly by increasing the number of barriers. Also, $p_s$ and $p_v$ oscillate nearly periodically with the separation between barriers or wells and can be inverted by reversing $M$.