Valley and spin resonant tunneling current in ferromagnetic / nonmagnetic / ferromagnetic silicene junction

We study the transport properties in a ferromagnetic/nonmagnetic/ferromagnetic (FNF) silicene junction in which an electrostatic gate potential, U, is attached to the nonmagnetic region. We show that the electrostatic gate potential U is a useful probe to control the band structure, quasi-bound states in the nonmagnetic barrier as well as the transport properties of the FNF silicene junction. In particular, by introducing the electrostatic gate potential, both the spin and valley conductances of the junction show an oscillatory behavior. The amplitude and frequency of such oscillations can be controlled by U. As an important result, we found that by increasing U, the second characteristic of the Klein tunneling is satisfied as a result of the quasiparticles chirality which can penetrate through a potential barrier. Moreover, it is found that for special values of U, the junction shows a gap in the spin and valley-resolve conductance and the amplitude of this gap is only controlled by the on-site potential difference, ∆z. Our findings of high controllability of the spin and valley transport in such a FNF silicene junction may improve the performance of nano-electronics and spintronics devices. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4942043]


I. INTRODUCTION
2][3][4][5][6] In silicene the low-energy excitations are governed by the Dirac equation near the K and K ′ points. 7,81][12] The large spin-orbit interaction of silicene couples the spin and valley degrees of freedom and it plays an important role in the valley and spin transport.The low-buckled geometry of silicene with strong atomic intrinsic spin-orbit interactions leads to a gap of 1.55 meV between the conduction and valence bands. 7,8Also opening the energy gap leads to the topological phase transition in silicene by applying electric field and the conductance can be controlled by the gate voltage. 129][20] The valley-valve and valley-filter effects were originally proposed in graphene nanoribbons with zigzag edge. 18,20The valleytronics is protected by the suppression of intervalley scattering via a potential step and it is controllable by local application of a gate potential.The two valleys are inequivalent Dirac points in the Brillouin zone, K and K ′ and they are degenerate in energy and related to the time reversal symmetry.Therefore the valley degree of freedom is similar to the spin degree of freedom and it provides another probe to control electron.Due to the strong spin-valley coupling and the tunability of the spin-splitting band gap by an external electric field in silicone, it is worth studying the valleytronics in silicene and comparing the results with those in graphene in which the spin-orbit interaction is weak.
Recently, the transport properties of silicene-based tunneling junction have attracted much attention.Yokoyama showed that the current through the normal/ferromagnetic/normal (NFN) silicene junction is valley and spin polarized due to the coupling between the valley and spin degrees of freedom and it can be tuned by an external electric field. 21Also remarkable spin/valley polarization can be accessed through the spinor relying resonant tunneling mechanism in the normal/ferromagnetic/normal multiple silicene junction by aligning the spin and valley-resolve confined states in magnetic well. 224][25] Also the valley and spin transport in ferromagnetic/ferromagnetic barrier/ferromagnetic 26 and ferromagnetic/nonmagnetic/ ferromagnetic 27 silicene junctions strongly depends on the local application of a vertical electric field in the middle regions and effective magnetization configuration of the ferromagnetic layers.
The spin-valve effect which is the resistance of a device against switching the relative orientation of the magnetizations is in the heart of spintronics. 289][30][31][32] Investigations of spin transport, spin dynamics and spin relaxation are fundamental studies of spintronics.Hence, one of the typical questions posed in spintronics is: what is an effective way to polarize the spin current in solid state systems?Motivated by the development of spintronics devices with the novel 2D-materials, we study the spin and valley polarized current through the silicene-based ferromagnetic/nonmagnetic/ferromagnetic (FNF) spin-valve junction where an electrostatic gate potential is attached to the nonmagnetic segment.Actually, due to the importance of nonmagnetic tunneling junction for making relativistic devices 26,33,34 and novel physics in ferromagnetic silicene junction, here, we study the valley and spin transport in a silicene-based FNF junction in the presence of the on-site potential difference ∆ z and the electrostatic gate potential U. Note that our proposed FNF silicene junction is different from Refs. 26 and 27 in those there is no electrostatic gate potential in the middle regions.In fact, we propose a nonmagnetic barrier spacer layer between two ferromagnetic silicene layers.The magnetism in the left and right silicene regions could be induced by the magnetic proximity effect with a magnetic insulator EuO, which is proposed and realized for graphene. 21,35,36The magnetization direction in two ferromagnetic regions can be up and down, so there are two effective magnetization configurations.We show that the electrostatic gate potential U is a useful probe to control the band structure, quasi-bound states in the nonmagnetic barrier as well as the transport properties of the FNF silicene junction.In particular, by introducing the electrostatic gate potential, the spin and valley conductances of the junction show an oscillatory behavior.The amplitude and frequency of such oscillations can be controlled by U. Interestingly, we obtained that by increasing U, the second characteristic of the Klein tunneling is satisfied because of the chiral nature of the quasiparticles which can penetrate through the barrier.In addition, it is shown that at special height of U, the junction exhibits a gap in the spin and valley conductances and the amplitude of this gap can be controlled by the on-site potential difference, ∆ z .
The rest of this paper is organized as follow: In Sec.II, we explain our formalism and analytical calculations of the spin and valley dependent transmittance and conductance through the junction.The results are given in Sec.III, where we in particular treat the role of the electrostatic gate potential U on the transport properties of the junction.Finally, we end the paper with conclusion in Sec.IV.

II. THEORETICAL CONSIDERATIONS
For the model of calculation, we consider a wide planar two-dimensional ferromagnetic/nonmagnetic/ferromagnetic (FNF) silicene junction in the xy plane.The proposed experimental setup of our model is shown in figure 1.The two ferromagnetic silicene regions which can be produced by the magnetic proximity effect with a magnetic insulator substrate have been separated by a nonmagnetic