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

When a drift current flows from a ferromagnetic to non-magnetic metal, the spin accumulation from the ferromagnetic metal may be drifted into the non-magnetic metal. This effect is called the Spin Injection The spin injection only modifies the distribution of the spin accumulation across the contact, which was initially established due to the Spin Proximity effect.

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Content

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(1). Common single origin and common mechanisms of Spin Hall effect and Inverse Spin Hall effect:

 

 

 

 

 

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Note: The classical model of an electron gas (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.

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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

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page was made in 2014

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Incorrect classical view of the spin proximity & spin injection

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.

 

 

 

 

 

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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

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Classical model of spin-up/spin-down bands vs. the presented model

 

 

 

 

 

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.

 

 

 

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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.

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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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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;

 

 

 

Calculate by yourself

Matlab file: ProximityMetal0.m

Comsol file: Proximity.mph

 

 

 

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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 .

 

 

 

 

 

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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.

It is important:

The spin injection by electron and holes currents are of opposite signs, because holes and electrons transport the spin in opposite directions (See bellow). In a semiconductor the current is either electron-type or hole-type. This is the reason why the spin injection is efficient in a semiconductor. In a metal there are both the electron and hole currents. This is the reason why the spin injection is not efficient in a metal.

 

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Spin injection & Spin Proximity through a contact between a ferromagnetic metal and a non-magnetic metal

 

Figure 4 shows the calculated distribution of the spin polarization across the contact between the ferromagnetic and the non-magnetic metals for different values of the drift current flowing across the contact. The constants of the metal are the same as were used for the calculations of Fig. 3. In all cases the spin polarization changes smoothly (without a step) from one metal to other metal. Even without a drift current, the electron gas is spin-polarized inside the non-magnetic metal and the spin polarization in the ferromagnetic metal is smaller than its bulk spin polarization. This is because of the Spin Proximity effect. For a negative drift current (red lines) the spin accumulation is drifted from the ferromagnetic metal into the non-magnetic metal. The spin polarization in the non-magnetic metal becomes larger and the spin polarization in the ferromagnetic metal becomes near 0.6, which is its bulk spin polarization. For a positive drift current (blue lines) the spin accumulation from the non-magnetic metal is drifted back into the ferromagnetic metal and most of the spin accumulation is depleted. In the ferromagnetic metal the spin accumulation is drifted deep inside of the bulk and near the contact interface the spin accumulation is depleted.

 

 

 

 

 

 

 

 

 

Fig. 4 (b). Log of the spin polarization in the vicinity of the contact between ferromagnetic and non-magnetic metals as the function of drift current flowing through the contact. The direction of the current is shown by the arrow. . The picture is animated. Comsol\Matlab calculation files are provided	Fig. 4 (c) The effective spin diffusion length in the non-magnetic metal (black line) and ferromagnetic metal as the function of drift current flowing through the contact. Notice: spin diffusion length in non-magnetic metal without drift current is 464 nm	Fig. 4(d). The total spin current (blue), drift spin current (green) and diffuse spin current (red) flowing through the contact between ferromagnetic and non-magnetic metals as the function of drift current flowing through the contact. The direction of the charge drift current is shown by the arrow. . The picture is animated.

 

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Dependence of spin diffusion length on the drift current

(fact) The spin diffusion length may be modulated substanially by the drift current (a conventional electron current) !!!

It is a bulk property of a conductor (but not contact property), when

In each metal the spin polarization decays exponentially (See Fig. (4(b)). Therefore, the distribution of the spin polarization in each metal can be fitted as

where x is the coordinate across the contact, sp0 is the bulk spin polarization of the ferromagnetic metals, An and Af are constants and are the effective spin diffusion lengths in the non-magnetic and ferromagnetic metals, respectively.

