more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionScatteringsSpinpolarized/ unpolarized electronsSpin statisticselectron gas in Magnetic FieldFerromagnetic metalsSpin TorqueSpinTorque CurrentSpinTransfer TorqueQuantum Nature of SpinQuestions & Answersmore Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11

Spin Proximity Effect. Spin Injection
Spin and Charge Transport.In an equilibrium the electron gas is spinpolarized in a ferromagnetic metal and it is not spinpolarized in a nonmagnetic metal . At a contact between a ferromagnetic and a nonmagnetic metals, some spin accumulation from the ferromagnetic metal diffuses into the nonmagnetic metal. The spin polarization in the ferromagnetic metal near the contact becomes smaller and the spin polarization in the nonmagnetic metal becomes nonzero. This effect is called the Spin Proximity effect. This effect is called the Spin Proximity EffectWhen a drift current flows from a ferromagnetic to nonmagnetic metal, the spin accumulation from the ferromagnetic metal may be drifted into the nonmagnetic 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.Contentclick on the chapter for the shortcut(1). Common single origin and common mechanisms of Spin Hall effect and Inverse Spin Hall effect:.........Note: The classical model of an electron gas (the model of spinup/spindown 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. 711page was made in 2014Incorrect 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 nonmagnetic metals from the spin diffusion. 2) When a voltage is applied, the wall is removed and the spin accumulation diffuses into the nonmagnetic metal
Correct explanation of the Spin Injection and the Spin Proximity effects: 1) Even without an applied voltage the spin accumulation diffuses into the nonmagnetic 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 nonmagnetic metal; (b) For the opposite direction of the drift current, the spin accumulation is drifted back from the nonmagnetic metal into the ferromagnetic metal.
Spin Proximity EffectWhen two metals, which have different spin polarization, are in contact, in the vicinity of the contact interface some spinpolarized 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 nonmagnetic metal the electron gas is not spinpolarized and it is spinpolarized in the bulk of a ferromagnetic metal. Near contact between ferromagnetic and nonmagnetic metals the electron gas becomes spinpolarized in the nonmagnetic 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 spinup/spindown 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 spindiffusion conductivity describes the Spin Proximity effect
Classical model of spinup/spindown bands vs. the presented model
Within the model of spinup/spindown bands it is assumed that in a contact between a ferromagnetic metal and a nonmagnetic metal a spin accumulation is contained only inside the ferromagnetic metal and it does not diffuse into the nonmagnetic 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 nonmagnetic 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 nonmagnetic metal. The spin accumulation decays from the ferromagnetic metal through the contact deep into the nonmagnetic metal (Fig. 2 right). The drift current only modifies this distribution.
Click here to see other versions of Fig.2
The Spin Proximity effect. Ferromagnetic particle embedded into a nonmagnetic metalSpin 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 nonmagnetic 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 nonmagnetic metal is significantly spinpolarized. 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 nonmagnetic metal.
Spin proximity effect at a contact between a ferromagnetic and a nonmagnetic metalsSimplest case: 2D geometry; steplike conductivities Inside of a nonmagnetic metal the spin accumulation decays exponentially: where lambda_non_mag is the spin diffusion length in the nonmagnetic 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 nonmagnetic 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 nonmagnetic metal increase;
How to obtain Eq. (3.2) click here to expand
Let us assume that a contact between a ferromagnetic and a nonmagnetic metals at x=0 In the nonmagnetic metal (x<0) the spin accumulation along the spin diffusion is described as Corresponded the spin current in the nonmagnetic 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 yourselfMatlab file: ProximityMetal0.m Comsol file: Proximity.mph
The Spin Proximity effect vs. the Magnetic ProximityThe 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 spd 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 spindiffusion lengths. Because of the different effective lengths, the Spin Proximity effect and the Magnetic Proximity effect can be distinguished experimentally .
