ISHE Inverse Spin Hall effect V.Zayets

Inverse Spin Hall effect

Spin and Charge Transport

Abstract:

The Inverse Spin Hall effect (ISHE) describes the fact that when an spin- polarized electron current flows in a ferromagnetic metallic wire, an electrical current flows perpendicularly to the wire. The perpendicular current is linearly proportional to the spin polarization of the conduction electrons. The origin of the ISHE is spin- dependent scatterings of the conduction electrons.

The ISHE and the Spin Hall effect are two complementary effects, which have absolutely identical origins.

Content

ISHE in non-magnetic metal/ semiconductor. Spin injection in non-magnetic metal

Non-magnetic metal. ISHE under spin injection

Non-magnetic semiconductor. Spin injection by a circular- polarized light + Hall measurement

Non- magnetic metal. RF measurement of ISHE

6. Explaination video

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Spin Hall effect (SHE) and Inverse Spin Hall effect (ISHE) are fully complementary effect. They have identical origins and in a material they have the same magnitude

Inverse Spin Hall effect (ISHE)

(definition) The ISHE describes the fact that charge is accumulated at sides of metallic wire, when the conduction electrons are spin- polarized and an electron current flows through the wire
The conduction electrons (green balls) are scattered on a charged defect (blue ball). The conduction electrons are spin- polarized (spin- up). Due to the spin-orbit interaction, the scattering probability for spin-up electrons is higher for a scattering to the right than to the left. As a result, the electrons (the charge) is accumulated at the right side of wire
click on image to enlarge it

(origin) Dependence of scattering of conduction electrons on the spin of localized electrons

(interact with) Rotational (Orbital) Moment of conduction electrons

ISHE is proportional to the total spin of conduction electrons

(formula):

a_AH is the rotation angle of the Anomalous Hall effect (in mdeg). S_local is the total spin of localized electrons. Since the the total spin of the spin-polarized electrons is linearly proportional to the number of spin polarized electrons, the Eq. can be simplified as

where P_s is spin polarization. m is unity vector along spin- direction of spin-polarized conduction electrons

(What is the Inverse Spin Hall effect?) The Inverse Spin Hall effect describes the generation of an electron current ( a charge current) perpendicular to electron current flowing a metallic wire, when the conduction electron in the wire are spin- polarized (e.g. in a ferromagnetic metal)

(Origin of the Inverse Spin Hall effect. All contributions) The Inverse Spin Hall effect occurs due to the dependence of the magnetic field H_SO of spin- orbit interaction on the phase coordinates of a conduction electron. 6 phase coordinates= wave vector ( k_x, k_y, k_z) + spacial coordinates (x,y,z)

(Different contributions (origins) to the Inverse Spin Hall effect) Different contributions corresponds to different sources, which make the H_SO dependent on the electron phase coordinates.

Origin of ISHE: Spin- dependent scatterings

(spin- orbit interaction)

The scatterings of conduction electrons becomes spin- dependent due to the spin-orbit interaction

The electrical field of a localized electron (or defect) creates a magnetic field of spin- orbit interaction H_SO. The H_SO depends on movent direction and position of a conduction electron. Since the electrical field (shown as red lines) is opposite at the left and right side of localized electron, the H_SO is opposite at the left and right sides. When the spin of a conduction electron is along H_SO , the electron energy is smaller and the probability to scattered into such state is higher. When the spin of a conduction electron is opposite to H_SO , the electron energy is higher and the probability to scattered into such state is smaller. The difference in the scattering probabilities creates an electron current (Hall current) perpendicularly to the bias current.

(note) There are several origins (See below) , which make the magnetic field of spin- orbit interaction H_SO to become dependent on moving direction and position of a conduction electron and therefore originating the spin- dependent scatterings and ISHE effect.

(origin 1)Source: orbital moment of a conduction electron It makes H_SO dependent on electron movement direction.