Figure 4(c) shows the effective spin diffusion length in the non-magnetic and ferromagnetic metals as the function of the drift current. When the spin accumulation is injected from the ferromagnetic to the non-magnetic metal (negative drift current), the effective spin length increases in the non-magnetic metal and it decreases in the ferromagnetic metal. This effect is called the spin gain/damping (See here) . It occurs because of the conversion of the spin drift current into the diffusion spin current along the flow of the drift current. When the flow of the converted spin current is in the same direction as the flow the diffusion current, the converted spin current assists the flow of the diffusion spin current and the spin diffusion length increases. When the direction is the opposite, the spin diffusion current is damped and the spin diffusion length decreases. The decrease and increase of the spin diffusion length depending of the direction of the spin current is well-confirmed and measured experimentally.

 

Conclusions on Fig.4:

 

(1) The spin polarization sp monolithically (smoothly) changes through the interface between metals . The spin injection is the effect which occurs in the bulk of metals. The spin injection is not surface effect!!!

(2) The decay of spin accumulation into the bulk of metal is nearly exponential and it can be described by an effective diffusion length (Fig.4(c));

(3) The effective diffusion length in each metal depends on the current flowing through the contact (Fig.4(b)(c)). When the spin is injected into a non-magnetic metal, the effective spin diffusion length increase in the non-magnetic metal and decreases in the ferromagnetic metal. For opposite direction of current, the effective spin diffusion length increase in the the ferromagnetic metal and decreases in non-magnetic metal.

(4) Because of the Spin Proximity Effect, there is a diffusion spin current in both metals (Fig.4 (d)). The diffusion current is largest at the interface and its direction is from the ferromagnetic metal toward the non-magnetic metal. The diffusion spin current practically does not depend on the drift current.

(5) Distribution of spin accumulation in the vicinity of the contact practically does not change until the spin drift current becomes comparable with diffusion spin current.

 

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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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Calculation of the spin injection in the bulk of conductor

in this case the detection conductivity is zero and the conductivities are constant with coordinates

In this case the effective spin diffusion length can be calculated as

where the spin diffusion length without a charge current is calculated as

where the threshold current of spin injection is

,, are the spin-diffusion, charge and injection conductivities, q is the electron charge, sp0 is the equilibrium spin polarization of the metal, tau_spin is the spin life time and n_spin is the number of the "spin" states in the metal

It should be noted that Eq. (20.1) is obtained ignoring the dependence of the number of the spin states n_spin on the spin polarization of the electron gas (See here). However, the variation of n_spin is only 10 % (See here) and Eq. (20.1) can be considered as a good approximation

 

When the current J_charge flows through the contact between a ferromagnetic metal and a non-magnetic metal, the spin polarization at contact interface can be calculated as

 

 

 

 

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Dependence of spin injection efficiency on material parameters

 

 

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Spin injection within one material

The spin injection is an intrinsic property of the bulk of a material. It is not property of an interface or contact (Even though the injection conductivity might by larger in the vicinity of the interface (See here)). Therefore, the spin injection also occurs within a single material. For example, when the spin-polarization is excited by light.

The spin injection may occur not only between two metals, but within the same metal as well. Figure 6 shows the calculated spin polarization induced in the non-magnetic metal by circularly-polarized light at different voltages applied in the plane of the metal. When a voltage is not applied in-plane of the metal, the distribution of the spin polarization is Gaussian. When the voltage is applied, the spin polarization is drifted along the voltage. The drift only occurs in metals in which . The drift of the spin polarization similar to that calculated in Fig.6 was observed experimentally in n-GaAs (Fig.4 of this paper).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Incorrect interpretation of the spin injection in the classical model of the spin-up/spin-down bands.

Classical model assumes that without a drift current there is no spin accumulation in a non-magnetic metal at a contact with a ferromagnetic metal. All spin accumulation contains within the ferromagnetic metal. Step-like contact between the metals is considered as a wall for any spin diffusion into ferromagnetic metal. A drift current drugs some spin accumulation through the interface between metals into the non-magnetic metal. As the spin accumulation has passed the contact, it diffuses in the non-magnetic. This interpretation of the spin injection is incorrect.

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The spin proximity is described by

The spin-diffusion conductivity describes the conventional spin diffusion along a gradient of the spin polarization.

is large in both the metals and the semiconductors

In the case of a semiconductor, equals to the conventional conductivity .

