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Spin-Orbit Torque (SOT)

Spin and Charge Transport

Abstract: An electrical current generates the spin-polarized electrons due to the Spin Hall effect. These spin-polarized changes the magnetic properties of the nanowire. This effect is called the effect of spin-orbit torque (SOT). The change of magnetic properties by an electrical current may be substantial. For example, the magnetization can be reversed. The SOT effects describes the dependence of a magnetic properties of a magnetic nanowire on polarity and magnitude of electrical current.

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Magnetic parameters, which depend on polarity of current in a nanomagnet:

"magnetic field, which is induced by the spin accumulation; Anisotropy field Hanis; Energy of perpendicular magnetic anisotropy (PMA) Eanis;Coercive field Hc;Spin polarization;Logarithm of magnetization switching time; Logarithm of Retention time; Delta Δ;Hall angle;size of nucleation domain for magnetization switching

 

All these parameters depend linearly on the gate voltage. However, the dependencies are not clearly depend on each other. It indicates that there are several independent contributions to the SOT effect.

High precision measurements of current dependencies of these magnetic parameters are described below.


Content

click on the chapter for the shortcut

(1). 3-terminal MTJ

(2). Origin of Spin-Orbit Torque in short

(3). Magnetic parameters affected by SOT effect

(video:) Measurement of coefficient of spin- orbit interaction, anisotropy field in a nanomagnet and magnetic field created by a spin accumulation.

(4). Measurement of SOT

(measurement 1) "damp-like" torque
(measurement 2) "field-like" torque
(measurement 3) SOT modulation of anisotropy field Hanis and PMA energy
(measurement 4) SOT modulation of coercive field Hc
(measurement 5) SOT modulation of delta Δ and retention time
(measurement 6) SOT modulation of of effective magnetization Meff and effective size of nucleation domain
(measurement 7) SOT modulation of Hall angle
(measurement 8) SOT modulation of spin polarization

(5). What is the "damp-like" torque?

(6). Comparison between "damp-like" torque and "field-like" torque

(7). Influence of interface on SOT effect

(8). Measurements of the SO torque using 2d harmonic lock-in technique

(9). Current-induced magnetization reversal in FeBTb

Questions & Answers

(q1) about systematic errors of 2nd harmonic measurements
(q2) torque & spin dynamic & Quantum mechanic
(q3) about Field-Like torque

 

6. Explanation video

(video1) Measurement of coefficient of spin- orbit interaction, anisotropy field in a nanomagnet and magnetic field created by a spin accumulation.
(video2) Parametric magnetization reversal, Intermag 2022

 

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Two method of spin-reversal by spin- polarized electrons

(source 1 of spin- polarized electrons) Spin-transfer torque

In this case a current of the spin- polarized electrons flows from one material to another material. As a result, the spin-polarized electrons from one material are moved to another material and accumulated there. The spin- accumulated electrons force the magnetization of the 2nd material to reverse and to be the direction of the spin polarization.

(source 2 of spin- polarized electrons) Spin-orbit torque (SOT)

In this case, the spin-polarized electrons are generated (created) inside of the ferromagnetic material ( Specifically, at the boundary of the material) by an electrical current. The spin- accumulated electrons force the magnetization of the material to rotate or even reverse. The spin direction of the spin accumulated is different for the opposite directions of the current. Therefore, an electrical current of opposite directions switches the magnetization of a nanomagnet between its two stable states.

 


3 mechanisms of the magnetization reversal

(mechanism 1) Direct spin injection

In this case, the spin direction of the injected electrons is opposite to the spin direction of already- existed electrons. When the number of injected localized electrons of spin opposite to the magnetization becomes larger than the number of initially-existed localized electrons of the spin along the magnetization, the magnetization of the nanomagnet is irreversibly reversed. The spin injection can be due to both the spin-transfer or spin-orbit torque

(mechanism 2) Parametric reversal

In this case, the injected spin-polarized electrons (or their magnetic field) slightly change the magnetization direction in the resonance with the magnetization precession causing an increase of the precession angle. The magnetization of the nanomagnet is irreversibly reversed, when the precession angle becomes larger than 90 degrees. The parametric injection can be due to both the spin-transfer or spin-orbit torque

(mechanism 3) thermally-activated reversal

In this case, due to a random interaction with a non-zero-spin particle, like a magnon or a circularly polarized photon, the number of localized electrons of spin opposite to to the magnetization may become larger than the number of initially-existed localized electrons of the spin along the magnetization. As a result , the magnetization of the nanomagnet is irreversibly reversed.

