Because of the technical difficulties of solving spin transport equations in inhomogeneous systems, different resistor networks are widely applied for modeling spin transport. By comparing an analytical solution for spin injection across a ferromagnet -paramagnet junction with a resistor model approach, its essential limitations stemming from inhomogeneous spin populations are clarified.
PACS numbers:Conventional electronics is based on a single parameter of electron, its charge. Therefore, electronics deals only with electron trajectories. It does not involve electron spin, its internal degree of freedom. The new paradigm of spin-based electronics, or spintronics, is based on active involvement of electron spin in transport and optical phenomena, and on employing electron spin for both information processing and information storage. During the last decade, semiconductor spintronics developed into a wide and diversified field. Early review papers [1, 2] were followed by more recent surveys covering specific scientific problems and technological perspectives of this rapidly developing field [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. There exists close connection between the recent work on electric spin manipulation in low-dimensional systems and the previous work on anomalous Hall effect [18], electric dipole spin resonance [19], optical orientation [20] and photogalvanic effect [21,22] in three-dimensional systems. Strong impetus for semiconductor spintronics was given by the discovery of giant magnetoresistance in metallic systems [23,24] and by its impressing practical applications.Spin injection from ferromagnetic sources into paramagnetic media is believed to be an important part of the new phenomena and applications in the field of the spin-polarized electron transport. The concept of a field effect spin transistor [25] served as one of the stimuli. Successful experiments on spin injection into superconductors [26] and normal metals [27] were very promising, and theoretical work supported reliability of the idea [28,29,30,31,32,33]. Successful detection of the floating potential (spin-e.m.f., electromotive force [34]) at a ferromagnetic probe became an independent confirmation of efficient spin injection. Meantime, the methods that resulted in a remarkable success in spin injection from ferromagnetic metals into paramagnetic metals turned inefficient as applied to the spin injection from ferromagnetic metals into semiconductors. Spin injection at the level of only about 1% was reported [35,36], and persuasiveness of the results was disputed [37,38]. Absence of any measurable spin-e.m.f. also indicated that the concentration of the electrically injected nonequilibrium spins was vanishingly small [39].Inefficiency of a "perfect" contact between a ferromagnetic metal and a semiconductor as a spin emitter, that seemed puzzling, found its natural explanation in the framework of the conductivity mismatch concept [40]. The next step was proposing resistive spin selective contacts, like tunnel or Schottky barriers, a...