Spin manipulations through electrical and thermoelectrical transport in magnetic tunnel junctions

Transcription

1 SCIENCE CHINA Physics, Mechanics & Astronomy. Review. Progress of Projects Supported by NSFC Spintronics January 213 Vol. 56 No. 1: doi: 1.17/s x Spin manipulations through electrical and thermoelectrical transport in magnetic tunnel junctions ZHU ZhenGang 1,3 &SUGang 2* 1 School of Electronics, Eletrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 149, China; 2 School of Physics, University of Chinese Academy of Sciences, Beijing 149, China; 3 Institut für Physik, Martin-Luther-Universität, Halle-Wittenberg Nanotechnikum-Weinberg, Heinrich-Damerow-Strasse 4 D-612 Halle (Saale), Germany Received October 1, 212; accepted November 7, 212; published online December 26, 212 A brief review is presented, which includes the direct current, alternate current, electrical and thermoelectrical transport as well as spin transfer effect in a variety of spin-based nanostructures such as the magnetic tunnel junction (MTJ), ferromagnet(fm)-quantum dot (QD)/FM-FM, double barrier MTJ, FM-marginal Fermi liquid-fm, FM-unconventional superconductor-fm (FUSF), quantum ring and optical spin-field-effect transistor. The magnetoresistances in those structures, spin accumulation effect in FM-QD-FM and FUSF systems, spin injection and spin filter into semiconductor, spin transfer effect, photon-assisted spin transport, magnonassisted tunneling, electron-electron interaction effect on spin transport, laser-controlled spin dynamics, and thermoelectrical spin transport are discussed. spintronics, magnetic tunnel junction, spin transport, magnetoresistance, spin transfer torque, spin injection, spin filter, spin-valve, spin-orbit PACS number(s): b, d, j, Mk Citation: Zhu Z G, Su G. Spin manipulations through electrical and thermoelectrical transport in magnetic tunnel junctions. Sci China-Phys Mech Astron, 213, 56: , doi: 1.17/s x 1 Introduction The research on the magnetoresistance (MR) has a long history, which was made considerable achievements till today. Modern advancements have been accompanied with the ability of fabrication of higher quality nanostructures where hybrid materials are usually integrated together. The breakthrough is the discovery of giant magnetoresistance (GMR) in Fe/Cr/Fe multilayer junction [1]. This achievement was awarded with Nobel prize in 27. The GMR effect states that the resistance is low or high when the magnetizations of the two ferromagnetic (FM) layers align parallel or antiparallel. It was observed further that the interlayer exchange coupling oscillates damply with the Cr or Ru spacer layer thickness in Co/Ru, Co/Cr and Fe/Cr superlattice systems [2], which suggests that the quantum-well states be formed in the *Corresponding author ( gsu@ucas.ac.cn) spacer layer. This is because the electrons may meet multireflections at the interfaces between the ferromagnets and the spacer layer, leading to the oscillation of density of states (DOS) of electrons at the Fermi level, and thereby giving rise to the oscillation of the interlayer exchange coupling with the spacer thickness [3]. This inspired researchers to explore various MR or spin effects not only on fundamental physics but also on potential applications in many sorts of nanostructures and materials, emerging a research field coined spintronics (see refs. [4,5]). On the other hand, the magnetic tunnel junction (MTJ) system, that is FM/insulator(I)/FM, was investigated as early as in 197s [6]. Julliére observed a 14% tunnel magnetoresistance (TMR) effect in Fe/Ge/Co MTJ [7] in However a breakthrough has been made in 1995 by Moodera et al. [8] that rather high TMR of 11.8%, 2%, and 24% was reproducibly observed in CoFe/Al 2 O 3 /Co(NiFe) at 295 K, 77 K and 4.2 K, respectively. Recently, the use of a single-crystal c Science China Press and Springer-Verlag Berlin Heidelberg 212 phys.scichina.com

2 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No MgO barrier in a MTJ has already generated a rather high TMR ratio, reaching a maximal of 5% [9]. In addition, the current perpendicular-to-plane geometry of the MTJ makes it easy to be integrated into a nanoelectronic device, and in fact, the TMR-based read heads have been commercialized [1]. Comparing with the junction systems incorporating the normal metal in the central layer, MTJ has the advantages of high resistance with better matching semiconductors, high MR, and low power. These characters and technical advances enable the TMR effect to possess even more essential industrial applications than the GMR effect in information storage and spin-based electronic devices. Significant progress has been made both experimentally and theoretically in the last decade. Following these pioneering works, many different types of nanostructures with FM materials were explored, manifesting the versatile phenomena related to ferromagnetism. An opposite phenomenon to the GMR and TMR effects, termed as the spin-transfer effect, was predicted independently by Berger [11] and Slonczewski [12] in The spin transfer effect states that when the spin-polarized electrons flowing from one FM layer into another FM layer with the magnetization aligned by a relative angle may transfer a transverse angular momenta to the local spins of the second free FM layer, thereby exerting a spin-transfer torque (STT) on the magnetic moments. By applying a sufficient large current density into the second FM layer, it is possible to switch the magnetic state of this free FM layer. This is expected to serve as a rapid and convenient way to control the magnetic states in terms of electrical current instead of a magnetic field (see refs. [13] for a review). This new phenomena was confirmed soon experimentally after its first proposal [14]. It is now well established that STT-based writing heads or random access memory (MRAM) could be developed. Recently, a nonvolatile STT memory has been demonstrated [15]. Since a large current is needed to flip the magnetization of the FM layer, FM/normal metal (NM)/FM junction was investigated first where large current density is easier to obtain because of low resistance. Later with an improvement on the techniques of fabricating high quality and sufficiently thin aluminum oxide or single-crystal MgO layer, MTJs have been researched extensively. In the following, we shall give a brief review on our works in the past decade in three aspects: direct current (DC) spin transport, alternate current (AC) spin transport and thermoelectrical spin transport. The systems we studied include single MTJ, FM-insulator-NM-FM system, quantum dot (QD)-ring-MTJ structure, FM-QD-FM, FM-FM- FM double MTJ, FM-marginal Fermi liquid-fm, and FMunconventional superconductor-fm structure. 