Theory of the perpendicular magnetoresistance in magnetic multilayers

Abstract

By starting with the Boltzmann equation, we calculate the transport properties of magnetic multilayers for currents perpendicular to the layers. Our model takes into account both volume and interface spin-dependent scattering. We show that the macroscopic equations already used by Johnson et al. or van Son et al. are justified if the spin-diffusion length is much longer than the mean free path, even for individual layer thicknesses of the order of the mean free path. But, second, we show that Johnson's assumption of additive effects from independent interfaces in multilayers is incorrect and we obtain different results by taking into account the interplay between successive interfaces. The simple expressions derived for individual thicknesses much shorter than the spin-diffusion length are in agreement with the analysis of experimental results already proposed. It turns out that data on the perpendicular magnetoresistance can be used to separate clearly the volume and interface contributions to the spindependent scattering.

Efficient thermal spin injection using CoFeAl nanowire

“…As shown in Figure 2c, the dependences of the spin signal on the interval L for both devices were well fitted using the one-dimensional spin diffusion equation with transparent interfaces, which is given by [23][24][25] …”

Nonequilibrium spin-current detection with a single Kondo impurity

“…However, in the left lead, we expect μ L = μ L↑ − μ L↓ = 2μ L Q to be proportional to I spin . 40 Therefore, the function Q(V ) is highly nonlinear and needs a priori to be determined self-consistently. However, this turns out to be a very difficult task (this is a nonlinear and nonequilibrium interacting problem).…”

“…38 As demonstrated by Johnson 39 (see also Refs. [40][41][42], a spin current induces spin accumulation yielding spin-dependent chemical potentials μ ↑ = μ ↓ , which is equivalent to a spin bias. Using the equation of motion approach, Qi et al analyzed the fate of a Kondo resonance in the presence of spin accumulation.…”

Realization of high quality epitaxial current- perpendicular-to-plane giant magnetoresistive pseudo spin-valves on Si(001) wafer using NiAl buffer layer

“…[1][2][3] The demand of higher areal density exceeding 2 Tbit/in 2 in hard disc drives (HDDs) highlights current-perpendicularplane (CPP)-GMR devices as a potential successor of the present tunneling magnetoresistive (TMR) device for next generation read head sensors due to its intrinsically low resistance area product (RA) for higher frequency responses. [4][5][6][7] Recently, substantial large MR ratios at room temperature (RT) were realized in fully epitaxial CPP-GMR devices with the usage of the Co-based Heusler alloys such as Co 2 MnSi (CMS), 8 Co 2 Mn(Ga 0.25 Ge 0.75 ) (CMGG), 9 Co 2 (Fe 0.4 Mn 0.6 )Si (CFMS), 10 and Co 2 Fe(Ga 0.5 Ge 0.5 ) (CFGG). 11 Such a high MR output in a low resistance device has already satisfied the MR performance required for the areal density of 2 Tbit/in 2 according to the simulation by Takagishi et al 7 However, all of these high MR outputs have only been demonstrated for the epitaxial CPP-GMR pseudospin-valves (PSVs) grown on unpractical MgO single crystalline substrates, which are too expensive for mass production and incompatible with the current semiconductor industry processes.…”