(origin 2)Source: skew scattering on defects It makes H_SO dependent on electron movement direction.

(origin 3)Source: side- jump scattering on defects It makes H_SO dependent on electron spacial position.

(origin 4)Source: side- jump scattering across an interface It makes H_SO dependent on electron spacial position with respect to the interface.

(source of perpendicular Hall current) Spin- dependence of scattering probability of conduction electron. The scattering probability is higher when the spin of the scattered electron is parallel to H_SO and the scattering probability is lower when the spin of the scattered electron is anti parallel to H_SO. Therefore, when the spin direction of the spin- polarized conduction electrons is along, they are scattered in one direction than in the opposite direction, which creates the Hall current.

(magnetic field H_SO of spin- orbit interaction) The H_SO is the magnetic field, which an electron experiences when it moves perpendicularly to an electrical field. See about the spin- orbit interaction here.

(origin of the Inverse Spin Hall effect) Spin- dependent scatterings

(explanation in short) The spin dependent scatterings means that the scattering probability of spin- up electron is higher to the left and the scattering probability of spin- down electron is higher to the right . For example, if the spin direction of the spin polarized conduction electrons is up, there are more electrons scattered to the left and as a result there is a charge current flowing to the left

Measurement of Inverse Hall effect

Measurement of Inverse spin Hall effect

measuring a charge accumulation (Hall voltage)	metallic wire with a Hall probe

Fig. 10a An electron current flows from down to up. The OHE creates the Hall current flowing perpendicularly to the wire. The Hall current creates a charge accumulation at sides of the wire and therefore the Hall voltage, which is measured by a nanovoltmeter.	Fig. 10b A conventional measurement setup. A metallic nanowire with a pair of Hall probe. Two metal contacts contact the opposite sides of nanowire to measure the Hall voltage.	Fig. 10 c. Hall angle vs an applied magnetic field H measured in ruthenium Ru . The Ru thickness is 25 nm. The dependence is nearly perfectly linear. There are a very weak deviation from linear dependence (See below)

click on image to enlarge it

ISHE in non-magnetic metal/ semiconductor. Spin injection in non-magnetic metal

(fact) In a non-magnetic metal there is only one type of Hall effect: OHE. There are no AHE effect (since there are no localized d- electrons) and no ISHE effect (since conduction electrons are not spin polarized)

Why a Hall measurement in a non-magnetic conductor under spin injection is important?

(importance 1): It is possible to separate contributions to Hall effect from localized and conduction electrons. For about 70 years it has been believed that there is only one contribution to the Hall effect in a ferromagnetic metal (the AHE contribution) and both the conduction and localized electrons jointly contribute to the AHE effect. The experimental observation of the Hall effect in a non- magnetic conductor under the spin injection clearly indicates that each localized and conduction electrons contribute individually to the Hall effect and the contributions are very different from each other ( dependence on an external magnetic field etc.)

(importance 2): Since the Hall effect (the ISHE) exists in a non-magnetic metal, which does not have a localized electrons with aligned spins, it clearly indicates that the existence of Hall effect (additional to OHE) does not require the existence of localized electrons. The conduction electrons by themselves are able to produce the Hall effect.

(importance 3 (main)): The substantial difference in contributions into the Hall effect from localized and conduction electrons clearly indicates that the spin distributions of the conduction and localized electrons are very different. The spin distribution in a ferromagnetic metal is the classical spin-up/ spin- down distribution. In contrast, the spin distribution of conduction electrons is the sum of two distributions of groups of spin- polarized and spin- unpolarized electrons. (Details see here)

Non-magnetic metal. Non-local Spin detection using ISHE

also the method is described here

Spin Detection using ISHE

Fig.31. ISHE- type spin detection. Non-local configuration. Under the applied voltage, the charge current J_ch (blue arrow) flow in the copper nanowire between two left electrodes. The conduction electrons in Fe are spin- polarized, therefore the spin-polarized electrons are injected and accumulated in Cu. In contrast to the charge current J_ch (blue arrow), which can flow only along an electrical field, the charge current J_spin (red arrow) does require the electrical field and flows to the right. The spin current J_spin induces the Hall voltage due to ISHE effect, which is detected by the pair electrodes at right side

click on image to enlarge it

Non-magnetic metal. ISHE under spin injection

Zayets 2016

When spin polarized conduction electrons are injected into a non-magnetic metal, the ISHE effect exists additionally to the OHE effect.