Spin Injection
When a drift current flows through a contact between ferromagnetic and nonmagnetic metals, an additional spin accumulation is drifted from the ferromagnetic metal into the nonmagnetic metal. For the opposite direction of the current, the spin accumulation in the nonmagnetic 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 nonmagnetic 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 electrontype or holetype. 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.
Spin injection & Spin Proximity through a contact between a ferromagnetic metal and a nonmagnetic metal
Figure 4 shows the calculated distribution of the spin polarization across the contact between the ferromagnetic and the nonmagnetic 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 spinpolarized inside the nonmagnetic 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 nonmagnetic metal. The spin polarization in the nonmagnetic 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 nonmagnetic 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.
Material Parameters (Click to expand) and Comsol/Matlab calculation files. Calculate by yourself!!
Material parameters The contact area is 0.01 um^2. 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 spindiffusion 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 is calculated by solving numerically the Spin/Charge Transport Equations by Finite Difference Method (FDM) 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 filesProximityMetal.m (comsol : ProximityMetal.mph)
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 nonmagnetic and ferromagnetic metals, respectively. Figure 4(c) shows the effective spin diffusion length in the nonmagnetic and ferromagnetic metals as the function of the drift current. When the spin accumulation is injected from the ferromagnetic to the nonmagnetic metal (negative drift current), the effective spin length increases in the nonmagnetic 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 wellconfirmed 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 nonmagnetic metal, the effective spin diffusion length increase in the nonmagnetic 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 nonmagnetic 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 nonmagnetic 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.
Experimental evidencesIt should be noticed that all above descriptions of the spin injection and the Spin Proximity effects were wellmatched to experimental observations. For example, in this paper the spin injection from Fe into nGaAs 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 nGaAs, an increase of the spin accumulation in the nGaAs is observed (Fig. 7(c), Fig.7 (e) of this paper) and the spin diffusion length is elongated in the nGaAs. For the opposite direction of the current (Fig. 7(d), Fig.7 (f) of this paper), the spin accumulation in the nGaAs decreases and the spin diffusion length is shortened.
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 spindiffusion, 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 how to obtain Eq.(20.1), click here to expand
In the case when conductivities are constant and =0, the spin/charge transport equations (See Eq.12) can be simplified as The first equation is the Poisson equation. The second equation is simplified as The charge current can be calculated as Substitution of Eq.(20.6) in Eq.(20.5) gives The solution of Eq. (20.7) can be found as where is the spin polarization at x=0; Substituting Eq. (20.8) , Eq. (20.7) is simplified as
or where Solving Eq. (20.11), the effective spin diffusion length is calculated as
When the current J_charge flows through the contact between a ferromagnetic metal and a nonmagnetic metal, the spin polarization at contact interface can be calculated as
how to obtain Eq(30.1), click here to expand
A spin current can be calculated as The boundary condition of the continuous spin current through the contact interface gives In the region of the ferromagnetic metal(x>0), the spin current can be calculated as The boundary condition of the continuous spin current through the contact interface gives
Simplifying Eq.(30.4), we obtain Solving Eq.(30.5), the spin polarization at contact interface sp(x=0) is obtained as
Dependence of spin injection efficiency on material parameters
Dependence of spin injection efficiency on material parameters (click here to expand)
Dependence of spin injection efficiency on material parameters
Material Parameters (Click to expand)
Material parameters The contact area is 0.01 um^2. 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 spindiffusion 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 is calculated by solving numerically the Spin/Charge Transport Equations by Finite Difference Method (FDM) 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).