2 Direct current spin transport In this section, we shall describe our studies on the DC spin transport in a few nanoscale junction systems. 2.1 Magnetic tunnel junction (MTJ) system Single MTJ A single MTJ is a basic ingredient in the applications, such as the writing heads and the STT-based MRAM. We begin from a tunneling Hamiltonian H = H L + H R + H T, (1) with H L = ε L kσ a kσ a kσ, kσ [ H R = (εr (q) σm 2 cos θ) c qσ c qσ M 2 sin θc qσ c ] q σ, H T = qσ kqσσ [ T σσ kq a kσ c qσ + h.c.], (2) where a kσ and c qσ are annihilation operators of electrons with momentum k and q and spin σ (=±1) in the left and right FM, respectively, ε L kσ = ε L(k) ev σm 1, M 1 = gμ B h L /2, M 2 = gμ B h R /2, g is the Landé factor, μ B is the Bohr magneton, h L(R) is the molecular field of the left (right) ferromagnet, ε L(R) (k) is the single-particle dispersion of the left (right) FM electrode, V is the applied bias voltage, T σσ kq denotes the spin and momentum dependent tunneling amplitude through the insulating barrier. Nonequilibrium Green function technique (NEGF) In this method, the tunneling current is obtained via I L (V) = e N L = 2e Re kq Tr σ {Ω kq G < kq (t, t)}, (3) T kq T kq where Ω kq = T kq R with T kq = T T and ( ) kq kq cos θ R = 2 sin θ 2 sin θ 2 cos θ, and Tr σ stands for the trace of matrix taking over the spin space. The lesser Green function, 2 G < kq (t, t ), is defined in a steady state as G < kq (t G,< t kq ) = (t t ) G,< kq (t t ) G,< kq (t t ) G,< kq (t t ), (4) with G σσ,< (t t ) i a kq kσ (t )b qσ (t). To obtain the lesser Green function, one needs to introduce a time-ordered Green function G t qk as G t qk (t G,t t qk ) = (t t ) G,t qk (t t ) G,t qk (t t ) G,t qk (t t ), (5) with G σσ,t qk (t t ) i T { b qσ (t)a kσ (t ) }. By using the standard NEGF technique, we can obtain dε [ ] [ f (ε) f (ε + ev) Trσ Tef f (ε, V) ], (6) 2π I L (V) = 2e where f (ε) is the Fermi function, T eff (ε, V) = 2π 2 T R D R (ε) R T D L (ε + ev), (7)

3 168 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No. 1 and D L(R) (ε) isa2 2 diagonal matrix with two nonzero elements being the corresponding density of states (DOS) of electrons with spin up and down in the left (right) ferromagnet. For a small bias voltage V, we obtain the tunneling conductance G = 2e2 h T eff, (8) where T eff = Tr σ [T eff (ε F, V = )], and ε F is the Fermi energy. In comparison to the Landauer-Büttiker formula, one may find that T eff can be regarded as an effective tunneling transmission coefficientwhich includesthecontributionfrom spin-flip scatterings. Eq. (8) can be explicitly rewritten as: G = G [1 + P 2 P P2 3 cos(θ θ f )], (9) where G = πe2 2 [(T T 2 2)D L + (T3 2 + T 4 2)D L ](D R + D R ), P 1 = (T 1 2 T 2 2)D L (T4 2 T 3 2)D L, P (T1 2+T 2 2)D L +(T3 2+T 4 2)D 2 = D R D R L D R +D R, P 3 = 2(T 1 T 2 D L +T 3 T 4 D L ), tan θ (T1 2+T 2 2)D L +(T3 2+T 4 2)D f = P 3 L P 1, D L = D L (ε + M 1 + ev), D L = D L (ε M 1 + ev), D R = D R (ε + M 2 ), and D R = D R (ε M 2 ). The conductance and TMR We use γ = T 2 /T 1 to character the magnitude of the spin-flip scattering. In Figure 1, we show the effect of spin-flip scattering on the conductance and TMR, where G = πe2 2 [T 1 2D L + T4 2D L ](D R + D R ), and TMR= (G(θ = ) G(θ = π))/g(θ = ). In absence of spin-flip scattering (γ = ), the conductance for parallel configuration is the largest (θ = ); while the lowest conductance is obtained for antiparallel configuration (θ = π) [16]. This just gives the spin-valve effect. With increasing the strength of the spin-flip scattering, more up spins are flipped into down state, giving rise to a decreased (increased) conductance for parallel (antiparallel) configuration. This is simply because the flipped down spins have less possibilities to enter into the right FM electrode for parallel configuration and more chances for antiparallel configuration. The model presented here is a general Hamiltonian for a single domain. In realistic systems, for example, nanoparticles in one ferromagnetic electrodes may be regarded as individual domains with magnetizations randomized in all directions as in an experimental work. Therefore, these nano-particles provide spin-flip scattering which will be enhanced at high temperatures. Thus with increasing the temperature the conductance for parallel (antiparallel) should be decreased (increased). Such an observation was confirmed in an recent experiment [17]. Spin transfer torque in single MTJ (see in Figure 2). The spin torque is captured via the time evolution rate of the total spin of the left or the right ferromagnet, i.e. t s 1,2(t) = i [H, s 1,2(t)]. Thisdefinition contains all the torques felt by the local magnetization. One is the equilibrium torque caused by the magnetic exchange interaction, and the other is from the electrons tunneling through the insulating barrier from the left side. The latter is the current-induced spin transfer torque defined by τ = i [H, s 2(t)]. The total spin of the right ferromagnet is s(t) = c 2 kμ c kν(r 1 χ μ ) σ (R 1 χ ν ), (1) kμν where χ μ(ν) is the spin state. Note that the total spin is now written in the xyz coordinate frame while the spins s 2 are quantized in the x y z frame. By using the NEGF technique, we can obtain [19] dε τ Rx = cos θr 2π Tr [ σ G < kq (ε)ˆσ 1T ] kq + sin θr kq dε 2π Tr [ σ G < kq (ε)ˆσ 3T ], (11) where σ 1 and σ 3 are usual Pauli matrixes. After some algebra, we can obtain τ P Rx = 21 + P23 sin ( ) θ θ f I e e 1 + P 2 P P2 3 cos ( ), (12) θ θ f TMR G/G θ= θ=π/3 θ=π/2 θ=π γ Figure 1 Effect of spin-flip scattering on the conductance in and TMR in. Mass of single electron in both ferromagnets is assumed as unity, the molecular fields in the two ferromagnets are supposed to be the same and taken as.7 ev, ε F =1.5 ev, and the coupling parameter T 1 is chosen as 1 ev. This figure is taken from ref. [16]. O z x S L FM I θ FM τ R S R Flipped Electrons flowing direction Figure 2 Schematic illustration of the spin transfer effect in MTJs.

