Spin accumulation in small ferromagnetic double-barrier junctions

Abstract

The nonequilibrium spin accumulation in ferromagnetic double barrier junctions is shown to govern the transport in small structures. Transport properties of such systems are described by a generalization of the theory of the Coulomb blockade. The spin accumulation enhances the magnetoresistance. The transient nonlinear transport properties are predicted to provide a unique experimental evidence of the spin accumulation in the form of a reversed current on time scales of the order of the spin-flip relaxation time. ͓S0163-1829͑99͒05302-3͔In the 1970s it was understood that electron transport in tunneling and heterostructures involving metallic ferromagnets is associated with nonequilibrium spins. 1,2 Compared to other time scales in electron transport the spin relaxation time is generally very long at low temperatures, being limited only by scattering at paramagnetic impurities and by spin-orbit scattering. The spin-relaxation time and the spindiffusion length which govern the spin accumulation has been measured by Johnson in polycrystalline gold films. 3 The concept of nonequilibrium spin accumulation plays an important role in the Boltzmann theory of transport of the giant magnetoresistance in the current perpendicular to the plane ͑CPP͒ configuration. 4,5 However, the experimental evidence for the spin accumulation is indirect at best. It can be shown that in the linear response regime the spin-and charge-distribution functions can be completely integrated out of the transport problem, which then depends exclusively on the scattering probabilities and the applied bias. 5 In this paper we show theoretically how unambiguous evidence for a nonequilibrium spin accumulation can be obtained by the dc and ac response of ferromagnetic double barrier junctions in the nonlinear regime. These junctions have to be small in order to observe large effects, which means that the complications of the Coulomb blockade have to be taken into account ͑for a review see Ref. 6͒. To this end we have to extend very recent theories of the Coulomb blockade in ferromagnetic double barrier junctions 7 to include time dependence and a nonzero spin relaxation time. 8 Ono et al. succeeded in fabricating a ferromagnetic single electron transistor, 9 which in principle can be used to test our predictions. Coulomb charging effects have also been seen in discontinuous multilayers 10 and in small cobalt clusters. 11 We first show that the spin accumulation in ferromagnetic double barrier junctions becomes relevant when the number of electrons in the island between the tunneling barriers is relatively small. In ferromagnetic structures where the tunneling rates depend on the electron spin, a finite current through the system is accompanied by a spin current out of or into the island (‫ץ‬s/‫ץ‬t) tr . This creates a nonequilibrium excess spin s on the island, which decays with the spin-flip relaxation time sf so that in steady state (‫ץ‬s/‫ץ‬t) tr ϭs/ sf . Energy relaxation is much faster than spin relaxation, so that the occupation of the states for...

Spectroscopy of discrete energy levels in ultrasmall metallic grains

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