SCIENCE CHINA Physics, Mechanics & Astronomy Article June 2014 Vol.57 No.6: 1057 1062 doi: 10.1007/s11433-014-5433-1 Spin filtering magnetic modulation and spin-polarization switching in hybrid ferromagnet/semiconductor structures XU HuaiZhe 1*, WANG LiYing 1, YAN QiQi 1, ZHANG YaPing 2* & ZHANG ShiChao 3 1 State Key Laboratory of Software Development Environment and Department of Physics, Beihang University, Beijing 100191, China; 2 Faculty of Engineering, The University of Nottingham Ningbo, Ningbo 315100, China; 3 School of Materials Science and Engineering, Beihang University, Beijing 100191, China Received December 18, 2013; accepted February 12, 2014; published online March 24, 2014 Electron spin-polarization modulation with a ferromagnetic strip of in-plane magnetization is analyzed in a hybrid ferromagnet/semiconductor filter device. The dependencies of electron spin-polarization on the strip s magnetization strength, width and position have been systematically investigated. A novel magnetic control spin-polarization switch is proposed by inserting a ferromagnetic metal (FM) strip eccentric in relation to off the center of the spin filter, which produces the first energy level spin-polarization reversal. It is believed to be of significant importance for the realization of semiconductor spintronics multiple-value logic devices. spin-dependent transport, spin polarization switch, magnetic manipulation, spin filter PACS number(s): 85.75.-d, 75.47.-m, 72.25-b, 72.25.Dc Citation: Xu H Z, Wang L Y, Yan Q Q, et al. Spin filtering magnetic modulation and spin-polarization switching in hybrid ferromagnet/semiconductor structures. Sci China-Phys Mech Astron, 2014, 57: 1057 1062, doi: 10.1007/s11433-014-5433-1 1 Introduction Recently, the spin-related effects in various semiconductor structures have stimulated extensive interest in the development of spintronics devices [1], where not only the electron charge, but also its spin is employed in achieving new functionalities in microelectronic devices. The spintronics devices are expected to have nonvolatility, higher integration densities, lower power operation and higher switching speeds. By using the interaction of the intrinsic spin of a two-dimensional electron gas (2DEG) with the magnetic field via the giant Zeeman Effect [2 16], the electron-spin polarization properties have been brought out in a wide variety of structures, such as magnetic dots, superlattices, quantum wires, and transverse steps, whose structures are *Corresponding author (XU HuaiZhe, email: hzxu@buaa.edu.cn; ZHANG YaPing, email: yaping.zhang@nottingham.edu.cn) realizable experimentally in non-planar 2DEG [17], or by patterning ferromagnetic material or superconducting material [18]. Examples of this new area of research are studies of giant magnetoresistance (GMR) devices, spin-dependent tunneling devices, and spin transistors. The interesting features of these devices rely on both the spin of the current carriers and the relative magnetization of two or more ferromagnetic films to achieve modulation of electrical transport properties. Previously, it had been proposed that a simple spin filter device could be realized by depositing two ferromagnetic metal (FM) strips on top of semiconductor 2DEG heterostructures [19], and the spin polarization of this hybrid spin filter could be electrically modulated by inserting a Schottky-metal (SM) strip. By changing the applied voltage of SM strip, the electron spin-polarization of the spin filter would be easily shifted. However, the electric control could never realize the spin-polarization reversal, although it is critical Science China Press and Springer-Verlag Berlin Heidelberg 2014 phys.scichina.com link.springer.com
