Dr. Vadym Zayets

Possible confusion!!: from 2014 to 2017 I have used names TIA and TIS for groups of spin-polarized and spin-unpolarized electrons, respectively. The reasons are explained here.

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1.Basis of the models

Model of the spin-up/spin-down bands

Assumption: There are two independent spin-up/spin-down bands, which may have different Fermi energies. The electron spins of one band are aligned in the opposite direction to the spin direction of the electrons of the other band.

Weak point: It fails to describe the case when the direction of spin polarization changes in the space.

It has many contradictions. Because of the contradictions, it needs to use a large number of "toy" models in order to fit this model to experimental facts.

Model of the TIA/TIS assemblies

Quantum-mechanical fact: The spin direction may be rotated after spin-independent scatterings.

as result: The electrons in the electron gas can be divided into two groups. In one group there is no spin alignment. In this group electron spins are distributed with an equal probability in all directions. The Fermi energy is the same for all electrons.

This model has no contradiction. It is matched well with all experimental facts.

Comments

if the basis of the spin-up/spin-down bands is based on the assumption (that all spins are directed only in two opposite directions), the presented model is based on the solid Quantum-mechanical fact (that spin are rotated after frequent spin-independent scatterings)

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2.Spin/Charge Transport Equations

For both models the Spin/Charge Transport Equations are derived from the Spin and Conservation Laws.

Model of the spin-up/spin-down bands

The independent variables and the chemical potential and the difference of spin-up and spin-down chemical potentials

where beta is the relative difference between the spin-up and spin-down conductivities.

 

Model of the TIA/TIS assemblies

independent variables and the chemical potential (mju) and the spin polarization of electron gas sp

Comments

Even though the spin/charge transport equations in both models are similar, there are still substantial differences. If in the presented model the transport is described by 4 conductivities, in the model of spin-up/spin-down bands, the transport is described only by 2 conductivities.

The model of spin-up/spin-down bands incorrectly predicts that

It means that the spin injection effect and spin detection effect should exists always simultaneously. That is clearly incorrect. For example, it means that the spin detection effect should exists in the bulk of a ferromagnetic metal and semiconductor. It contradicts with the experimental data.

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3.Spin Injection

The spin injection is drifting of a spin accumulation from one point to another point (Usually from a ferromagnetic metal into a non-magnetic metal or a semiconductor). The spin injection is described by the spin injection conductivity (in the both models)

Model of the spin-up/spin-down bands

In this model, the spin injection is an interface effect. At an interface between a ferromagnetic metal and a non-magnetic metal, a drift spin current are converted into a diffusion spin current and the diffusion spin current diffuses into the non-magnetic metal.

The injection conductivity is:

- always zero in a non-magnetic metal.

-always non-zero in a ferromagnetic metal, because of different density of states for the spin-up and spin-down bands

-in a semiconductor: it is zero, when there is no a spin accumulation. It is not zero, when there is a spin accumulation. It is because the conductivity of a semiconductor depends on a position of the Fermi level. When the the Fermi level of the spin-up and spin-down bands are different, the conductivities of bands becomes different.

Model of the TIA/TIS assemblies

In this model, the spin injection is the effect, which occurs in the bulk of a conductor. Even without a charge current, the spin accumulation diffuses from a ferromagnetic metal into a non-magnetic metal, because of the Spin Proximity effect. The charge current only modifies the spin distribution in the vicinity of the contact.

Origin of the spin injection: The spin diffusion length elongates or shorten when spins diffuse along the flow of a charge current. This effect is well studied and verified experimentally (See here)

The injection conductivity is:

- large in a semiconductor

-small (but non-zero) in metals (ferromagnetic and non-magnetic)

There are two types of the spin injection:

1) the bulk spin injection. It is the case when the spin-injection conductivity of ferromagnetic and non-magnetic metals is of the same sign (electron-type or hole-type). In the case the spin accumulation increases deeply in the bulk of the non-magnetic metal when charge current flows through the contact.

2) the interface spin injection. It is the case when the signs of the spin-injection conductivity of ferromagnetic and non-magnetic metals is opposite . In the case the spin accumulation increases at the contact interface, but it decreases deeply in the bulk of the non-magnetic metal.

Comments

The model of the spin-up/spin-down bands can not explain the features of the spin injection (for experimental facts See here). For example, it can not explain the bulk increase/decrease of spin diffusion length the spin proximity effect and related features. Even though in a semiconductor, the model can describe the change of the spin diffusion length, the description by this model is still incorrect, because of incorrect prediction of the non-zero spin detection conductivity.

 

 

 

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4.Spin Detection

Along the spin diffusion the charge may be accumulated. The voltage, which is induced by the charge accumulation, can be measured and the magnitude of the spin current can be evaluated.

Model of the spin-up/spin-down bands

In this model, a spin current is detected when the conductivity of the spin-up and spin-down bands is different.

The spin-detection conductivity is equal to

The spin-detection conductivity is:

- always zero in a non-magnetic metal.

-always non-zero in a ferromagnetic metal, because of different density of states for the spin-up and spin-down bands

-in a semiconductor: it is zero, when there is no a spin accumulation. It is not zero, when there is a spin accumulation. It is because the conductivity of a semiconductor depends on a position of the Fermi level. When the the Fermi level of the spin-up and spin-down bands are different, the conductivities of bands becomes different.

- can be large in tunnel junction, when the tunnel resistance is the spin-dependent.

 

Model of the TIA/TIS assemblies

In this model, a spin current is detected when the conductivity of the TIA assembly (spin-polarized electrons) and the conductivity of the TIS assembly (not spin-polarized electrons) are different.

The spin-detection conductivity is:

-zero in the bulk of metals and semiconductors without defects.

-non-zero in the vicinity of the contact

- non-zero in the bulk of metals and semiconductors with defects.

Comments

I do not know any experiment, which indicate that there a significant spin detection in the bulk of a metal or a semiconductor. The spin detection occurs only in the vicinity of a contact. It is exactly as the model of the TIA/TIS assemblies predicts. Obviously, the prediction of the Model of the spin-up/spin-down bands about a large spin detection in the bulk of ferromagnetic metals and semiconductors is incorrect.