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Spin Detection

Spin and Charge Transport

The Spin Detection is used to measure a spin current. 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.

 


The same content can be found in this paper (http://arxiv.org/abs/1410.7511 or this site for a more upgraded version) .Chapter 4, pp. 12-13
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.

 

How to measure a spin accumulation???

A multimeter can not measure a spin accumulation!

For the electrical measuring, the spin information must be converted into the charge information. This job of

A spin accumulation in an electron gas can be detected by measuring the magnetic field induced by the accumulated spins. However, this magnetic field is rather small and practically it is difficult to measure such a small magnetic field. The spin detection is an effect, which allows to measure a spin current and a spin accumulation electrically by measuring an electrical voltage.

 

Methods to measure the spin accumulation:

1. Measurement of the magnetic field.

This is a direct measurement. The measured magnetic moment is linearly proportional to the number of accumulated electrons.

Difficulties: 1) to achieve a spatial nanoscale resolution is difficult. 2) screening by the localized d- or f- electrons.

merit: direct measurements

2. Optical measurements. The measurement of absorption difference between left- and right-circulary polarized light (MCD) or the Kerr rotation or the Faraday rotation.

This is an indirect or near-direct measurement.

Even though the measured optical signal is proportional to the spin accumulation, the optical signal depends significantly on the band properties of a material.

Merit: spatial resolution of a few hundreds of nanometers

3. Electrical measurements. The measurement of a voltage induced by the charge accumulated along the spin diffusion. This method is called the Spin Detection

This is an indirect measurement. The measured signal is proportional to the total charge, which is accumulated in the sample.

Demerit: indirect measurements, the measured signal is influenced by many factors.

Merit: simple experimental setup

 

 

 


The origin of the spin detection

Fig.8. A diffusion spin current in metal. The spin-polarized electrons (electrons of the TIA assembly) diffuse from the region of a higher spin accumulation (on left side) to the region of a lower spin accumulation (on right side). The spin-unpolarized electrons (electrons of the TIS assembly) diffuse in the opposite direction from right to left. (a) The case when equal amounts of spin-polarized electrons and spin-unpolarized electrons diffuse in opposite directions. There is no charge accumulation. (b) The case when the number spin-polarized electrons, which diffuse from left to right, is larger than the number of spin-unpolarized electrons, which diffuse in the opposite direction. This causes an increase of the number of electrons at the left side and a decrease of the number of electrons at the right side. This means the diffusion spin current causes a charge accumulation at the left side and a charge depletion at the right side of the metal.

 

The Origin of the Spin Detection Effect

In the electron gas the charge and spin are transported by electrons. An electron has spin and charge and it transports both the charge and spin simultaneously. However, a current of electrons, which transports only spin but not the charge, is possible. It is the case when the spin polarized electrons (electron of the TIA assembly) diffuse in one direction and exactly the same amount of the electrons, which are not spin-polarized (electron of the TIS assembly), diffuse in the opposite direction. When the spin-polarized and spin-unpolarized currents are the same, in total there is no charge diffusion, but there is a spin diffusion. Such a case is only possible in a material in which the conductivities of the electrons of the TIA and TIS assemblies are the same. For example, it is the case of conduction in the bulk of a high-purity conductor. In a conductor with defects or in the vicinity of an interface there is a slight difference of conductivities of the TIA and TIS assemblies. In this case the spin diffusion is accompanied by a small charge diffusion. In contrast to a spin current, which needs only a source, a charge current needs both a source and a drain. A charge current without a drain builds up a charge accumulation, which induces a strong electrical field. The induced electrical field causes a charge current in the direction opposite to the direction of the diffusion charge current. The build up of the charge accumulation is stopped when the drift charge current becomes equal to the diffusion charge current and in total there is no charge current. By measuring the voltage induced by the build-up charge accumulation, the amount of spin current and the spin accumulation can be evaluated.

 

Figure 8 explains the origin of the spin detection. The figure shows a diffusion spin current flowing from region of higher spin polarization (on left) to the region of greater spin polarization (on right). Figure 8(a) shows the spin current in a metal, in which the conductivities of electrons of the TIA and TIS assemblies are equal. In this case, equal amounts of spin-polarized electrons and spin-unpolarized electrons move in the opposite directions and there is no diffusion charge current. For example, 4 spin-polarized electrons move left and 4 spin-unpolarized electrons moved right. There is a spin movement from left to right, but there is no charge movement. Figure 8(b) shows the spin current in a metal where the conductivity of electrons of the TIA assembly is larger than the conductivity of electrons of the TIS assembly. In this case, two more electrons flow from left to right, there is a diffusion charge current and there is a charge accumulation at right side.

 

 

 

 

 

 

 

 


The spin detection is described by

measures a spin accumulation!

When is non-zero, the charge is accumulated along a spin diffusion and the spin current can be detected.