1058 Xu H Z, et al. Sci China-Phys Mech Astron June (2014) Vol. 57 No. 6 for the realization of spin logic calculations [20]. Here, we explore the possibility of magnetic modulation of the spin-polarization in a spin filter device by introducing an in-plane magnetization FM strip. First, we systematically characterize the electron spin-polarization and the relative spin conductance excess dependences on the new magnetic barrier s width, magnetization strength, and position. Then, we design a magnetic control spin-polarization switch that is realized by properly inserting the new FM strip off the center of the spin filter device, which shows the spinpolarization reversal of the first energy level. This interesting spin polarization switching effect is of importance for the development of semiconductor spintronics multiplevalue logic devices, and the use of spin in conjunction with charge leads to switching devices with very low power dissipation. 2 Model and theoretical calculations We consider a typical spin-filter device consisting of a double magnetic-barrier structure, which can be achieved by depositing two FM strips on top of semiconductor 2DEG, with the two FM strips being magnetized parallel to the surface of the 2DEG, but opposite to each other [19,20]. We assume that a third FM strip is inserted between the two ferromagnetic strips. Its magnetization direction could be parallel to the left or right of FM strip, and its magnetization strength is tunable by varying its magnetization current, as schematically illustrated in Figure 1. The magnetic field for such an arrangement can be expressed as: with B B ( x ) z, (1) Bz ( x) B1[ ( x) ( x d)] B2[ ( x d w1) ( x d w1 b)] B1[ ( x d w1 b w2) ( x 2 d w w b)]. z 1 2 Here B 1 and B 2 are the strength of the magnetic fields, d and b are the width of the magnetic barriers, w 1 and w 2 are the (2) distances of the new magnetic barrier to the front or to the rear magnetic barrier, respectively. The magnetic field B z (x) is assumed to be homogeneous in the y direction and only varies along the x direction. The magnetic vector potential A(x) in the Landau gauge is given as: B1 y, 0 x d, 0, d x d w1, A( x) B y, d w x d w b, 2 1 1 0, d w1 b x d w1 b w2, B1y d w1 b w2 x d w1 b w2, 2. To evaluate the effect of magnetic manipulation on spin polarization, we have systematically characterized the dependence of P T and P G on the magnetization strength (B 2 ) of the inserted FM strip and its width (b), as well as its position relative to the two FM strips (w 1 or w 2 ). Here, the spin polarization is defined by the polarization of transmitted beams P T =(T T )/(T +T ) and the relative spin conductance excess P G =(G G )/(G +G ), where T (G ) and T (G ) are the transmission probability (conductance) of electrons with spin up and down, respectively [21]. 3 Results and discussions In the following numerical calculations, all the relevant quantities are expressed in dimensionless units [19,20]. The material parameters of an InAs system are used, with the electron effective mass m*=0.024m 0 and g*=15, m 0 the free electron mass in vacuum, and the structural parameters assumed as d=0.5l B, B 1 =9.0B 0, and L=w 1 +w 2 +b=1.5l B, respectively. Figures 2(a) and (b) show P T and P G at magnetic barrier strength B 2 =0, 2, 3, 4, respectively. Here b is taken to be 0.5. It is seen that the whole spectrum shifts gradually to higher energies as B 2 increases, with P G at the resonance energies still being close to unity (~100%), even though the system s effective potential symmetry is broken by inserting the extra magnetic barrier. It is also seen that the maximum of P G forms a plateau with its width coinciding with that of the (3) Figure 1 (a) and (c) show FM strips arrangement and magnetizations, respectively; (b) and (d) show the corresponding magnetic field profiles, respectively.
Xu H Z, et al. Sci China-Phys Mech Astron June (2014) Vol. 57 No. 6 1059 Figure 2 (Color online) (a) and (b) show P T and P G with B 2 =0, 2.0, 3.0, 4.0, and b=0.5, respectively; (c) and (d) show E +/ (+/ are for spin up or spin down) and E=(E E + ) vs. B 2, respectively. resonance energy spin splitting E=(E E + ), and the plateau of E 1 is wider than that of E 0 due to a wider spin splitting of E 1. However, the conductance plateau value drops as the energy transits from the spin-up to the spin-down resonance energies, and the decrease trend for E 1 is more obvious than that for E 0. Figure 2(c) shows E +/, (+/ are for spin-up or spin-down) versus B 2. As B 2 increases, the shift-up of E 0 becomes more obvious than that of E 1, which finally leads to the spin-up energy of E 0 crossing the spin-down energy of E 1 at B 2 ~9.2. Figure 2(d) shows