My Research and Inventions

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Spin Proximity Effect. Spin Injection

Spin and Charge Transport. Model of TIS/TIA assemblies.

In an equilibrium the electron gas is spin-polarized in a ferromagnetic metal and it is not spin-polarized in a non-magnetic metal . At a contact between a ferromagnetic and a non-magnetic metals, some spin accumulation from the ferromagnetic metal diffuses into the non-magnetic metal. The spin polarization in the ferromagnetic metal near the contact becomes smaller and the spin polarization in the non-magnetic metal becomes non-zero. This effect is called the Spin Proximity effect. This effect is called the Spin Proximity Effect


Note: The model of spin-up/spin-down bands is unable to explain the Spin Proximity effect and it gives incorrect predictions for the Spin Injection.

The same content can be found in this paper (http://arxiv.org/abs/1410.7511 or this site for a more upgraded version) .Chapter 3, pp. 7-11
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.

Spin Injection. Incorrect description by the model of spin-up/spin-down bands

1) Without an applied voltage, all spin accumulation contains only inside the ferromagnetic metal. It is like an invisible wall separates the ferromagnetic and non-magnetic metals from the spin diffusion.

2) When a voltage is applied, the wall is removed and the spin accumulation diffuses into the non-magnetic metal

 

Correct explanation of the Spin Injection and the Spin Proximity effects:

1) Even without an applied voltage the spin accumulation diffuses into the non-magnetic metal

2) The drift current only modifies the distribution of the spin accumulation across the contact:

(a) For one direction of current (the polarity of current depends on the metals), more spins are drifted from the from the ferromagnetic metal into the non-magnetic metal;

(b) For the opposite direction of the drift current, the spin accumulation is drifted back from the non-magnetic metal into the ferromagnetic metal.

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The Spin Proximity Effect

When two metals, which have different spin polarization, are in contact, in the vicinity of the contact interface some spin-polarized electrons (electrons of TIA assembly) diffuse from the metal of a larger spin accumulation into the metal of a smaller spin polarization. For example, in the bulk of a non-magnetic metal the electron gas is not spin-polarized and it is spin-polarized in the bulk of a ferromagnetic metal. Near contact between ferromagnetic and non-magnetic metals the electron gas becomes spin-polarized in the non-magnetic material, because of the spin diffusion into this region from the neighboring region of the ferromagnetic metal. Correspondingly, the spin polarization in the ferromagnetic metal becomes smaller near the contact than in the bulk, because spins were diffused out of there.

It should be noticed that the model of spin-up/spin-down bands is unable to explain the Spin Proximity effect.

The spin diffusion length is the effective length from the contact where the spin diffuses.

The spin-diffusion conductivity describes the Spin Proximity effect


 

The classical model of spin-up/spin-down bands vs. the presented model of the TIS/TIA assemblies

 

Fig.2 Spin Proximity effect. Classical vs. Presented Model

click on picture to enlarge it
Model of the spin-up/spin-down bands. The spin accumulation contains only inside the ferromagnetic metal and can not diffuse into the non-magnetic metal. Presented model. Spin Proximity effect. The spin accumulation diffuses from the ferromagnetic metal into the non-magnetic metal.

 

 

 

 

Within the model of spin-up/spin-down bands it is assumed that in a contact between a ferromagnetic metal and a non-magnetic metal a spin accumulation is contained only inside the ferromagnetic metal and it does not diffuse into the non-magnetic metal (Fig.2 left). Only when a voltage is applied to the contact and a drift current flows through the contact, some of the spin accumulation may be drifted into the non-magnetic metal. This story contradicts with experimental observations . The presented model explains the spin injection and the spin transport through the contact differently. Even without a current nothing prevents a diffusion of a spin accumulation from the ferromagnetic metal into the non-magnetic metal. The spin accumulation decays from the ferromagnetic metal through the contact deep into the non-magnetic metal (Fig. 2 right). The drift current only modifies this distribution.

