The Spin Detection is the effect of conversion of the spin accumulation into the charge accumulation in the electron gas of conduction electron . From a measurement of the built-up voltage due to the charge accumulation, the amount of the spin accumulation can be evaluated. The spin detection is used to measure the magnitude of the spin current.

---

The part content can be found in this paper (JMMM (2014) or http://arxiv.org/abs/1410.7511 or this site for a more upgraded version) .Chapter 4, pp. 12-13

---

---

Content

click on the chapter for the shortcut

(1). How to measure a spin accumulation???

(2). Electrical spin detection. Two methods

(3). Differences between ISHE- type and conventional- type of the spin detection

(4).Conventional- type spin detection

(5).Physical mechanism of Conventional- type Spin Detection Effect

(6). Spin detection using Inverse Spin Hall effect (ISHE)

(2).Physical mechanism of ISHE- type Spin Detection Effect

 

.........

 

---

What is the spin detection?

It is the generation of the electrical voltage proportionally to the flow of spin- polarized electrons. Therefore, from the measurement of this voltage the magnitude of the spin current can be estimated.

 

How to measure a spin accumulation???

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. Magnetic spin detection. 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 spin- detection.The measurement of absorption difference between left- and right- circular 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 (see Furis et. al (2017))

3. Electrical spin detection. 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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

Electrical spin detection. Two methods

 

(method 1)conventional- type spin detection

(method 2) ISHE- type spin detection

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

Origins of each method of spin detection:

 

Origin of the ISHE- type spin detection: Spin- dependent scatterings

E.g. spin- polarized electrons (spin-up) are scattered more to the right than to the left. As a result, a charge is accumulated at the right side of the metallic wire, which can be detected by a pair of Hall electrodes.

 

Origin of the conventional- type spin detection: Spin- dependent conductivity

The spin diffusion current is the sum of two opposite currents of spin- polarized and spin-unpolarized electrons. The flows are exactly the same, but opposite. When the conductivity is spin-independent, there is a balance between opposite electron flows and the spin diffusion current does not transform any charge. In contrast, when the conductivity is different for the spin-polarized and spin- unpolarized electrons, there is no balance and a different number of electrons flowing in opposite directions. As a result, a charge is accumulated along the flow of spin diffusion current and therefore an electrical voltage is built-up along the flow of the spin-current

---

Differences between ISHE- type and conventional- type of the spin detection:

Origin: (conventional- type detection): spin-dependent conductivity; (ISHE- type detection): spin- dependent scatterings

Direction of electrical field build-up : (conventional- type detection): along the spin current; (ISHE- type detection): perpendicularly to the spin current

Requirement for detection electrodes: (conventional- type detection): a special electrode with a strong spin- dependent conductivity should be used; (ISHE- type detection): no requirements. Any electrodes can be used

material properties, which determine the spin detection efficiency: (conventional- type detection): spin-dependent conductivity if the detection electrode (MgO:Fe); (ISHE- type detection): Inverse Spin Hall effect (ISHE) in non-magnetic metal (Cu)

detection of spin accumulation or spin current : (conventional- type detection): spin accumulation; (ISHE- type detection): spin current

reliability, repeatability, controllability of the spin detection : (conventional- type detection): low/moderate; (ISHE- type detection): moderate/high

 

---

Conventional- type spin detection

 

 

The conventional spin detection effect occurs in material, which conductivity is spin dependent. It means that the conductivity is different for the spin- polarized and spin- unpolarized electrons.

Spin diffusion current does not transform any charge. It is a flow of only the spin. Therefore how it is possible that the spin diffusion current creates a charge accumulation and a built-up voltage along its flow?

Spin diffusion current is the flows of equal amounts of spin- polarized and spin-unpolarized electrons in opposite directions. Both flows transforms the charge, but the charge transfer in the opposite directions and exactly equal. The spin detection effect occurs in a material, in which the conductivities of spin- polarized and spin- unpolarized electrons are slightly different. As a result, the rate of moving electrons in one direction becomes faster than in the opposite direction. In order to establish a balance the charge is accumulated along the path of the spin current. The charge accumulation is decays along the propagation distance of the spin current. Due to the inhomogeneity of the charge accumulation, the electric field is created. The electrical field accelerates the current in one direction and slows down the current in the opposite direction. As a result, the electron flows in opposite directions become balanced.

The conventional spin detection effect is described (is calculated ) by the detection conductivity σ_detection, which is defined as a difference between conductivities of spin- polarized and spin- unpolarized electrons. See details here.