mechanisms of magnetization reversal by an electrical current (SOT effect)

(fact): There are 3 possible mechanism of magnetization reversal: 1: spin-injection into the bulk of nanomagnet; 2: parametric reversal; 3: thermally-activated reversal
(mechanism 1): Direct spin injection   (mechanism 2) Parametric reversal   (mechanism 3) thermally-activated reversal
   
(SOT method 1: spin injection): Spin- polarized conduction electrons (spin-down) are created at a nanomagnet interface by an electrical current. The spin polarized electrons diffuses into the bulk of the nanomagnet and fill empty spin- down states of the localized electrons. It causes a magnetization precession or, in the case of the larger spin injection, the magnetization reversal   (SOT method 2: parametric magnetization reversal): Spin- polarized conduction electrons are created at a nanomagnet interface by an electrical current. These spin-polarized electrons creates a magnetic field HSO , which tilts the magnetization direction. When is modulated in resonance with a frequency of the magnetization precession, the magnetization is reversed due to the parametric resonance.   A thermal fluctuation can excite a spin-down electron of a lower energy to the upper-energy spin-down level. A thermal fluctuation may make a half of spin-up electrons be excited to the spin-down level. In this case, the magnetization is reversed. SOT effect is often assisted by thermally- activated magnetization reversal in a nucleation domain. The nucleation domain is an unstable magnetic domain, which exists for a very short time at an initial step of the magnetization reversal
(mechanism of magnetization reversal): When the spin- polarized conduction electrons (small bright-green balls) are injected into a nanomagnet, some of them are scattered into unoccupied spin-down energy level of localized electrons. As a result, there is a precession of the total spin (shown as a light blue ball) of the localized electrons around the internal magnetic field Hint (blue arrow). When the electron number on the upper spin-down energy level becomes equal to the electron number on the lower spin-down level, the magnetization reverses its direction.   (mechanism of of the parametric reversal): The magnetic field, which is created by accumulated spin-polarized electrons, slightly tilts the magnetization. When this magnetic field is modulated in the resonance with magnetization precession and the conditions of the parametric resonance are met, the magnetization angle increase until the magnetization reversal.   (mechanism of thermal activated magnetization reversal): When conditions are closed to the magnetization reversal,,at first the domain wall (blue line) is formed. Within this domain the magnetization is reversed by a thermal activation (Neel mechanism). Next, the domain wall moves along the nanowire. When it stops, only a small domain remains. Its magnetization is reversed by a thermal-activation as well.
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Spin accumulation due to an electrical current (SOT effect)

(fact): An electrical current creates a spin accumulation at boundary of nanomagnet
Spin accumulation due to spin-dependent scatterings across interface   Spin Hall effect   Spin accumulation at interface due to an electrical current
   
Fig.1b .Side- jump scattering mechanism across the interface as the mechanism of the Spin Hall effect.   The spin is accumulated at sides of metallic wire, when an electron current flows through the wire   Spin accumulated at boundary of nanomagnet and magnetic field HSO , which is created by this this accumulation.
For a spin- up electron: scattering probability to shift position to the left is higher than the probability to the right. As a result, there is a current of spin-up electrons to the left. For a spin- down electron: scattering probability to shift position to the right is higher than the probability to the left. As a result, there is a current of spin-down electrons to the right.   The conduction electrons (green balls) are scattered on a charged defect (blue ball). The conduction electrons are spin- unpolarized (spins are distributed equally in all directions)). 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 and in contrast the scattering probability for spin-down electrons is lower for a scattering to the right than to the left. As a result, the spin-up electrons is accumulated at the right side of wire and the spin-down electrons is accumulated at the left side of the wire   Both the spin-transfer torque due to spin diffusion into the bulk of the nanomagnet and the parametric resonance due to are the origins of the magnetization reversal by an electrical current
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3-terminal MTJ memory

3 terminal MTJ memory cell
Fig.1 . The writing and reading circuits are separated in this design. The reading current flows though the tunnel barrier. The writing current flows through the non-magnetic metal. The spin current is generated at free-layer/ non-magnetic-metal interface, which reverses the magnetization of the free-layer due to SOT effect and a data is recorded.
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The SOT effect is used as a writing mechanism for the 3-terminal MTJ memory

 

merit: Reading circuit and writing circuits are separated.