4 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No where I e indicates the electrical current. The angular dependence of the STT is shown in Figure 3, where γ 1 = T 2 /T 1 and γ 2 = T 3 /T 1. The angular shift is clearly seen, leading to a nonzero torque when θ = andπ in contrast to the case in absence of spin-flip scattering. Electron-electron interaction on the conductance. To study the electron-electron interaction on the spin transport, an analytical approach is developed based on the scattering matrix theory [19]. A self-consistent Hartree potential is determined by the Schrödinger equation and Poisson equation together [2]. It is found that in single MTJ junction the conductance varying with the bias shows oscillations which are not present in the free model MTJ with one inserted normal metal layer TMR (%) Experiment Theory d (A) It is predicted that TMR in a MTJ with an extra inserted NM layer between the insulating barrier and one FM electrode will shown decaying oscillation with increasing the thickness of the NM layer (see in Figure 4). It was observed in an experiment conducted by Yuasa et al. [21]. We proposed a model to interpret it [22]. It is found that this effect can be reproduced rather nicely if there exists a thin and mixed layer formed at the interface of the insulator and the NM layer. From an atomic point of view, such a layer is possible because the crystals of insulator and the NM are different. When contacting them together, a buffer layer could be formed to link them. We use a scattering matrix method to work out the transmission probability and investigated how the TMR varies with the thickness of the NM layer Quantum dot-ring-mtj structure In this subsection, we investigate a system in which the central region formed by connecting a MTJ and a QD into a quantum ring structure is linked to two FM electrodes [23]. It is assumed that the QD is constructed by metallic gates from τ Rx /I e γ 1 =γ 2 = γ 1 =γ 2 =5 γ 1 =γ 2 =.1 γ 1 =γ 2 = θ ( ) Figure 3 θ dependence of τrx I e for γ 1 = γ 2, h L = h R =.9 ev,e f = ev, and T 1 = T 4 = 1 ev. Torque per unit current is measured in unit of /e. Thisfigure is taken from [18]. Figure 4 Tunnel magnetoresistance as a function of the thickness of the normal metal layer. Solid line is obtained from the present model at zero temperature, while the dash-squared line shows the experimental data at 2 K adopted from ref. [21]. In numerical calculations, we have taken the parameters as follows: d 1 = 18 Å, d 2 =.15d, V 1 = 2 ev, V 2 =.8eV,V 3 = 2.35 ev, V 4 = ev,v 5 = 25 ev, E f =.785 ev, and h L = h R = ev. d 1 is the thickness of the insulator, d 2 is the thickness of the extra layer, V 1,2,3,4,5 are the potentials in the left FM, insulator, the extra layer, NM layer, and the right FM layer, respectively. This figure is taken from [22]. two-dimensional (2D) electron gas in which Rashba spin orbit interaction (SOI) exists. The ring structure is an interesting system where Aharonov-Bohm interference can occur in presence of an external magnetic flux threading the ring. This is because the vector potential in the upper and lower arm enters into the phase of the wave function, leading to a tunable phase by the external flux. The upper arm of the system can be regarded as a MTJ and the lower arm is composed of FM-QD-FM. The presence of the Rashba SOI will split the degeneracy of the spin up and down states and characterized by γ = k R d where k R = αm / 2, α is the Rashba SOI strength, and d is the thickness of the middle region. It is found that the angular dependence (the relative orientation between the two FM electrodes) of the STT show still vanishing value at θ = andπ. However, the nonzero at other angles will be altered dramatically, meaning a positive STT may be changed into a negative one by changing the flux or the Rashba SOI strength. The sign of spin current is changed in accordance with the change in the STT. An interesting feature is that the sign of the extremum point of the STT can also be changed by shifting the impurity level from below to above the Fermi level [23]. This shows the possibility to control the STT by a gate voltage applied to the QD. This may benefit to the future application of the STT FM-QD-FM FM-QD-FM system (see in Figure 5) has been attracted a lot of attention recently. Previous theoretical works on the spindependent transport through QDs are mainly focused on the

5 17 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No. 1 T kl T kr V/2 ε +U θ V/2 ε I s /I.4.2 θ= θ=π/3 θ=π/2 θ=2π/3 θ=π FM QD Figure 5 Schematic illustration of the system consisting of two ferromagnets and a quantum dot separated by the tunnel barriers, where T kα (α=l,r) stands for the coupling matrix between the α electrode and the QD, and both magnetizations are aligned by a relative angle θ. tunnel electrical current and the TMR effect for collinear configuration [24] and noncollinear configuration [25]. However, the investigations on the spin current and the current-induced spin transfer torque (CISTT) in such systems are sparsely reported. It is the purpose of this subsection to show results for the spin current and spin transfer torque in FM-QD-FM coupled MTJs [26]. The total Hamiltonian is H = H L + H R + H d + H T,where H L(R) is given in eq. (2), H d = ε d σd σ + Un n, (13) σ FM H T = T kα a kασ d σ + h.c., α = L, R. (14) kασ The electrical current (I) and spin current (I s ) will be G s /G θ= θ=π/3 θ=π/2 θ=2π/3 θ=π ev/γ Figure 6 Bias dependence of the spin current I s and spin differential conductance G s for different angle θ at P=.4. The other parameters are ε = 1Γ, U = 4Γ and k B T =.3Γ.Thisfigure is taken from [26]. P=.4 I(V) = I L (V) + I L (V), I s (V) = I L (V) I L (V), I L (V) = 2e R T kl G,< kl (t, t), kl I L (V) = 2e R T kl G,< kl (t, t). (15) kl τ Rx /Γ 6 U=2Γ U=25Γ U=3Γ U=35Γ U=4Γ Conductance and spin conductance It is known that the conductance grows two peaks around at ε and its counterpart level ε + U (the real positions for these two level should further be modified by adding the real part of the selfenergies of the electrodes). In Figure 6, we further study the spin current and the spin differential conductance defined by G s = di s /dv for different angles. At V >, when θ<π/2, the spin currents show steplike behavior and I s > ; while for θ>π/2, I s exhibits behavior similar to a basinlike shape, and I a < at the bottom of the basin. From the figure, we know up spins from the left electrode are blocked for the angle larger than π/2 since the down spins are easier to tunnel into the right electrode [26]. Spin Transfer Torque From Figure 7, it can be seen that a peak exists around at position of the main level ε and a plateau for the bias higher than ε + U. In between these two levels, STT is low. The STT increases dramatically when the bias is beyond the level ε + U which can be understood as that the counterpart level opens an opposite spin channel 5 1 ev/γ Figure 7 The bias dependence of the current induced spin transfer torque for different interaction U at θ = π/3. The other parameters are the same as in Figure 6. This figure is taken from [26]. to the level ε, thereby leading to two opened spin channels and higher torque [26]. Spin accumulation in the QD From above, it is clear that spin will accumulate in the QD when the magnetizations are in anti-parallel configurations. This spin accumulation will lift the effective chemical potential for up and down spins respectively in the QD. Thus we investigated this effect selfconsistently. The important step is to add two such terms in the QD Hamiltonian H d = ε d σ d σ + Un n δμ n δμ n, (16) σ