 

 

 

Click here to see other versions of Fig.2
Contact between ferromagnetic and non-magnetic metals
Classical model. The spin accumulation contains only inside the ferromagnetic metal and can not diffuse into the non-magnetic metal. Presented model. Spin Proximity effect. The spin accumulation diffuses from the ferromagnetic metal into the non-magnetic metal.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Contact between ferromagnetic and non-magnetic metals
Classical model. The spin accumulation contains only inside the ferromagnetic metal and can not diffuse into the non-magnetic metal. Presented model. Spin Proximity effect. The spin accumulation diffuses from the ferromagnetic metal into the non-magnetic metal.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

The Spin Proximity effect. Ferromagnetic particle embedded into a non-magnetic metal

Spin polarization of the electron gas in a ferromagnetic particle is reduced, because the spin accumulation diffuses out from it.

Spin polarization sp of electron gas in ferromagnetic nano-cylinder embedded in a non-magnetic metal

 

Fig. 3. Calculated spin polarization of an electron gas in a ferromagnetic cylinder embedded in a non-magnetic metal. The diameter of the cylinder is 500 nm. The boundary of the cylinder is shown by the black circle. There is a significant spin diffusion from the ferromagnetic metal into the non-magnetic metal.

Notice: more than 3 times reduction of the spin polarization in cylinder compared with the spin polarization of the bulk of the ferromagnetic metal

Material Parameters (Click to expand) and Matlab/Comsol files. Do calculations by yourself !!!!!

Material parameters

The spin polarization of the ferromagnetic metal: 0.6.

The charge conductivity : 2E7 S/m (metal 1) ; 2E7 S/m (metal 2)

. The density of the states at the Fermi level: 2E22 1/cm3/eV (metal 1) .2E22 1/cm3/eV (metal 2)

The spin life time: 30 ps (metal 1); 30 ps (metal 2)

The spin-diffusion conductivity : 2.6E7 S/m (metal 1) ; 2.6E7 S/m (metal 2)

The injection conductivity: 1.4E7 S/m (metal 1) ; 1.4E7 S/m (metal 2)

. The detection conductivity: 0 (metal 1) ; 0 (metal 2)

Temperature is the room temperature.

Data were calculated using the Finite Difference method.

It was assumed that the conductivity near the interface is the same as the bulk conductivity and there is no contact conductivity. It is very rough assumption (See here).

 

 

 

Matlab/Comsol calculation files

calculate by yourself !!!

CrookerMetal.m (Comsol only: CrookerMetal.mph )

CrookerMetalScan.m

 

 

 

The smaller the size of the particle is, the smaller is the spin polarization of the electron gas inside of it.

 

 

 

 

Figure 3 shows the calculated distribution of spin polarization of an electron gas in a ferromagnetic cylinder embedded in a non-magnetic metal. The diameter of the cylinder is 0.5 um. The spin polarization is largest at the center of the cylinder and it becomes smaller at the edge. Even at the center of the ferromagnetic cylinder the largest spin polarization is about 0.13, which is significantly reduced from the bulk spin polarization of 0.6. Around the cylinder the electron gas in the non-magnetic metal is significantly spin-polarized. Therefore, the Spin Proximity effect causes the significant reduction of spin polarization of the electron gas in the ferromagnetic cylinder and it causes a spin polarization of the electron gas in the non-magnetic metal.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Spin Polarization at contact between a ferromagnetic and a non-magnetic metals.

The Spin proximity effect at a contact between a ferromagnetic and a non-magnetic metals.

Fig.3 The ratio of spin polarization at contact interface sp_interface to the equilibrium spin polarization sp0 of the ferromagnetic metal

(left) as the function of the ration of the spin diffusion lengths in the metals. The conductivities of metals is the same;

(right) as the function of the ration of the spin-diffusion conductivities. The spin is the same;

Spin proximity effect at a contact between a ferromagnetic and a non-magnetic metals

Simplest case: 2D geometry; step-like conductivities

Inside of a non-magnetic metal the spin accumulation decays exponentially:

where lambda_non_mag is the spin diffusion length in the non-magnetic metal.