The detection conductivity describes the charge accumulation along the diffusion of a spin accumulation

is zero in the bulk of the metals and the semiconductors with a low density of defect

In a metal with defects, becomes non-zero.

 

In the vicinity of an interface, becomes non-zero in a metal.

In the vicinity of a high-resistance contact (when the scattering conductivity becomes a dominated transport mechanism), becomes non-zero in metals and semiconductors.

 

 

 

 

 

 

 

 

 

 

 

 


Features of the spin detection

Approximation 1: case when is constant over all volume of a conductor

(It is a rough approximation. The detection conductivity is negligibly small in the bulk of a conductor and it becomes large in the vicinity of interface)

 

Feature 1: The spin detection voltage does not depend on the spin life time and the spin diffusion length

Dependence on spin diffusion length

 

3 orders of increase of magnitude of charge accumulation !!!!!

detection voltage does not change despite of significant change of the charge accumulation!!!!!

Fig. 9 (a) Spin polarization, charge accumulation and spin detection voltage in a metal wire. Animated parameter is the spin diffusion length.

 

Comsol\Matlab calculation files are provided

Material parameters

Conductivity: 2E7 S/m Density of states at the Fermi energy: 2E22 1/cm^3/eV

Detection Conductivity: 0.9*Conductivity;;; Injection Conductivity: 0

Spin Conductivity: 1.15*Conductivity

Wire area: 0.01 um2; permittivity : 11.8

Matlab/Comsol calculation files

Comsol/Matlabv: SpinDetectionLine.m (Comsol only: SpinDetectionLine.mph) Matlab: SpinDetectionLineScan.m

 

 

 

 

 

 

 

 

 

 

 

 

 

Dependence on spin diffusion length

.Fig.9. (right) accumulated charge and (left) detection voltage along a spin diffusion in a metal wire. Metals with different spin life time and spin diffusion length are shown. At zero distance the spin polarization sp equals 0.6 in all cases.

 

 

 

 

Figure 9 shows the accumulate charge and the detection voltage along the spin diffusion in a non-magnetic wire. The cases of metals with different spin life times and spin diffusion lengths are shown. The diffusion starts at spin polarization sp=0.6, which corresponds in graphs to the zero diffusion distance. In metals with shorter spin life time the charge accumulation is larger at zero diffusion distance. Approximately one order shorter spin life time corresponds to one order larger charge accumulation. In contrast, the detection voltage does not depend on the spin life time. As can be seen from Fig. 9(b) the voltage between the point of the zero diffusion distance and a distant point is the same for metals of different spin life time. It should be noticed that in this case the detection voltage does not depend also on the drift current. Therefore, the detection voltage can be reliably used to detect the magnitude of a spin accumulation.

 

 

 

 

Feature 2: The spin detection voltage does not depend on the drift current

 

Dependence on a value and direction of drift current

 

1 orders of increase of magnitude of charge accumulation !!!!!

Reason: the change of the spin diffusion length.

detection voltage does not change despite of significant change of the charge accumulation!!!!!

Fig. 10 Spin polarization, charge accumulation and spin detection voltage. Animated parameter is the value of the drift current flowing along the spin diffusion.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Feature 3: There is no magneto-resistance effect

Dependence on a value and direction of drift current

Fig. 11. IV characteristic of a conductor, in which the detection conductivity is zero (black line) and non-zero (red line).

 

There is a charge accumulation, but the resistance does not dependent of the spin polarization

 

 

 

Figure 11 shows the IV characteristic of a conductor, in which the detection conductivity is zero (black line) and non-zero (red line).

There is an offset between lines, because of the charge accumulation.

However, lines are parallel. This means the resistivity is the same in both cases and there is no magneto-resistance.

 

 

 

 

 

 

 

 

 

 


"Dirty" Spin Current

It is important:

There is no "pure" spin current or "dirty" spin current

There is a drift current, which may be spin-polarized

There is a spin diffusion current, along which a charge may be accumulated

Click on picture to enlarge it.

"Pure" spin current

At present many researchers in the field of Spintronics use the term "pure" spin current. I guess such term is very impressive for the funding agencies.

I believe usage of the term "pure" spin current is incorrect.

I guess the definition is

The "pure" spin current is the spin current without a charge current.

The "dirty" current is the current, which is a mixture of the charge current and spin current.

Fact 1: A diffusion spin current is always the "pure" spin current !!!

A charge current needs a source and drain. A spin current needs only a source. (For details See here). Even if a spin diffusion current is accompanied by a diffusion charge current (The case when ), a charge is accumulated along diffusion. It induces the current in the opposite direction. It causes that the net charge current becomes zero along the spin diffusion.

Fact 2: In the bulk of metals and semiconductors, there is not charge accumulation along the spin diffusion.

Perhaps, the "pure" spin current is defined as a spin diffusion spin current, along which there is no charge accumulation.

It is the case when . However, it is is the most common case of the transport in the bulk of metals and semiconductors!!!! (See here Fig.5)

 

 

 

 

 

 

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