6 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No where δμ σ denotes the chemical potential shifts caused by the change of charge densities induced by the spin accumulation in the central QD, which should be determined selfconsistently. The findings are (1) the two resonant peaks at ε and ε + U are moved towards small biases; (2) TMR is largely enhanced [27]. Three-terminal spin transistor with sources We further studied a QD-based multi-fm-terminal system. In contrast to previous studies on three-fm-terminal system [28] where the third terminal is introduced as an inelastic scattering resource and there is no net current flowing through this terminal, we consider a system with multi-terminals which are independent with each other and supplied with the bias source independently. In Figure 8, we proposed a three-terminal spin transistor with source [29]. When the magnetization of the first and second terminals align parallel, the current flowing through the second terminal is diminished when the relative angle θ 3 is increased. In contrast, the current from the second terminal for antiparallel configuration is enlarged when θ 3 is larger. This is just a three-terminal spin transistor in which the current can be enlarged or suppressed by changing the direction of the magnetization of the third terminal [29]. 2.2 FM-FM-FM double MTJ In this subsection we shall turn to another system, which is FM-FM-FM double barrier tunnel junction. It is anticipated that new features will be emergent when compared to the other nano-systems, such as the formation of quantum well states and the resonant tunneling phenomenon [3]. In order to observe the coherent tunneling through the stucture, people have attempted to improve the junction quality to eliminate the influences from the interface roughness and impurity scattering, and remarkable advances have been achieved on this aspect. Recently, an unusual magnetotransport phenomenon in this system was reported by Zeng et al. [31]. They observed that, when the magnetization of center (free) Current (e/h) FM 1 FM 3 μ 3 (t) θ 3 FM 2 θ P=.4, J 2 2,P.16 P=.4, J 2,AP μ 1 (t) μ P=.6, J 2,P V 2 (t) g P=.6, J 2,AP 8 P=.8, J 2,P P=.8, J 2,AP θ/π Figure 8 The left panel shows the current flowing through the second terminal vs the angle θ = θ 3, where index P(AP) indicates the magnetization of the second FM terminal is parallel (antiparallel) to the first one. The parameters are V = 5, ε = 8, and k B T =.1Γ. The right panel describes the geometry of the three-terminal, i.e. spin-transistor with source. This figure is taken from ref. [29]. magnetic layer was antiparallel (AP) to the magnetization of the two outer pinned magnetic layers, the conductance and TMR oscillate distinctly with the applied bias voltage, while for the parallel (P) situation, no such oscillation was seen. Unlike the previous oscillatory tunnel magnetoresistance, Zeng et al. [31] suggest that this unusual phenomenon can neither be explained by Coulomb blockade effect, since the middle FM layer is continuous, the charge effect should be equal in P and AP configurations, and the charging energy is negligible, nor be attributed to the resonant tunneling, because the observed period of oscillation is too small to account for the energy level spacing of the quantum well states. Considering that the conductance oscillation is asymmetrical for P and AP configurations, and the energy level of the unusual phenomenon is the same as the typical energy of a magnon, they speculated that the unusual oscillation behavior could be induced by the magnon-assisted tunneling. This is because in the AP state, the nonequilibrium spin density, which is proportional to the applied bias, could be accumulated near the interfaces in the middle region to emit spin waves, and the magnon-assisted tunneling would contribute to the conductance, while in the P state, the spin-wave emission is forbidden due to the spin angular momentum conservation, as discussed previously. We therefore study this structure where the magnetizations of the left and right FM electrodes are assumed to be parallel and that for the central FM layer is fixed anitparallel to those of the left and right electrodes. The Hamiltonian reads H = H L + H R + H C + H LC + H CR [32], where H α = ε kα σa k α σ a k α σ,α= L, R, k α σ H C = ε kσ c kσ c kσ + ω q b q b q, H LC = kσ q T d k L k (a k L σ c kσ + h.c.) (17) k L kσ + 1 T J k N L k q S (q)(a k L c k k L k q a k L c k + c k a k L c k a k L ) + 1 2S (a k N L c k b q + c k a k L b q k L k q T J k L k q + a k L c k b q + c k a k L b q ), H CR = H LC (the index L is changed to R ), where a kα σ and c kσ are annihilation operators of electrons in the α electrode and in the middle FM layer, respectively, ε kα σ = ε kα σm α ev α, with ε α being the single electron energy and M α the molecular field in the α electrode; ε kσ = ε σm, with ε k being the single electron energy and M being the molecular field in the middle layer. The b q is the annihilation operator of magnon with momentum q in the middle region, ω q is the magnon energy, N = q n s q with n s q = b qb q is the number of the magnons, S (q) = S n s q where

7 172 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No. 1 S = 1/2 is the spin of electron, Tk d α k are tunneling matrix elements between the α electrode and the middle FM layer, T J k α kq are coupling matrix elements between the electrons in the α electrode and magnons in the middle FM region. In Figure 9, the conductance and TMR are shown varying with the bias. γ characterizes the relative strength of the coupling between electrons and the magnons to the tunneling coupling between electrons. It can be clearly seen that there is no oscillation in the conductance and TMR in absence of the magnons, but in presence of them. Further calculation shows that these peaks are the magnon-assisted resonances with the aid of calculation on the magnon number [32]. This confirms the experimental observations. Spin transfer torque in FM-FM-FM system To study the spin transfer effect in this multi-layer system, we ignore the magnon effect in the middle FM layer and only keep the main s-d exchange interaction in it, leading to [33] ( ) H C = ε k c kσ c kσ (c k, c k )ˆσ M ck c, k kσ H LC(CR) = k α kσσ k ( T σσ k α k a k α σ c kσ + h.c.), (18) where α = L or R for H LC or H CR, respectively. The total Hamiltonian reads H = H L + H R + H C + H LC + H CR. From Figure 1, we can observe that the maximum of the STT is enhanced when the magnetization of the middle layer is larger. This is consistent with the observation made in FM-QD-FM system. The STT is vanishing at θ = and π. In Figure 1, we observe that the STT increases with a larger bias. This rising is enveloped by oscillations which are caused by formation of quantum well states in the middle