Hall effect in non-magnetic metal under spin-injection. Spin Injection using the spin Proximity effect. (Fig.10)

non-magnetic Au nanowire under injection of spin-polarized electrons.	experimental setup	ferromagnetic FeTbB nanowire

Hall angle measured in Au(15nm)/FeBTb(9 nm) periodic structure in Au only region. Spin-polarized electrons are injected into from FeBTb into Au due to the spin proximity effect.	thin a narrow ferromagnetic stripes of FeTbB on non-magnetic Hall bar, which is made of Au. Stripes width 70 nm and gap between stripes 70 nm (See SEM image here). The conductivity of Au is substantially higher. As a result, a electrical current flow mainly in Au.	The Hall angle measured in FeBTb (20 nm)
Measured conductivity is 1.1E7 S/m2. Because of a low conductivity of FeBTb layer, contribution of this layer to Hall effect is negligible.	Conduction electrons are spin- polarized in FeTbB stripes. The spin- polarized electrons diffuse into Au from FeTbB (even without an electrical current). See spin proximity effect. As a result, the ISHE effect exists in Au. The polarity of the ISHE effect is different in Au and FeTbB is different. The Hall angle is measured under stripe (left Hall pair) and in the gap between strip (right Hall pair)	Measured conductivity is 0.06E7 S/m2.

Notice: Polarities of loops in Au and FeBTb are different !!!

this experiment I did in 2016. Main purpose was to study the features of the the spin proximity effect

click on image to enlarge it

Why this study is interesting?

A. The properties of the ISHE effect without disturbance of the AHE effect can be clarified and studied..

There are no localized d- electrons in a non-magnetic metal. As a result, the AHE effect does not exists in a non-magnetic metal at any conditions. (one exception is an interface with a ferromagnetic metal)

The conduction electrons are not spin- polarized in a ferromagnetic metal and there is no ISHE effect in an equilibrium. However, the spin-polarized can be injected in a non-magnetic metal. In this case, the ISHE effect starts to exist in the non- magnetic metal

(Note) The ISHE effect in a ferromagnetic metal is strong, but the similar AHE effect also exists in the ferromagnetic metal and it is difficult to separate the AHE and the ISHE effects (See details here). As a result, it is difficult to study features of the ISHE in the ferromagnetic metal, because they can be originated from ISHE.

(experiment 1) Spin injection from a ferromagnetic metal + Hall measurements in a nonmagnetic metal

this experiment I did in 2016-2018 in Au: FeTbB samples

( Main idea): To inject spin- polarized electrons from a ferromagnetic metal into a non-magnetic metal, while measuring the Hall effect in the non-magnetic metal. To use the ferromagnetic and non-magnetic metals with opposite polarity of the ISHE.

(Main challenge): The Hall effect in the ferromagnetic metal should not contribute to the measured the Hall angle

(solution 1): To use the ferromagnetic and non-magnetic metals with opposite polarity of the ISHE. As a result, the contributions from each metal can be distinguished by the polarity of the hysteresis loop.

(solution 2): the use of the ferromagnetic metal with a small conductivity and the non- magnetic metal with a high conductivity. As a result, near-all current flows in the non- magnetic metal, nearly no current flows ferromagnetic metal and therefore the main contribution to the Hall angle would be from the non- magnetic metal and only a little contribution would be from ferromagnetic metal.