All data below are calculated by solving numerically the Spin/Charge transport equations The spin injection efficiency is characterized by the change of the efficient spin diffusion length in the nonmagnetic and ferromagnetic metals and the change of the spin polarization at the contact interface
Dependance on the polarity of the charge current
Case 1. Injection conductivity is electrondominated for both the ferromagnetic and the nonmagnetic metals. <0; <0 Polarity: "" to the ferromagnetic metal; "+" to the nonmagnetic metal (spin injection) increases in the nonmagnetic and it decreases in the ferromagnetic metal. increases. The amount of spinpolarized carriers in the nonmagnetic metal increases. It is always smaller than the equilibrium spin polarization of the ferromagnetic metal sp0. Polarity: "+" to the ferromagnetic metal; "" to the nonmagnetic metal (spin depletion) decreases in the nonmagnetic and it increases in the ferromagnetic metal. decreases. The amount of spinpolarized carriers in the nonmagnetic metal decreases.  Case 2. Injection conductivity is holedominated for both the ferromagnetic and the nonmagnetic metals. >0; >0 Polarity: "+" to the ferromagnetic metal; "" to the nonmagnetic metal (spin injection) increases in the nonmagnetic and it decreases in the ferromagnetic metal. increases. It is always smaller than the equilibrium spin polarization of the ferromagnetic metal sp0. The amount of spinpolarized carriers in the nonmagnetic metal increases. Polarity: "" to the ferromagnetic metal; "+" to the nonmagnetic metal (spin depletion) decreases in the nonmagnetic and it increases in the ferromagnetic metal. decreases. The amount of spinpolarized carriers in the nonmagnetic metal decreases.
 Case 3. Injection conductivity is holedominated in the ferromagnetic metal and electrondominated in the nonmagnetic metals. >0; <0 Polarity: "+" to the ferromagnetic metal; "" to the nonmagnetic metal (spin accumulation at interface) decreases in both the nonmagnetic and in the ferromagnetic metal. In the ferromagnetic metal, may change its sign. increases. It can be larger even than the equilibrium spin polarization of the ferromagnetic metal sp0
Polarity: "" to the ferromagnetic metal; "+" to the nonmagnetic metal (spin depletion) increases in both the nonmagnetic and in the ferromagnetic metal. is nearly a constant. (With increasing current, in increases or decreases. and next it is saturated at constant value)
Dependence of the spin life time in metalWhen the spin life time in the metal decrease, its spin length decreases, which causes decreasing
t
Spin injection within one materialThe 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 spinpolarization 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 nonmagnetic metal by circularlypolarized light at different voltages applied in the plane of the metal. When a voltage is not applied inplane 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 nGaAs (Fig.4 of this paper).
Incorrect interpretation of the spin injection in the classical model of the spinup/spindown bands.Classical model assumes that without a drift current there is no spin accumulation in a nonmagnetic metal at a contact with a ferromagnetic metal. All spin accumulation contains within the ferromagnetic metal. Steplike 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 nonmagnetic metal. As the spin accumulation has passed the contact, it diffuses in the nonmagnetic. This interpretation of the spin injection is incorrect.
The spin proximity is described by
The spindiffusion 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 .
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 110% of the conventional conductivity . It is because the directions of spin transfer is opposite for the electron and hole currents in the metal.
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 ntype semiconductor the charge and spin are transported by electrons. The negativelycharged electrons move from a ““source towards a “+” drain and the spin is drifted in the same direction. In a ptype semiconductors the charge and spin are transported by holes. The positivelycharged holes move from a “+“ towards a “” drifting the spin in the same direction. Therefore, the spin drifting direction is opposite in the ntype and ptype 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 spinpolarization 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 nonmagnetic metal, the sign of should be the same for the ferromagnetic and nonmagnetic 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 .
It is important: An efficient spin injection is important for a variety of different application. For example, the largest spintransfer torque is one of main required parameters for a cell of magnetic randomaccess memory (MRAM). The largest spintransfer 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
What is the spin injection???
Q. Is this the breaking of the spin throughout a contact between a ferromagnetic and a nonmagnetic 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)
Experimental proof of spin proximity effect
1) Anomalous Hall effect in Au
Possible confusion!!: from 2014 to 2017 I have used names TIA and TIS for groups of spinpolarized and spinunpolarized electrons, respectively. The reasons are explained here.

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