layer. This can be evidenced by varying the thickness of the middle layer, i.e. L m, leading to the change of the positions of the oscillations shown in Figure 1. It is well known that a sufficient large current through the system can reverse the magnetization of the free FM layer by the STT. There would be a critical current and a critical bias drop across the system. A previous study [34] derived a relation between the critical current and the magnetization of the FM layer in a model calculation, which shows the critical current is proportional to the magnetization. However, our calculation shows that the relation between them is more complex than a simple proportionality. Therefore, a self-consistent calculation is used by combining the NEGF method and the generalized Landau-Lifishiz-Gilbert equation. It is found that the critical voltage and current varying with M show steplike behavior. It can be understood that a larger STT is needed to switch larger M and the STT increases with voltage in a non-monotonous way [33]. It can be readily seen in Figure 11 that the relationship between I c and V c looks nearly linear in trend, and for different P, all curves of I c against V c almost fall into the same curve, in particular, at small V c regions, which also reveals that the critical differential resistance remains almost constant with polarization P. G/G TMR γ=.15 (AP).175 (AP).2 (AP) (AP) (P) ev/γ Figure 9 Bias dependence of the differential conductance G in, and TMR in for the different γ = T J /T d,where ω q =.5Γ, ε = 3.Γ and ε = 2.Γ. For simplicity, the energy of the middle layer is taken as the Fermi energy. This figure is taken from ref. [32]. τ θ /Γ 1 5 M=2Γ L m =6. nm L m =5.6 nm L m =5.3 nm 3Γ 4Γ.2 5Γ ev/γ θ/π Figure 1 Angular and bias dependence of the spin transfer torque is shown in and respectively. M = 3Γ, ev=1γ and P =.8 in and M = 15Γ and P =.7 in.thisfigure is taken from ref. [33]. 2.3 FM-Superconductor-FM Normal state of the unconventional superconductor: FM-marginal Fermi liquid-fm double MTJ Intriguing experimental and theoretical investigations on the spin-polarized transport in FM-high Tc superconductor tunnel junction have been reported recently [35]. It is thought that the anomalous normal state properties of high Tc cuprates in the optimally doped regime can be well described by the marginal Fermi liquid (MFL) [36] where the interactions between electrons in the cuprates are phenomenologically included in a one-particle self-energy due to exchange of charge and spin fluctuations. Therefore, the study on the spin-dependent transport in FM-MFL-FM tunnel junctions

8 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No λ=.1 I c /I ev c /Γ P=.9 P=.8 P=.7 P=.6 P=.5 Figure 11 Critical current I c versus the critical voltage V c for different P for the side FM layer is depicted. The uniaxial anisotropy field H k =5 Oe, the molecular field M = 1Γ 12 Oe, Γ = 2 mev, the Fermi level is 13 Γ, k B T = 2Γ, the damping coefficient α =.1, the junction area is taken 8 nm 8 nm, the thickness of the middle FM is 5.6 nm. This figure is taken from ref. [33]. would be noteworthy since it would be useful for understanding the transport properties of FM-high Tc cuprate junctions in the normal state. The Green function for the MFL can be written as G r (ε) = [ ε εk Σ r Σ(ε) + iη] 1,whereΣ r is just the self-energy induced by electrodes, η = +,and Σ(ε) = λ [ε ln xec i π2 ] x, (19) where λ is a coupling constant, E c is a cut-off energy, and x = max ( ε, k B T). When λ =, the MFL junction recovers the conventional Fermi liquid. The findings [37] are: (1) the current tends to more nonlinear dependence on the bias voltage for larger λ; (2) The conductance shows a linear dependence on the bias voltage and becomes larger for stronger interactions; (3) TMR shows a sharp peak around the zero bias and decays with increasing the bias as shown in Figure 12. In another study [38], we studied the behavior of the STT in such a structure. It is found that the maximum of the STT can be enhanced by increasing the interaction strength and the maximum of the torque is linear in λ. This may be caused by broadening of the density of state in the MFL, thereby making more electrons tunnel through the barrier into the right FM electrode and resulting in an increase of the spin torque with λ FM-unconventional superconductor-fm system For ferromagnet/conventional superconductor (FCS) tunnel junctions, there are a number of studies showing that the superconductivity in superconductors is suppressed by the injection of spin-polarized tunneling current (see refs. [39,4]). However, theoretical investigations on ferromagnetunconventional superconductor-ferromagnet (FUSF) junc- TMR (%) TMR (%) T= k B T=.2Γ ev/γ Figure 12 Tunnel magnetoresistance as a function of the bias voltage at T = in and k B T =.2Γ in, respectively, for a FM-MFL-FM double junction. The coupling constant are λ =.1,.2,.3,.5,.8 andp =.5. This figure is taken from ref. [37]. tions are still relatively sparse. In particular, there are some recent experimental studies on ferromagnetinsulator-high-tc superconductor tunnel junctions [35], showing that the superconducting critical current is suppressed due to nonequilibrium spin accumulation in superconductors. Suppression of the superconductivity by spin accumulation The effect of spin accumulation in the FUSF system was shown in this subsection [41]. It shows that the spin accumulation can induce spatially the phase inhomogeneity in the central superconductor at lower temperatures when the magnetizations of both ferromagnetic electrodes are antiparallel. This spin accumulation exists near the interfaces, owing to the spin imbalance, thereby giving rise to an equivalent, small magnetic field that acts as a pair-breaking field, which leads to a suppression of superconductivity [41]. Order parameter It was found by Fulde and Ferrel (FF) [42], and Larkin and Ovchinnikov (LO) [43] that the superconducting (SC) state order parameter can be modulated in real space by a spin-exchange field of a ferromagnet. As the nonequilibrium-spin accumulation may lead to an equivalent magnetic field in the central supercondutor, the Fulde-Ferrel- Larkin-Ovchinnikov (FFLO) state, which is simply omitted in the previous treatment, might be inevitable in the FM-US- FM double-tunnel junction. Figure 13 presents the bias-voltage dependence of the SC order parameter and the chemical potential shift at T/T c =.2, with T c the SC critical temperature, for the antiparallel alignment. It is observed that the order parameter remains almost constant at low biases and is in the homogeneous BCS state until a specific bias voltage V = 1.36Δ /e at which Δ drops

