Charge and spin diffusion in mesoscopic metal wires and at ferromagnet/nonmagnet interfaces

Abstract

Issues related to ''charge-spin coupling'' and the diffusive transport of nonequilibrium spin polarized electrons in nonmagnetic materials and at the interface between ferromagnetic and nonmagnetic materials are discussed theoretically. Equations that govern charge and spin transport in three dimensions are derived and appropriate boundary conditions are discussed. These results are applied to a numerical calculation of spin accumulation and diffusion in a two-dimensional Van der Pauw cross. A detailed model of spin transport at ferromagnetic-nonmagnetic metal interfaces is reviewed, the limiting cases of high and low interface conductance are treated, and the relevance of ''resistance mismatch'' for a variety of experimental systems is analyzed.Two fundamental properties reside with each conduction electron, the unit charge e and the unit magnetic moment B , the Bohr magneton, which is related to the quantum mechanical spin S by B ϭϪ(eប/mc)S, with m the electron mass and c the speed of light. The emerging field of Spintronics ͑Ref. 1͒ relies on ''charge-spin coupling:'' 2 characteristics of charge transport, such as voltage or current, can be modulated in a device structure by manipulating the spin, introducing new control parameters such as magnetic field, or new material properties such as magnetization. Distinct charge-spin coupling effects exist inside bulk materials and also at the interface between a ferromagnetic ͑F͒ and nonmagnetic ͑N͒ material.In a continuous ͑bulk͒ nonmagnetic system, the chargespin coupling that resides with individual electrons leads to the intuition that charge and spin are closely coupled for populations of carriers. This intuition is falsely reinforced by simple one-dimensional transport models where charge and spin flow along the same path. 3 For an ensemble of particles, in fact, the coupling is statistical and is generally weak. There are many possible spin distributions for any single charge distribution. Yet because of the statistics of large populations, the coupling of charge and spin results in substantial effects that can be used for device modulation.Boundary conditions for charge and spin transport are intrinsically different. 4 The electron charge is quantized and never changes, so that total charge is conserved in any conducting sample. By contrast, although electron spin is quantized, spin transport effects are based on spin orientation, a dynamic property. Spin orientation is not conserved in any sample, and the average orientation of a spin population is a continuous variable. Thus, ordinary electrodes on a conducting sample act as both sources and sinks for charge current. A ferromagnetic electrode can act as a source for spinpolarized current, but the sink for spin orientation is random, isotropic spin relaxation. 5 At a ferromagnet/nonmagnetic ͑F-N͒ material interface, the diffusion of polarized spins on both sides of the interface alters charge flow. Electronic interface properties such as resistance are changed, and the net transport of spin across the interfa...

Spin-flip scattering and dimensional effect on transport of charge and spin across metal/ferromagnet material interfaces

“…[8][9][10][11][12] This effect causes the spin-coupled interface resistance, and makes the spin diffusion length in the ferromagnetic material the limiting factor determining spin polarization. 13,14 This problem, called the conductivity mismatch, results in the poor efficiency of spin injection from a metallic ferromagnet into a semiconductor. [15][16][17][18][19] Surprisingly, one way to enhance the efficiency is to insert a thin insulating layer between the two materials.…”

Time-dependent spin-polarized transport through a resonant tunneling structure with multiterminals

“…It is found that the direction of the magnetization of the third FM lead can affect remarkably the current flowing through the first and the second FM leads when the magnetizations of these two leads align antiparallel. In this case, the intrinsic spin relaxation time in the central spacer was assumed to be sufficiently shorter than the order of the time between successive tunneling events such that the spin accumulation effect [21] could be negligible. Furthermore, Jedema et al [22,23] investigated the spin injection and spin accumulation in an all-metal lateral mesoscopic spin valve with multi-terminal.…”

Enhanced spin injection efficiency in a four-terminal quantum dots system

“…Rashba 7 suggested that tunnel contacts can dramatically increase spin injection efficiency, which was supported by subsequent theoretical works. [8][9][10][11] Jiang et al 12 demonstrated that the spin injection efficiency could be improved dramatically by inserting a MgO tunnel barrier between the ferromagnetic contact and the semiconductor. By using circular polarized excitation and detection, it has been demonstrated that the injected spinpolarized carriers are quite robust and maintain their polarization memory even after passing through a dense array of misfit dislocations.…”