IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010 1323 Achieving Highly Localized Effective Magnetic Fields With Non-Uniform Rashba Spin-Orbit Coupling for Tunable Spin Current in Metal/Semiconductor/Metal Structures Takashi Fujita , Mansoor B. A. Jalil , and Seng Ghee Tan Information Storage Materials Laboratory, Electrical and Computer Engineering Department, National University of Singapore, Singapore 117576 Data Storage Institute,A*STAR (Agency for Science, Technology and Research), Singapore 117608 Computational Nanoelectronics and Nano-device Laboratory, Electrical and Computer Engineering Department, National University of Singapore, Singapore 117576 We theoretically study the spin-dependent transport of conduction electrons across typical metal/semiconductor (SC)/metal struc- tures, where the SC channel exhibits Rashba spin-orbit coupling (SOC) and the metal contacts do not. The spatial discontinuity of the Rashba SOC is shown to result in highly localized, effective magnetic field barriers at the device interfaces. As a result, electrons with oppositely polarized spins along the injection direction are found to be transmitted with different probabilities, resulting in a finite spin polarization. The value of the spin polarization depends sensitively on the Rashba SOC strength within the SC channel, which is well known to be adjustable by an applied gate bias. Thus the proposed structure could be useful as a tunable source of spin-polarized current in spintronic applications. Index Terms—Semiconductor spintronics, spin injection, spin-orbit coupling. I. INTRODUCTION S PIN-DEPENDENT transport across magnetic barriers have been extensively studied in the literature for various barrier shapes. Such proposals naturally define spin filters [1], in which an unpolarized injection current results in a spin-po- larized output current. The shape of the magnetic barrier profile depends on the exact manner in which it is formed. Typically, it involves the lithographic patterning of ferromagnetic (FM) gating structures [2]–[4] or the use of electric currents [2]. The- oretically, spin filtering using magnetic fields was first studied for magnetic barriers formed using FM stripes with in-plane magnetization deposited above a two-dimensional electron gas (2DEG) based trilayer structure [5]. In this configuration, the fringing fields emanating from the stripes penetrate the 2DEG below, forming spatially localized magnetic barriers at the structure interfaces [2]. The resulting magnetic field configuration is often approximated as a pair of asymmetric -Dirac functions [5] (resembling that shown in Fig. 1(c)). Subsequently, many researchers have studied this configura- tion. It has since been established that the asymmetric magnetic field configuration does not result in spin filtering. Instead, a spatially symmetric pair of barriers is required for achieving this purpose [6]–[9]. The use of the -Dirac approximation is attractive due to its simplicity, and because the spin-dependent transport can be characterized by closed analytical formulae of the system pa- rameters. The predicted spin polarization achievable from these Manuscript received October 22, 2009; revised January 14, 2010; accepted March 04, 2010. Current version published May 19, 2010. Corresponding au- thor: T. Fujita (e-mail: t.fujita@nus.edu.sg). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2010.2045478 barriers can approach 100% under certain conditions [7]. How- ever, they are clearly difficult to realize in practice. Experimen- tally, localized magnetic barriers of width 100 nm have been formed e.g. in [10]. For the nanoscale ( 10 nm) structures of interest in our study, such barriers are deemed wide and cannot be suitably modeled as -Dirac functions. Recently, the intrinsic spin-orbit coupling (SOC) in semicon- ductors (SC) has become an important area of study in the field of spintronics. The SOC effect is present in materials and struc- tures which have spatial inversion asymmetry, and causes elec- trons to experience an effective, momentum-dependent mag- netic field which breaks the spin degeneracy of electrons. The structural inversion asymmetry (SIA) of 2DEGs formed in semi- conductor heterojunctions results in the Rashba effect [11], [12], whilst the bulk inversion asymmetry (BIA) of crystal lattices lacking an inversion center results in the Dresselhaus effect [13]. The SOC is important as it allows one to generate spin-polarized currents without the use of external magnetic fields [14]–[20]. In this paper, we consider a typical trilayer structure with a SC channel that is sandwiched between two metallic (M) con- tacts. The SC channel is assumed to have Rashba SOC, while the M contacts do not. We show that the sharp discontinuity of the Rashba SOC inherently gives rise to highly localized effective magnetic field barriers at the interfaces. These effective mag- netic fields are different from the above mentioned momentum- dependent magnetic fields which characterize the SOC. Instead, they result from the spatial discontinuity of the Rashba SOC when viewed from the non-Abelian gauge field picture [21]. In particular, when the Rashba SOC spatial profile is taken to be an ideal step function, the effective fields are perfect -Dirac barriers. We study the spin-dependent transport through the ef- fective fields, showing that a spin-polarized current can be in- duced by them. Numerical simulations of the spin-dependent transport and resulting spin polarization are presented for a typ- ical InGaAs-based heterostructure. We find that the polarization 0018-9464/$26.00 © 2010 IEEE