9 174 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No. 1 Δ/Δ δμ/δ BCS P=.4 T/T c =.2 BCS P=.4 T/T c = N ev/2δ Figure 13 Bias dependence of the order parameter Δ in and the chemical-potential shift in under the antiparallel alignment of magnetizations at P =.4, T/T c =.2, where a discontinuity from the first-order phase transition is observed. The dashed line is for the normal state. This figure is taken from ref. [44]. suddenly, where P =.4, and Δ is the BCS zero-temperature energy gap. Then, Δ goes into the inhomogeneous FF state with q, decreases with the bias, and vanishes completely at V = V c, where superconductivity is quenched as shown in Figure 13. At V = V, there is a discontinuity for Δ, implying that a first-order phase transition from the homogeneous BCS phase to the FF phase exists in the system. The chemical-potential shift grows in the homogeneous BCS state with an increasing bias, exhibits a jump at V, then increases slowly in the FF state until V c, and is linear for V V c in the normal state, as shown in Figure 13. We have found that the FF state can coexist with the BCS state at V [44]. Phase diagram In Figure 14, two phase diagrams for central superconductor of a ferromagnet-s-wave superconductor double tunnel junction in Figure 14 and central superconductor of a ferromagnet-d-wave superconductor are shown in Figure 14, respectively. It has been found that the phase transition from the homogeneous s-wave BCS state to the inhomogeneous FFLO state is of first order, which gives rise to the oscillating behaviors of the TMR and conductance. These oscillating features can be used as an alternative way to examine the existence of the FFLO state. It is shown in Figure 14 that, as the SC gap in a d-wave superconductor is anisotropic, it would induce more exotic behaviors than in a s-wave superconductor. It is shown that the phase transitions from the homogeneous d x 2 y 2-wave BCS state to the inhomogeneous FFLO state, and from the FF FF FFLO state with the azimuthal angle of the momentum θ q = to that with θ q = π/4, are of the first order, whereas the transitions from all SC states to the normal state at critical voltages are of the second order [45]. 2.4 Spin injection and spin filter In this subsection, we present two works about spin injection and spin filter. To utilize the spin degree in the semiconductor, one first needs to generate spin current in the semiconductor. This is not easily resolved. There are a few methods to generate such spin current [4], for example by optical ways, that is, applying a circularly polarized light, or by a FM source. For the latter, it is found that the efficiency of the injection is low for a direct-contact junction. This is readily realized that the conductances are not matched for the FM metal and semiconductors. One way to rescue it is to insert an insulator between the FM and semiconductor. Since spin is conserved in the tunneling processes, the injection efficiency T/T c T/T c 1..5 QCP B BCS Δ(r)=Δ d-wave BCS C 1 V * V c FFLO V c ev/2δ LP Δ(r)=Δ q e iqr Normal P=.4.2 θ q =π/4 θ q = C 2 θ B q = 1 B V 2 B 3 QCP FF C N (Δ=) ev/2δ Figure 14 Schematic phase diagram of the central s-wave superconductor in the T-V plane for the antiparallel alignment of magnetizations at P =.4. Three phases are observed: the homogeneous BCS state is separated by the V boundary line via a first order phase transition from the inhomogeneous FF state, and the SC states are separated by the V c boundary line via a second-order phase transition from the normal state. Phase diagram of the central d x 2 y2-wave superconductor in the temperature-bias voltage plane for the antiparallel alignment of magnetizations at P=.4. Four phases are observed: the homogeneous d x 2 y2-wave BCS state with zero momentum pairing, the FFLO states with finite momentum pairing q for θ q = and π/4, and the normal state. This figure is taken from refs. [44,45].

10 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No is improved dramatically. Another method is to use a dilute magnetic semiconductor (DMS) as a spin source, which has both ferromagnet and semiconductor properties. The resistances for hybrid junctions of DMS and conventional semiconductor should be matched better and thus spin injection efficiency will be enhanced. We studied first a multi-layer structure, i.e. ZnSe/Zn 1 x - Mn x Se [46]. When there is no applied magnetic field, the Mn concentration in the paramagnetic layer is chosen so that the offsets of conduction and valence bands are rendered nearly zero, and the alternation of ZnSe and Zn 1 x Mn x Se may be used to build up spin superlattice. With applying a magnetic field perpendicular to the junction, Landau level will be formed in the layers. The degeneracy of spin subbands is removed and a spin-dependent potential is induced. Up- (down-)spin electrons see a barrier (well) in a paramagnetic layer. For a double-paramagnetic-layer structure, up (down) spin electrons see a double-barrier (well) structure. Since the resonant condition for such two different structures are different, the up and down spins meet resonances in a different condition. This physics manifests itself as a tunable polarization of the out-put current with varying the magnitude of the external magnetic field shown in Figure 15. The polarization of the out-put current is defined P out = (J (B) J (B))/(J (B) + J (B)) where J σ are the out-put current with spin σ. It is seen that the polarization can change its sign with increasing the magnitude of the magnetic field rather its direction. The thicknesses of the central ZnSe layer and the paramagnetic layer can affect the polarization dramatically since the thickness will determine the resonant condition [46]. To find a more efficient method to control the spin injection into semiconductor materials, it is better to use electrical way to control. Researches along this idea have been undertaken, for example the spin Hall effect where spin current is P out b=2 nm b=3 nm b=4 nm b=5 nm W=8 nm W=8.4 nm W=1 nm W=12 nm B(T) Figure 15 Polarization of the out-put current varying with the magnitude of the external magnetic field is shown with the thickness of the central ZnSe layer b in and thickness of the paramagnetic layer W in, respectively. W = 1 Å in and b = 4 Å in. E f = 5 mev is used for both. This figure is taken from ref. [46]. flowing in a direction which is perpendicular to both the spin and the external electric field. We consider an FM layer as a spin source, and a perpendicular QD as a channel [47]. Thus the polarized electrons will tunnel through the QD into a semiconductor layer. The advantage of this method is that the levels in the QD can be controlled easily by a gate voltage. From Figure 16, it is observed that the out-put polarization of current is easily controlled by changing the gate voltage. Not only the magnitude but also the sign of the out-put polarization can be controlled. This is because the levels in the QD is spin-splitting since the spin degeneracy in the FM layer is lifted. This spin splitting can be regarded as a consequence of a magnetic field effect in the QD but caused by the spinsplitting in the coupling between the QD and the FM layer. This character is actually noteworthy in the real application since the perpendicular QD can be easily made now. Our proposal could be useful in the future QD-net circuit in spintronics. 3 Alternate current spin transport 3.1 Single MTJ Spin transfer torque We begin from a Hamiltonian which is similar to eqs. (1) and (2) with replacements ε L (k) ε kl (t) = ε kl +Δ L(t) ev with Δ L (t) = ev L cos ω t,andε R (q) ε qr (t) = ε qr +Δ R(t) with Δ R (t) = ev R cos ω t. Δ L(R) (t) is from the applied ac bias. It is found that the tunneling current is time dependent. For small ac signal (small V ac ), the current varies with time in a cosine manner. For stronger signals, there appear some resonant peaks which can be regarded as being resulted from the photon-assisted tunneling. To study the time-averaged behavior, we define a time-averaged quantity A(t) = (1/T ) T /2 dta(t)wherea(t) is an arbitrary time-dependent physical quantity. It is found that the time-averaged current T /2 increa- P out P=.2 P=.4 P= Figure 16 Gate voltage V g dependence of P out. α = 1 and T =.5, where α =Γ R /Γ, Γ R = 2πρ R t R 2, ρ R is the density of state of the semiconductor, t R is the coupling between the QD and the semiconductor, and the energy unit is Γ.Thisfigure is taken from ref. [47]. V g