 

(note) Usually the conductivity of a metal is spin- independent. Only in special cases the conductivity becomes spin- dependent. E.g. conductivity in a magnetic tunnel junction (MTJ) is spin- dependent

 

Why the switching field for magnetization of Fe is different for the detector and injector parts?

The coercive field (switching field) is different due to the difference of size of nucleation domains for the magnetization switching (or size and shape of static domains in the case of larger electrodes). The size of the nucleation domains depends on the shape, size, number of defects and shape imperfection in the ferromagnetic electrode (See details here).

Why does the detection voltage depend on the mutual magnetization directions in the injector and detector parts?

The direction of spin polarization of injected conduction electrons is along the magnetization of Fe in the injection part. When the spin- polarized conduction electrons reach the detector, they diffuse into the bulk of Fe of the detector part and create a charge accumulation due to the spin- dependent conductivity in this part. The depth of their diffusion depends on direction of their spin- polarization with respect to the magnetization of Fe. When the spin polarization is along the spin polarization of Fe, the diffused spin- polarized electrons penetrate deeper into the bulk of Fe than in case the spin direction is opposite. As a result, the charge accumulation and therefore the detector voltage is different for the different mutual directions of spin- polarized electrons and the magnetization of Fe in detector part..

Does the detector voltage linearly depend on the spin polarization of the conduction electrons?

No. The dependence is non- linear. Only in the case of the ISHE- type of the spin detection, the detection voltage depends linearly on the spin polarization of the conduction electrons.

 

Does the conventional spin detection effect occur only in the MTJ? Are conventional spin detection effect and the spin-dependent conductivity are feature of an interface? Can the bulk conductivity of a metal be spin- dependent? Can conventional spin detection effect occur in the bulk of a metal.

The MTJ is just an example, in which the spin detection effect is very strong. The bulk conductivity of a metal can be spin- dependent and therefore the conventional spin detection effect may occur in the bulk of metal.

 

Materials, which conductivity spin- dependent and in which the effect of conventional spin detection occurs:

magnetic tunnel junction (MTJ)

strength: strong

(reason why the conductivity is spin- dependent) The tunneling is the spin- dependent process, which strongly dependent on the spin directions on states between which the electron is tunneling.

ferromagnetic metal due to spins of localized d- electrons (Kondo effect)

strength: weak/moderate

(reason why the conductivity is spin- dependent) The conductivity of a ferromagnetic metal may depend on spin direction of conduction electrons with respect to the spin direction of the localized d- electrons (See AMR effect and AHE effect). In this case the conductivity is different when spins of conduction electrons is along or opposite to the spins of the localized d- electrons (magnetization direction).

non-

strength: weak

(reason why the conductivity is spin- dependent) The

 

 

Do the spin- dependent scatterings make the conductivity spin- dependent?

No. (at least from a simple view). The spin- dependent scatterings make more spin- up scattered into the left and more spin-down electrons to the left, but it does not makes the conductivity spin- dependent!

 

---

 

Physical mechanism of Conventional- type Spin Detection Effect

(fact about spin diffusion current) 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 diffuse in one direction and exactly the same amount of the spin- unpolarized electrons diffuses 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.

(normal case without the spin detection) Usually the conductivities of a metal is spin- independent. The conventional electron transport does not distinguish the electron spin. Some spin- dependent effect should influence the electron transport in order for the conductivity to become spin-dependent

In this case, there is no charge accumulation along flow of a diffusion spin current. When the conductivity is spin- independent, equal amounts of spin- polarized and spin-unpolarized flow in opposite directions at the same rates and therefore there is no charge accumulation.

How the charge accumulation is created?

The charge accumulation is created at the moment when spin diffusion current starts to flow. Since the conductivities of the spin- polarized and spin- unpolarized electrons are slightly different, more electrons flow in one direction than in the opposite direction and the spin diffusion current is accompanied by a small charge current. The charge current builds up a charge accumulation, which induces an electrical field in the opposite direction to the flow of the charge current. The induced electrical field causes a charge current in the direction opposite to the direction of the 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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

Spin detection using Inverse Spin Hall effect (ISHE)

 

The ISHE type spin detection effect occurs in material, in which there are spin- dependent scatterings of conduction electrons. It means that the electron scattering probability is different for the electrons with spin direction e.g. up and down. The scattering probability of the spin- dependent scattering is different towards the left and towards the right. The spin- dependent scattering originate the Spin Hall effect and the Inverse Spin Hall effect (ISHE).