the spin-splitting width E for E 0 and E 1 versus B 2. The spin-splitting for both E 0 and E 1 becomes narrower as B 2 increases, and the spin splitting E of E 1 is larger than that of E 0 due to the stronger Zeeman interaction of E 1. Figures 3(a) and (b) show P T and P G curves with b=0, 0.25, 0.5, 0.75, and B 2 =3.0, respectively. Both E 0 and E 1 shift to higher energies as b becomes wider. But E 0 moves rapidly at b<1.0, and it is saturated at 1.0<b<1.5; while E 1 shifts slowly at b<0.5, it shifts faster at 0.5<b<1.0, and finally, it is saturated at 1.0<b<1.5. Figures 3(c) and (d) plot the resonance energies (E +/ ) and the spin-splitting width E for E 0 and E 1 versus b. The spin splitting E of E 0 reaches the maximum at b~l/2, while the spin splitting E of E 1 reaches the maximum at b~2l/3. Figures 4(a) and (b) show P T and P G curves with w 1 =0.25, 0.5, 0.625, 1.0, respectively, and Figures 4(c) and (d) show the corresponding resonance energies E +/ and the spinplitting E of E 0 and E 1 versus w 1. Here B 2 =3.0 and b=0.25. It is interesting that the spin splitting of both energy states could be significantly modulated by changing the inserted strip s position, as the resonance energies E 0 (w 1 ) and E 1 (w 1 ) reflect the electron s probability distribution variation between the two magnetic barriers. When the magnetic barrier is located at a position where the electron probability is larger, the interactions between the magnetic field and the electron are stronger, and thus lead to an obvious shift of resonance energy. In addition, the resonance energies and the spin splitting are also asymmetric to the center due to the asymmetric arrangement of the magnetic field. When the new FM is inserted off the center of the device, the spin splitting of E 0 could be larger than that of E 1, and thus the spin polarization of E 0 can be reversed. When the magnetization direction of the inserted strip is changed to parallel to the right strip, as is shown in Figures 1(c) and (d), all the results shown in Figures 2 and 3 will not change, but w 1 and w 2 in Figure 4 will exchange with each other, as the profile of Figure 1(b) is asymmetric to that of Figure 1(d). Based on the results illustrated in Figure 4, we designed two spin-polarization switches, and their configurations are schematically shown as the insert in Figure 5. With B 2 =3.0, b=0.25, w 1 =1.0 and w 2 =0.25 for strip A; or with B 2 = 3.0, b=0.25, w 1 =0.25 and w 2 =1.0 for strip B, respectively, these two switches were realized with the spin filter for the first energy level spin-polarization reversal, as shown in Figures 5(a) and (b). Similar spin polarization switch could also be realized by using ferromagnet/graphene or ferromagnet/topologic insulator structures, even though the motion of electrons is described by 2D Dirac Hamiltonian, rather than the Schrödinger equation [22 24].
1060 Xu H Z, et al. Sci China-Phys Mech Astron June (2014) Vol. 57 No. 6 (Color online) (a) and (b) show P T and P G with b=0, 0.25, 0.5, 0.75, and B 2 =3.0, respectively; (c) and (d) show E +/ and E=(E E + ) vs. b, respec- Figure 3 tively. Figure 4 (Color online) (a) and (b) show P T and P G with w 1 =0.25, 0.5, 0.625, 1.0, and B 2 =3.0, b=0.25, respectively; (c) and (d) show E +/ and E=(E E + ) vs. w 1, respectively. Recently, the experimental demonstrations of similar structure devices had been reported by several groups. For examples, Lin and coworkers [25], Overend and coworkers [26] had fabricated a hybrid Hall device, in which a microstructured ferromagnetic film was incorporated on top of a micron scale Hall cross. This system has potential applications as a magnetic field sensor, a logic gate, or as a nonvolatile storage cell. Wrobel et al. [27] had made a device in which cobalt and permalloy micromagnets were deposited on the GaAs/AlGaAs wire to produce a local in plane spin-dependent potential barrier for high-mobility electrons. Hong et al. [28] had fabricated a device by depositing two 300 nm thick micromagnets on top of the InAs 2DEG mesa by e-beam evaporation of Co. The fringing magnetic fields emanating from nanomagnets in these hybrid ferromagnetic/semiconductor devices were used to modulate the con-