The spin polarization at the contact interface can be calculated as

 

Properties of the Spin Proximity effect:

From Eq. (3.2), the larger amount of spins, which diffuse from the ferromagnetic metal to the nonmagnetic metal, becomes larger when

(1) the conductivity of the non-magnetic metal decrease;

(2) the conductivity of the ferromagnetic metal increase;

(3) the spin diffusion length in the ferromagnetic metal decrease;

(4) the spin diffusion length in the non-magnetic metal increase;

 

 

How to obtain Eq. (3.2) click here to expand

Let us assume that a contact between a ferromagnetic and a non-magnetic metals at x=0

In the non-magnetic metal (x<0) the spin accumulation along the spin diffusion is described as

Corresponded the spin current in the non-magnetic metal is calculated as

In the ferromagnetic metal (x>0) the spin accumulation is described as

where sp0 is the equilibrium spin polarization in the ferromagnetic metal.

Corresponded the spin current in the ferromagnetic metal is calculated as

Through the interface, the spin polarization and the spin current are continuous without a steps. Theses boundary conditions give

or

From Eq.(3.15), the spin polarization at the contact interface is calculated as

 

 

Calculate by yourself

Matlab file: ProximityMetal0.m

Comsol file: Proximity.mph

 

 

 


The Spin Proximity effect vs. the Magnetic Proximity

The Spin Proximity effect should be distinguished from the Magnetic Proximity effect (2014 Review is here). The Magnetic Proximity effect describes the change of magnetic properties of the localized d- or f- electrons in the vicinity of an interface, because of the interlayer exchange coupling. In contrast, the Spin Proximity effect describes the change of the spin polarization of the electron gas of the delocalized sp- electrons, because of the spin diffusion through the interface. Because of the sp-d exchange interaction between the localized and delocalized electrons, both effects are correlated. Still they can be distinguished, because of their different effective lengths. The effective length of the Magnetic Proximity effect and the interlayer exchange coupling does not exceed a few monolayers . In contrast, the effective length of the Spin Proximity effect is longer than several spin-diffusion lengths. Because of the different effective lengths, the Spin Proximity effect and the Magnetic Proximity effect can be distinguished experimentally .

 

 

 

 

 



 

What is the spin injection???

Is it about the breaking of the spin through a contact between a ferromagnetic and a non-magnetic metals?

Answer: It is not. It is a bulk effect.

Click on picture to enlarge it

Spin Injection

 

When a drift current flows through a contact between ferromagnetic and non-magnetic metals, an additional spin accumulation is drifted from the ferromagnetic metal into the non-magnetic metal. For the opposite direction of the current, the spin accumulation in the non-magnetic metal is drifted back into the ferromagnetic metal. This effect is called the spin injection. It is important to emphasize that the spin injection just changes the amount of spin accumulation in the non-magnetic metal, which already was there when there was no current.

 

The spin injection only modifies the distribution of the spin accumulation across the contact, which was initially established due to the Spin Proximity effect.

 

 

 

 

 

 

 

 

 

 

 


 

Experimental evidences

It should be noticed that all above descriptions of the spin injection and the Spin Proximity effects were well-matched to experimental observations. For example, in this paper the spin injection from Fe into n-GaAs was studied and the spin accumulation in the GaAs was directly imaged using the Hanle effect. When the direction of the drift current is such that the electrons flow from the Fe into the n-GaAs, an increase of the spin accumulation in the n-GaAs is observed (Fig. 7(c), Fig.7 (e) of this paper) and the spin diffusion length is elongated in the n-GaAs. For the opposite direction of the current (Fig. 7(d), Fig.7 (f) of this paper), the spin accumulation in the n-GaAs decreases and the spin diffusion length is shortened.

 

 



 

 

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