Hall effect in non-magnetic metal under spin-injection. Conventional Spin Injection. (Fig.11)

Spin injection from top FeTbB electrode

thin a narrow ferromagnetic stripes of FeTbB on non-magnetic Hall bar, which is made of Au. Stripes width 70 nm and gap between stripes 70 nm (See SEM image here). The voltage is applied between top of FeBTb stripes and Au. One pair of Hall probe is connected under FeTbB stripe and another pair is connected between stripes. The spin polarized conduction electrons are injected from FeTbB into Au. The spin- polarized electrons induce the Hall effect in Au. (Inverse Spin Hall effect (ISHE))

click on image to enlarge it

(possibility 2). Classical spin injection. Spin injection from top FeTbB electrode

In this case, the electrical voltage is applied between the FeTbB strips and the Au nanowire. There is a spin injection from the FeTbB

Non-magnetic semiconductor. Spin injection by a circular- polarized light + Hall measurement

Hall effect induced by photo- excited spin- polarized current

Hall effect in n-GaAs/i-GaAs/ p- GaAs wire (GaAs pin- photo detector) illuminated by circular- polarized light.

ACW- circular polarized light (45 deg of λ /4 plate) -> spin- up photo- excited electrons	linear polarized light (45 deg of λ /4 plate)-> no spin polarization	CCW- circular polarized light (45 deg of λ /4 plate) -> spin- down photo- excited electrons

a positive Hall voltage	There is no Hall voltage	a negative Hall voltage

merit: Hall effect is induced only by spin-polarized conduction electrons (ISHE effect). There are no localized d- electrons in i- GaAs. As a result, there is no AHE effect.

Measurement of Hall angle in GaAs pin- photodetector illuminated by circular- polarized light

similar experiment is described here: Wunderlich et.al. Nat. Phys. (2009)

Output linearly- polarized light from the laser becomes circular- polarized. When the circular- polarized light illuminates the GaAs pin- photo detector, it excites spin- polarized electrons in i-GaAs, which flows from p-GaAs to n-GaAs. Their spin- polarized current is detected by a pair of Hall probe and the Hall voltage is measured.

Yellow arrow shows the polarization of light.

i- GaAs: (undoped, non-conductive); n-GaAs (donor- doped, electron- type conductivity); p-GaAs (acceptor- doped, hole- type conductivity);

click on image to enlarge it

See a similar experiment: Wunderlich et.al. Nat. Phys. (2009)

( Main idea): The circular- polarized light creates spin- polarized conduction electrons in a non- magnetic semiconductor. As a result, the the ISHE effect starts to exist under illuminations of a circular- polarized light.

Hall effect induced by photo- excited spin- polarized current


Controlling of spin direction of photo excited elections in pin- GaAs photodiode by rotating axis of λ /4 waveplate	Hall Voltage as a function of polarization of light (schematic)

Rotation of λ /4 waveplate does not affect light intensity, only it changes the light polarization.

Yellow arrow shows the polarization of light. Red mark on λ /4 waveplate shows its axis direction

click on image to enlarge it

Non- magnetic metal. RF measurement of ISHE.

in this case spin polarized electrons injected in a no

Video

Measurement of Anomalous Hall effect, Inverse Spin Hall and spin polarization of conduction electron

Conference presentation.MMM 2020

Questions & Answers

I am strongly against a fake and "highlight" research

Dr. Vadym Zayets

v.zayets(at)gmail.com

more Chapters on this topic:

Spin and Charge Transport

Abstract:

The ISHE and the Spin Hall effect are two complementary effects, which have absolutely identical origins.