Xu H Z, et al. Sci China-Phys Mech Astron June (2014) Vol. 57 No. 6 1061 Figure 5 (Color online) The first energy level spin-polarization reversal are realized with two configurations of the spin-polarization switches. ductance of a semiconductor channel, allowing the nonvolatile features of magnetism to be introduced into field-effect structures. Thus, we consider that our proposed design is experimentally realizable in the future. 4 Conclusion It has been demonstrated theoretically that the spin-polarization in a hybrid ferromagnet/semiconductor spin filter structure can be effectively modulated by introducing an extra magnetic barrier. As the magnetic barrier strength increases, the spin polarization spectrum shifts gradually to the higher energies, but the extremes of the spin polarization at the resonance energies are still close to unity (~100%); even though the system s effective potential symmetry is broken by the inserted magnetic barrier. Strikingly, the spin polarization of the ground state electrons can be reversed by inserting the magnetic barrier eccentrically. This interesting feature provides an alternative method for the realization of magnetic control spin polarization switches. This spin polarization switching effect provides an important function for the development of semiconductor spintronics multiple-value logic devices. This work was supported by the National Basic Research Program of China (Grant No. 2013CB934003) and the State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2013ZX-28). 1 Wolf S A, Awschalom D D, Buhrman R A, et al. Spintronics: A spin-based electronics vision for the future. Science, 2001, 294(16): 1488 1495 2 Muller J E. Effect of a nonuniform magnetic field on a two-dimensional electron gas in the ballistic regime. Phys Rev Lett, 1992, 68(3): 385 388 3 Matulis A, Peeters F M, Vasilopoulos P. Wave-vector-dependent tunneling through magnetic barriers. Phys Rev Lett, 1994, 72(10): 1518 1521 4 Ibrahim I, Peeters F M. Two-dimensional electrons in lateral magnetic superlattices. Phys Rev B, 1995, 52(24): 17321 17334 5 Dobrovolsky V N, Sheka D I, Chernyachuk B V. Spin- and wavevector dependent resonant tunneling through magnetic barriers. Surf Sci, 1998, 397: 333 338 6 Kubrak V, Rahman F, Gallagher B L, et al. Magnetoresistance of a two-dimensional electron gas due to a single magnetic barrier and its use for nanomagnetometry. Appl Phys Lett, 1999, 74(17): 2507 2509 7 Tan S G, Jalil M B A, Liew T. Spin current induced by in-plane magnetoelectric δ-barriers in a two-dimensional electron gas. Phys Rev B, 2005, 72: 205337; Tan S G, Jalil M B A, Liu X J, et al. Spin transverse separation in a two-dimensional electron-gas using an external magnetic field with a topological chirality. Phys Rev B, 2008, 78: 245321 8 Xu H Z, Okada Y. Does a magnetic barrier or a magnetic-electric barrier structure possess any spin polarization and spin filtering under zero bias. Appl Phys Lett, 2001, 79(19): 3119 3121; Xu H Z, Zhang Y F. Spin-filter devices based on resonant tunneling antisymmetrical magnetic/semiconductor hybrid structures. Appl Phys Lett, 2003, 84(11): 1955 1957 9 Ngo A T, Villas-Boas J M, Ulloa S E. Spin polarization control via magnetic barriers and spin-orbit effects. Phys Rev B, 2008, 78: 245310 10 Chen X, Li C F, Ban Y. Tunable lateral displacement and spin beam splitter for ballistic electrons in two-dimensional magnetic-electric nanostructures. Phys Rev B, 2008, 77: 073307 11 Wang Y, Chen N F, Jiang Y, et al. Ballistic electron transport in hybrid ferromagnet/two-dimensional electron gas sandwich nanostructure: Spin polarization and magnetoresistance effect. J Appl Phys, 2009, 105: 013708 12 Governale M, Boese D. Magnetic barrier in confined two-dimensional electron gases: Nanomagnetometers and magnetic switches. Appl Phys Lett, 2000, 77(20): 3215 3217 13 Papp G, Vasilopoulos P, Peeters F M. Spin polarization in a twodimensional electron gas modulated periodically by ferromagnetic and Schottky metal stripes. Phys Rev B, 2005, 72: 115315 14 Zhai F, Xu H Q, Guo Y. Tunable spin polarization in a two-dimensional electron gas modulated by a ferromagnetic metal stripe and a
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