11 176 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No. 1 ses with frequency of the ac field linearly but with small oscillations until saturation. Conversely it is suppressed by the larger magnitude of the ac field. The STT is shown also suppressed by a larger signal of the ac field. These results are derived by including a DC and an AC voltage at the same time. Thus the suppression of the STT by a larger ac signal maybeusedasawaytoturnoff the STT Linear and nonlinear conductances Büttiker s scattering matrix theory [19] was extended to spindependent transport in MTJ junction systems [48]. The current can be expanded with respect to the voltage V α for α-th electrode as: I α = G αβ ()V β + G αβγ ()V β V γ +, (2) β βγ where G αβ () = G αβ (ω = ) and G αβγ (ω = ) are the weakly linear and nonlinear coefficients which correspond to the dc transport. In the ac case, G αβ (ω) = δi α /δv β represents the linear response of the current δi α through contact α for a small voltage in reservoir β. For low frequency case, it can be further simplified as: G αβ (ω) = G αβ () iωe αβ, (21) where E αβ is the emittance matrix. It is observed in Figure 17 that the linear coefficient is mainly determined by the part G 11 and the spin-valve effect. From Figure 17, E 11 has sharp resonant peaks at certain energies.7, 2., 4.1 Ry, which is the quantum-mechanical characteristics of the single-electron tunneling. It is almost vanishing at energies away from those resonant points. The spin-dependent part E 11 is nearly vanishing, resulting in a low-frequency emittance coefficient that looks the same as E 11 [48]. The nonlinear coefficient G 111 is shown to develop into some peaks which correspond to energies at resonant points of the linear conductance. Away from these resonant points, the nonlinear coefficient is almost vanishing. The antisymmetry of the second-order nonlinear conductance when exchanging the indices is demonstrated in numerical calculations as well. From Figure 18, it is seen the behavior of the nonlinear coefficient is different to the linear one. There are two positive peaks around at θ =.4π and.7π. Around π, G 111 is negative. This character shows that the nonlinear effect might reduce the spin-valve effect [48] Geometric phase effect driven by adiabatic timevarying potential in the insulator A special effect, that is, geometric phase effect, on the spinpolarized transport in single MTJ is investigated [49]. An adiabatic time-varying potential is considered to be applied to the insulator region. A geometric phase (i.e. Berry phase) Figure 17 Linear coefficient and corresponding spin-dependent parts of single MTJ vs angle θ in the energy dependence of the emittance coefficient is shown in. The molecular field is taken to be 9. Ry and U =.2 Ry being the barrier height. G ++ = G 11, G+ = G 11,andG is the total linear coefficient. The indexes in the emittance are of the same meaning. In, θ = π/5. This figure is taken from ref. [48]. will be acquired in the wave function and related to the spatial gradient and time derivative of the potential. If the voltage drop in the insulator does not depend on the coordinate, the geometric phase will not give rise to any observable effect on the differential conductance and TMR. It is found that the conductance varying with the amplitude of the voltage drop is affected by the geometric phase largely, for example the conductance will be smaller than the one without the phase. This is because of the interference effect of the phase, meaning that the incident wave and the reflected wave in the insulator bear different geometric phases. They will interfere with each other. This is also the reason for a smaller TMR, which is not only reduced but also taking a non-monotonous change with the magnitude of the voltage drop. Namely, the TMR shows a wide dip at some special points. 3.2 Double MTJ Wang et al. [48] investigated the double MTJ systems. Com-

12 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No characterized by m =, ±1, ±2,...which correspond to the shifts of the energy levels caused by the ac field in the central spacer. We have found that the resonant peaks of the ETC become sharper and higher as the orientations of the magnetizations of the left and the right ferromagnetic leads vary from antiparallel to parallel. With increasing θ, the amplitudes of the resonant peaks are noticed to become small. In addition, we have observed that the resonant magnitude of the transmission coefficient is sensitive to the ratio of the strength and the frequency of the AC field, say, α = V /ω. With increasing α, the main resonant peak of the ETC at ε = E f is suppressed, while more resonant peaks with large m appear, as manifested in Figure 19. For a given m (e.g. m = ) the resonant peaks of the TMR can be suppressed or enhanced with increasing α. Figure 18 The second weakly nonlinear coefficients vary with the angle θ. Energy is taken at 2.2 Ry, the molecular field is 9. Ry and U =.2 Ry. This figure is taken from [48]. paring to the single MTJ junction, the emittance also shows peaks with varying energy and their positions are accordance with the resonant peaks for the linear conductance. The nonlinear conductance G 111 shows a different dependence on the angle θ, which develops a single peak around θ =.1π and decreases to zero around θ = π/2. For θ [π/2, π], G 111 is identically vanishing. 3.3 FM-QD-FM We studied AC spin transport in FM-QD-FM system [29]. The formulas are explained in the preceding subsection about the dc transport in FM-QD-FM. In the system with two FM terminals, we shall consider a particular situation in which only a DC bias is applied between the two terminals while an ac bias voltage is applied to the central spacer region such as Δ d (t) = V cos(ω t). In this case, J L ( mn m n ) = J2 m ( V ω ) = J R ( mn m n ), m = n and ε L = εr = ε + mω = ε. The timeaveraged current becomes J = e ( ) dω V 2π J2 m [ f L (ω) f R (ω)] ω m Tr σ [Γ L G r d (ω, ε )Γ RG a d (ω, ε )], (22) where J m ( V ω ) is the m-th order Bessel function. The effective transmission coefficient is given by T ef f = 1 2 m Jm 2 ( V ω )Tr σ [Γ L G r d (ω, ε )Γ RG a d (ω, ε )]. At low temperature and under a small dc bias, the integral can be performed by noting lim T,Vdc ( f L (ω) f R (ω))/ev dc = δ(ω E f ). As a result, we can get the tunnel conductance G = 2e2 h T ef f(e f ) as well as the TMR= (G P G AP )/G P. It can be seen that the effective transmission coefficient and