In the case of a metal, is larger than the conventional conductivity (See here) and it depends on the spin polarization of the electron gas .

 

 

 

 

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The spin injection is described by

 

The injection conductivitydefines a ratio of how much the spin polarization of the drift current smaller than the spin polarization of the electron gas. It describes the ability of a drift current to transport a spin accumulation.

is small in a metal and it is large in a semiconductor

In the case of a semiconductor, equals to the conventional conductivity .

In the case of a metal, is small and it is only 1-10% of the conventional conductivity . It is because the directions of spin transfer is opposite for the electron and hole currents in the metal.

 

 

 

 

 

 

 

 

 

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Why spin injection conductivity is small in a metal and it is large in a semiconductor?

 

The spin polarization of a spin current in a semiconductor is almost equal to the spin polarization of the electron gas. In contrast, in a metal the spin polarization of a spin current is significantly smaller than the spin polarization of the electron gas. This fact is proved here from a solution of the Boltzmann transport equations. A simplified explanation of this fact can be given as follows. In an n-type semiconductor the charge and spin are transported by electrons. The negatively-charged electrons move from a “-“source towards a “+” drain and the spin is drifted in the same direction. In a p-type semiconductors the charge and spin are transported by holes. The positively-charged holes move from a “+“ towards a “-” drifting the spin in the same direction. Therefore, the spin drifting direction is opposite in the n-type and p-type semiconductors. This is the reason of the opposite signs of for n- and p- semiconductors. The electrical conduction in a metal can be seen as a drift of electrons and hole in opposite directions (Fig.7). Since the charge of electrons and holes is opposite, the electron and hole currents transport the charge in the same direction, but they transport the spin in opposite directions. Since the number of electrons and holes is about the same in a metal, the spin drifting by electrons and holes nearly compensate each other. This causes a small spin-polarization of a drift current in a metal and a small value of . The sign of in a metal may be either negative or positive depending on whether there are more electrons or holes in the metal. The later condition is determined by the sign of the gradient of the density of the states of the metal at the Fermi energy. The sign of is important for an effective spin injection. For example, for an effective spin injection from a ferromagnetic metal to a non-magnetic metal, the sign of should be the same for the ferromagnetic and non-magnetic metals. The polarity of the applied voltage should correspond to the sign of . The sign of can be evaluated from the sign of the Hall voltage in the metal .

 

 

Drift spin current in a metal

Fig. 7 The negatively-charged electrons (green balls) moves from "-" to "+". The positively-charged holes (blue balls) moves from "+" to "-". Therefore, the electron and hole currents transform the charge in the same direction, but the spin in opposite direction. Since in a metal about the same number of holes and electrons, the spin-transfer efficiency (spin-injection efficiency) is small in a metal.

 

 

 

 

 

 

 

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It is important:

An efficient spin injection is important for a variety of different application. For example, the largest spin-transfer torque is one of main required parameters for a cell of magnetic random-access memory (MRAM). The largest spin-transfer torque is only possible in the case when there is an efficient spin injection between the electrodes of the MRAM cell (See here) . It is possible only when metals with the largest value of are used as electrodes of the MRAM cell.

The effect of the spin transfer torque occurs because of the spin injection from one electrode of a MTJ to another electrode. For largest spin transfer torque, metals with largest injection conductivity are preferable as a material for electrodes

 

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What is the spin injection???

 

Q. Is this the breaking of the spin throughout a contact between a ferromagnetic and a non-magnetic metal???

A. It is not!! It is a bulk effect

Q. Is the amount of the spin accumulation, which is drifted through the contact, linearly proportional to the drift current?

A. It is only in the case of current larger than the the threshold injection current J0.

Q. What the spin injection do???

A. The spin injection is:

a) The change of spin diffusion length due to the drift current. The change occurs in the bulk of a metal.

b) The change of the amount of the spin accumulation at the contact interface between two metals, because of the change of the spin diffusion length in each metal. (see Fig. 3)

 

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Experimental proof of spin proximity effect

 

1) Anomalous Hall effect in Au

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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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.