classic model ofspin transportmodel of spindown/spinup bandsmore chapters on this topic:IntroductionBasic Transport equationsSpin and charge currentsSpin drainNonmagnetic metalsFerromagnetic metalsSemiconductors (Basic)Threshold spin currentSpin gain/dampingSpin RelaxationSpin Hall/ Inverse Spin Hall effectseeinteractionclassic model ofspin transportmodel of spindown/spinup bandsmore chapters on this topic:IntroductionBasic Transport equationsSpin and charge currentsSpin drainNonmagnetic metalsFerromagnetic metalsSemiconductors (Basic)Threshold spin currentSpin gain/dampingSpin RelaxationSpin Hall/ Inverse Spin Hall effectseeinteractionclassic model ofspin transportmodel of spindown/spinup bandsmore chapters on this topic:IntroductionBasic Transport equationsSpin and charge currentsSpin drainNonmagnetic metalsFerromagnetic metalsSemiconductors (Basic)Threshold spin currentSpin gain/dampingSpin RelaxationSpin Hall/ Inverse Spin Hall effectseeinteraction 
Introduction
Spin and Charge Transport. Classical model of the spinup/spindown band.It is important!!!! All data on this page are calculated based on the model of the spinup/spindown bands. The model of the spinup/spindown bands ignores the fact that the spin is often rotated after spinindependent scatterings(See here). Therefore, some predictions based on this model may be incorrect and differ from a experimental observation. . For the modified model, which includes all abovementioned facts, click here or hereAbstract:Based of assumptions of the model of the spinup/spindown bands, I will study the features of spin transport in different materials. I will obtain the equations, which describe spin and charge transport. I will explain several new spinrelated effects. I will show that there is a charge accumulation along spin diffusion in a ferromagnetic metal, which causes a shortening of the spin diffusion length. I will show that there is a substantial interaction between the drift and diffusion currents in semiconductors, which causes several new of spin transport. The effects of gain/damping of a spin current by a charge current and the existence of a threshold spin current in a semiconductor were described. Because of the substantial magnitude, these new spintronics effect might be used for new designs of efficient spintronics devices. I will discuss the influence of a spin drain on spin transport.Important note:
This part is based on the model of spinup/spindown bands. The model of spinup/spindown bands has been used and it is used by many researchers. There are several incorrect assumptions and oversimplifications of the model of the spinup/spindown bands. The basic assumption of this model, that electrons of only two opposite spin directions can coexist for a long time, is incorrect. This is because the spin rotation during frequent spinindependent scatterings mixes up the electrons all spin directions within a very short time. However, several results, which are predicted by this model, are the same as result obtained by the correct calculations. For example. the properties of Spin drain or the properties of the Drift Charge Current and Diffusive Spin Current are correctly described by this model. They are the same as obtained by the correct calculations.
My modifications of the model of spinup/spindown bands: In order to make model of spinup/spindown bands to be better fit to the realistic spin distributions in the electron gas, I have introduce several modifications to the model of spinup/spindown bands (See here): (1) I have assumed that the conductivities of the spinup and spindown bands are different. It significantly improves the correctness of the model. For example, in case of the spin transport in a semiconductor the modified model of spinup/spindown bands gives almost the same predictions as the correct calculations. (See here).
ContentSpin transport in bulk1. Spin and Charge Transport Equations For the last 20 years, spin transport in solids has been successfully described by the ValetFert spin diffusion equation:
The ValetFert equation describes spin diffusion from regions of larger spin accumulation towards regions of smaller spin accumulation. It does not include any term describing the interaction between a spin current and a charge current. I will show that in the case of a material with spindependent conductivity the requirement of spin and charge conservation leads to the spin/charge transport equations: These equations include terms that describe the interaction between charge and spin currents. 2. Spin transport in nonmagnetic metals A nonmagnetic metal is defined here as a conductive material, the conductivity of which is independent on spin polarization. I will show that in the case of nonmagnetic metals the spin/charge transport equations converge to ValetFert spin diffusion equation.
Utilizing simple approximations I will show that the spin relaxation is linearly proportion to spin chemical potential .
7.Semiconductors. Basic Equations. The conductivity of semiconductors is spindependent only in the presence of a spin accumulation. There is a substantial interaction between the diffusion and drift currents in semiconductors. Here I have obtained a set of 5 equation, which describes the spin and charge transport in the semiconductors.
The same content can be foundin V. Zayets Phys. Rev. B 86, 174415 (2012) (clich here to download pdf);or http://arxiv.org/abs/1205.1278

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