the TMR exhibit resonant peaks at certain values of ε,and the curves are symmetric to the axis ε = E f. These resonant peaks occur at the positions of the photonic sidebands 3.4 Spin dynamics excited by laser in semiconductor quantum ring and spin-field effect transistor Semiconductor is one of main avenue of the research of spintronics. A key issue for the spin-based applications relies on the spin-orbit interaction (SOI). The SOI has a key role in spin-interference device (e.g. quantum ring) [5] and the reputed spin field-effect transistor (SFET) [51]. A large conductance modulation effect was predicted to be the consequence of the spin interference in the former and the spininjection and detection in the latter. Our studies will be primarily concentrated on these two aspects in the quantum ring structure and SFET. The purpose is to explore if it is possible to have a strong and flexible ability to trigger or control the spin dynamics in these structures. We consider explicitly a type of laser which is linearly polarized, picosecond, asymmetric electromagnetic pulse. The optical cycle of the electric field of the asymmetric pulse consists of a short halfcycle followed by a much longer and weaker half-cycle of an opposite polarity. Hence, under certain conditions, the external field acts as a unipolar pulse and therefore it is referred to as a half-cycle pulse (HCP) [52]. Effective transmission coefficient m=2 m=3 (c) m=2 m=1 m=1 m= m=1 m= 1 m= 1 m= 2 m= 2 m= m= m= (d) m= m=3 m=2 m= m= ε Figure 19 Effective transmission coefficient and TMR vary with the energy of the central spacer, where α = V /ω, ω =.3, P =.6, and E f = 5. α = 1.4, α = 2, (c) α = 3, and (d) α = 4. The effective transmission coefficient is calculated at θ = π/3. α = V /ω.thisfigure is taken from ref. [29]. TMR

13 178 Zhu Z G, et al. Sci China-Phys Mech Astron January (213) Vol. 56 No Quantum ring Single HCP. In a series of papers, we studied the optical excited spin dynamics in semiconductor quantum ring in which Rashba SOI exists [53]. We investigated the spin-dependent dynamical response of a quantum ring with a spin-orbit interaction upon the application of HCPs. We found that (1) The SOI strength has a dramatic influence on the low frequency modulation of the dipole-moment envelope. The low frequency is associated with the difference between the frequencies of the involved levels near the Fermi level. The SOI strength can be tuned as to influence the phases of the involved wave functions changing thus the interference pattern; (2) The SOI shifts the frequencies of the resonant oscillations; (3) The SOI results in a SU(2) flux leading to a splitting of the phases of the up- and down-spin states. The symmetric axes of the spin-resolved, field-induced-nonequilibriumcharge-density variation for the up and down spins are rotated equally clockwise and anticlockwise when increasing the SOI. The total variation and the local and temporal polarization of the charge density are symmetric to, respectively, the light polarization axis and the axis perpendicular. The pulse-induced polarization is experimentally accessible by measuring the power spectrum of the emitted radiation. The oscillations of the generated dipole moment are sensitive to the parity of the occupation number in the ring and to the strength of the SO coupling. It is shown how the associated emission spectrum can be controlled via the pulse strength or a gate voltage. In the presence of the SOI and for a paramagnetic ring, the applied pulse results in a spinsplit, nonequilibrium local charge density. The resulting temporal spin polarization is directed orthogonal to the lightpulse-polarization axis and oscillates periodically with the frequency of the spin-split charge density. The spin-averaged, nonequilibrium charge-density possesses a left-right symmetry with respect to the pulse polarization axis. The calculations presented here can be applicable to nanometer rings fabricated in heterojuctions of III-V and II-VI semiconductors containing several hundreds of electrons. Two HCPs. If the pulse is absent but an external static magnetic field is present, there will be a persistent charge current and persistent spin current generated in the ring by the SOI. When a single pulse is applied further, no more net charge and spin current can be induced in the quantum ring because of the degeneracy of the orbital states (the degeneracy of clockwise rotating and the anticlockwise rotating) except the existing persistent charge and spin current. However, applying a second pulse with a perpendicular polarizationtothefirst one breaks such degeneracy and leads to a non-equilibrium dynamic charge (spin) current, in addition to the persistent charge and spin current. The variation of the PCC(PSC), DCC (DSC) and TCC (TSC) with the external flux φ are shown in Figure Optical spin field effect transistor In this subsection, we will study here the SFET with 1D channel to maximize the spin coherence (see in Figure 21). HCPs can be irradiated to the device. Our aim is to study if and how the spin dynamics and transport in the SFET can be controlled by the applied HCPs [54]. It is shown, for the polarization of the laser field in the transport direction, that (1) the pulse field delivers a transient momentum transfer (which is proportional to the momentary vector potential) and a net momentum given by the field-amplitude time integrated over the field duration; for harmonic fields this quantity vanishes whereas for HCP it is finite and is equal to the transferred momentum. (2) This momentum boost is experienced by all the electrons speeding up the device operation. (3) The phase difference between the up and down spins is maintained as for the static case, that is, the operation speed is changed by an amount proportional to the field strength while the spin coherence is unchanged, a fact exploitable for the realization of an ultrafast SFET. For the case where the polarization of the laser field is perpendicular to the 2D electron gas, the laser field will induce Charge current and spin current PCC PSC DCC DSC 4 TCC 4 (c) TSC φ/ φ Figure 2 Persistent charge (spin) current (PCC, PSC), the dynamical charge (spin) current (DCC, DSC), and the total charge (spin) current (TCC, TSC) are shown in, and (c), respectively. The solid lines stand for the charge current, and the dash lines are for the spin current. γ = 4,the electron number on the ring is N = 1, the radius of ring is a = 1 nm, the delay of the two pulses is τ = 26.3 ps, the magnitude of the laser field is F 1 = F 2 = 1kV/cm. Here Y indicates the strength of the SOI and related to tan γ = ω R /ω,where ω R = 2α R /a, α R being the Rashba coefficient, ω = 2 /(m a 2 )andm being the effective mass of the semiconductor material. This figure is taken from the second reference in ref. [53]. y z Ferromagnet Static E(t) field ε Gate Insulating layer Conductive channel Ferromagnet Figure 21 Schematics of the optically driven spin field transistor. Ferromagnetic leads are separated from the conductive channel by a tunneling barrier to enhance the spin injection efficiency. A metallic gate is used to tune the Rashba SOI via a static field ɛ. E(t) is the time-dependent electric field. x