The effect of generation of charge current across a flow of a spin current is called the Inverse Spin Hall effect (ISHE).

Spin diffusion current does not transform any charge. It is a flow of only the spin. Therefore how it is possible that the spin diffusion current creates a charge accumulation and a built-up voltage across its flow direction?

The spin flow is detected due to the spin- dependent scatterings. The conduction electrons with the same direction of the spin (spin- polarized electrons) are more scattered in one direction. As a result, an electron current (a charge current) flows in that direction. The charge current, which flows perpendicularly to the spin diffusion current, creates a charge accumulation at side of metallic wire, through which the spin diffusion current flows. The built- up voltage due to the charge accumulation is measured by a voltmeter and therefore the magnitude of the spin current is evaluated.

E.g. due to the spin- dependent scatterings more spin- up electrons are scattered towards the left and more spin-down electrons are scattered to the right. When the conduction electrons are not spin-polarized, the numbers of electrons scattered to the left and to the right are equal and therefore there is no electron current from the left to the right. When the electron gas is spin- polarized (e.g. spin- up polarized) and therefore there are more electrons with spin up, the more electrons are scattered towards the left than towards the right. As a result, the conduction from the right to the left.

 

Origin of ISHE-type spin detection: spin- dependent scatterings (See here)

There are several different mechanisms, which cause a spin- dependent scattering in a material

Mechanisms of ISHE-type spin detection:

(mechanism 1): due to a non-zero orbital moment of conduction electrons; (mechanism 2): Skew scatterings (mechanism 3): Side-jump scatterings at defect(mechanism 4): Side-jump scatterings across an interface.

What the ISHE- type spin detection is detecting? The spin accumulation or the spin current?

A. The spin current. A flow of an electron current is necessary condition for existence of the ISHE effect (See here)

Why the conventional spin detection method detect the magnitude of the spin accumulation, but the ISHE spin detection detect the magnitude of the spin current?

The existence of the spin- depending scatterings is a more common property in a material than the existence of the spin- dependent conductivity. Therefore, The ISHE- type spin detection can be made inside of the studied material (just by detecting the Hall voltage by a pair of Hall probe). For example, when a spin diffusion current flows in a metallic wire, it creates a Hall voltage at the wire edges. In contrast, for the conventional spin detection, a material or an object having a high spin- dependence of the conductivity (e.g. a MgO- type tunnel barrier) is required. Therefore, the spin detector is fabricated separately and connected to studied material, in which the spin current flows. The magnitude of the spin accumulation at the entrance of the spin detector determines the detection signal.

 

 

 

 

 

 

 

 

 

 

 

---

Physical mechanism of ISHE- type Spin Detection Effect

 

More details about Inverse Spin Hall effect is here

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

Calculations of Spin Detection

 

The following calculations is the calculation of the spin and charge transport in a metallic wire, which conductivity is spin- dependent.

 

 

 

 

---

The Conventional spin detection is described by σ_detection

The detection conductivity σ_detection is defined as a difference between conductivities of spin- polarized and spin- unpolarized electrons. See details here.

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

In a metal with defects, σ_detection may become non-zero.

In the vicinity of an interface, σ_detection may become non-zero .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

 

Numerical calculations of the conventional spin detection effect along a metal wire

it is the case when the bulk conductivity of a metal is different for spin- polarized and spin- unpolarized electrons

Approximation 1: case when σ_detection 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

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Feature 3: There is no magneto-resistance effect

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.

 

 

 

 

 

 

 

 

 

 

---

"Pure" spin current

At present,the term "pure" spin current is often used in order to describe a diffusion spin current, which is define as a spin current without flow of the charge

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

there are two possibility of "unpurity" of the spin current

(possibility 1 of "unpurity" of spin current) (Spin Flow + Charge Flow): a drift spin- polarized current, which flows along an electrical field. It is a flow of spin- polarized and spin-unpolarized conduction electrons. Spin Flow + Charge Flow.

(possibility 2 of "unpurity" of spin current) (Spin Flow + Charge Accumulation) a diffusion spin current accompanied by a charge accumulation. This spin current flows between regions of a higher and lower spin polarization (but not along an electrical field) in a material, in which the bulk conductivity is spin- dependent σ_detection ≠0 , and therefore in which a spin current is always accompanied by a charge current.

Fact : 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 σ_detection ≠0 ), 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. As a result, still the spin diffusion current is pure.