Content

Inverse Spin Hall effect (ISHE)

(What is the Inverse Spin Hall effect?) The Inverse Spin Hall effect describes the generation of an electron current ( a charge current) perpendicular to electron current flowing a metallic wire, when the conduction electron in the wire are spin- polarized (e.g. in a ferromagnetic metal)

(Origin of the Inverse Spin Hall effect. All contributions) The Inverse Spin Hall effect occurs due to the dependence of the magnetic field HSO of spin- orbit interaction on the phase coordinates of a conduction electron. 6 phase coordinates= wave vector ( kx, ky, kz) + spacial coordinates (x,y,z)

(Different contributions (origins) to the Inverse Spin Hall effect) Different contributions corresponds to different sources, which make the HSO dependent on the electron phase coordinates.

Origin of ISHE: Spin- dependent scatterings

(origin 1)Source: orbital moment of a conduction electron It makes HSO dependent on electron movement direction.

(origin 2)Source: skew scattering on defects It makes HSO dependent on electron movement direction.

(origin 3)Source: side- jump scattering on defects It makes HSO dependent on electron spacial position.

(origin 4)Source: side- jump scattering across an interface It makes HSO dependent on electron spacial position with respect to the interface.

(magnetic field HSO of spin- orbit interaction) The HSO is the magnetic field, which an electron experiences when it moves perpendicularly to an electrical field. See about the spin- orbit interaction here.

(origin of the Inverse Spin Hall effect) Spin- dependent scatterings

Measurement of Inverse Hall effect

Measurement of Inverse spin Hall effect

measuring a charge accumulation (Hall voltage)

metallic wire with a Hall probe

ISHE in non-magnetic metal/ semiconductor. Spin injection in non-magnetic metal

(fact) In a non-magnetic metal there is only one type of Hall effect: OHE. There are no AHE effect (since there are no localized d- electrons) and no ISHE effect (since conduction electrons are not spin polarized)

Why a Hall measurement in a non-magnetic conductor under spin injection is important?

Non-magnetic metal. Non-local Spin detection using ISHE

also the method is described here

Spin Detection using ISHE

Non-magnetic metal. ISHE under spin injection

Zayets 2016

non-magnetic Au nanowire under injection of spin-polarized electrons.

experimental setup

ferromagnetic FeTbB nanowire

Notice: Polarities of loops in Au and FeBTb are different !!!

Why this study is interesting?

this experiment I did in 2016-2018 in Au: FeTbB samples

Spin injection from top FeTbB electrode

Non-magnetic semiconductor. Spin injection by a circular- polarized light + Hall measurement

Hall effect induced by photo- excited spin- polarized current

Hall effect in n-GaAs/i-GaAs/ p- GaAs wire (GaAs pin- photo detector) illuminated by circular- polarized light.

ACW- circular polarized light (45 deg of λ /4 plate) -> spin- up photo- excited electrons

linear polarized light (45 deg of λ /4 plate)-> no spin polarization

CCW- circular polarized light (45 deg of λ /4 plate) -> spin- down photo- excited electrons

similar experiment is described here: Wunderlich et.al. Nat. Phys. (2009)

See a similar experiment: Wunderlich et.al. Nat. Phys. (2009)

Non- magnetic metal. RF measurement of ISHE.

Video

Measurement of Anomalous Hall effect, Inverse Spin Hall and spin polarization of conduction electron

Questions & Answers

I truly appreciate your comments, feedbacks and questions

(Different contributions (origins) to the Inverse Spin Hall effect) Different contributions corresponds to different sources, which make the H_SO dependent on the electron phase coordinates.

(origin 1)Source: orbital moment of a conduction electron It makes H_SO dependent on electron movement direction.

(origin 2)Source: skew scattering on defects It makes H_SO dependent on electron movement direction.

(origin 3)Source: side- jump scattering on defects It makes H_SO dependent on electron spacial position.

(origin 4)Source: side- jump scattering across an interface It makes H_SO dependent on electron spacial position with respect to the interface.

(magnetic field H_SO of spin- orbit interaction) The H_SO is the magnetic field, which an electron experiences when it moves perpendicularly to an electrical field. See about the spin- orbit interaction here.