It improves: (1) memory durability; (2) operational speed;

Data storage: By means of two opposite magnetization of the "free" layer.

reading circuit: The reading voltage is applied between "free" and "pinned" layers

The resistivity of the MTJ is lower, when the magnetizations of "free" and "pinned" layers are parallel.

The resistivity of the MTJ is higher, when the magnetizations of "free" and "pinned" layers are anti parallel.

writing circuit: The writing voltage is applied between sides of the non-magnetic metal

The spin current is generated at free-layer/ non-magnetic-metal interface , which induces the torque on the "free" layer due to the SOT effect.

The SOT torque is opposite for the opposite polarities of the writing current and it reverses the magnetization into two opposite directions.

 

2-teminals MTJ memory is described here

 


Effect of Spin-orbit torque (SOT)
There are two spin pumps. (spin pump 1): Localized d-electrons, which constantly creates spin-up conduction electrons. (spin pump 2): Due to Spin Hall effect, spin-left electrons is created.
Big ball shows a large number of spin-polarized electrons of electron gas. The small balls shows direction of injected spin-polarized electrons from two spin pumps.
Spin direction of the front spin pump is toward left. Spin direction of the backside spin pump is toward up.
arrows shows the spin-direction and the volume of balls is proportional to the number of the spin polarized electrons
Details on Spin Torque are here
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Origin of Spin-Orbit Torque in short

The creation (origin) of the spin-orbit torque can be divided into two steps. At the first step, the spin-polarized electrons are created by an electrical current. At the second step, the created spin-polarized electrons affects the magnetic properties of the nanomagnet

(step 1) Creation of of the spin-polarized electrons

The creation of the spin-polarized conduction electrons by an electrical current is called the Spin Hall effect (See here for details).

The major mechanism of creation of spin-polarized electrons is the spin-dependent scatterings (See Spin Hall effect for more details)

How an electrical current can create the spin- polarized conduction electrons?

When there are spin-dependent scatterings, the spin-polarized electrons are accumulated at side edges of an electrical wire (Spin Hall effect). For example, if initially the conduction electrons are not spin-polarized, the probability of a scattering of a spin-up electron is larger to the left with respect to current direction and the probability of a scattering of a spin-down electron is larger to the right, then there are more spin-up electrons at the left side of wire and more spin-down electrons at the right side of the wire.

 

Two sources of of generation of spin-polarized electrons:

Interface-source

The spin-polarization is created due to the spin-dependent scatterings across an interface. Typically spin-dependent scattering occurs at an interface between a non-magnetic heavy metal (like Pt, Ta, W) and ferromagnetic metal (like Fe,Co, FeCoB).

Bulk-source

The spin-polarization is created due to the spin-dependent scatterings in the bulk of ferromagnetic metal. Typically the spin-dependent scattering occurs in a ferromagnetic metal containing a heavy metal (like FeBTb)

 

The SOT effect is usually observed in a ferromagnetic metal, where there are two groups of conduction electrons: (group 1) spin-unpolarized electrons and (group 2) spin-polarized electrons (see here). Correspondingly, there are two origins for creations of new spin-polarized electrons.

Two origins of generation of spin-polarized electrons:

from spin-unpolarized electrons

Due to spin-dependent scattering, some spin-unpolarized electrons becomes spin-polarized. The spin-polarization of these created spin-polarized electrons are different on opposite sides of the wire.

from spin-polarized electrons

A spin-dependent scattering of already-existed spin-polarized electrons creates the spin-polarized electrons of different spin direction. As a result, there are two groups of spin-polarized electrons of different spin directions: (group 1) large group of "already-existed" spin-polarized electrons and (group 2) tiny group of "newly-created" of spin-polarized electrons. These two groups quickly interact with each other (See Spin Torque)

 

(step 2) Influence of created spin-polarized electrons on magnetic properties on a nanomagnet

(influence 1) Spin torque

See details on the spin torque here.

It is the case when the spin direction of "newly-created" spin-polarized electrons is different from the spin direction of "already-existed" spin-polarized electrons. In this case the Spin Torque is created. As a result, the spin direction of a large number of "already-existed" spin-polarized electrons rotates toward the spin-direction of a tiny number of "newly-created" spin-polarized electrons. This effect is called the Spin Torque.

Depending on the spin direction of "newly-created" spin-polarized electrons and the corresponded direction the Spin Torque., two torque torque can be distinguished: "damp-like" torque and "field-like" torque.

(influence 2) Change of size of nucleation domain for the magnetization switching

See details on thermally -activated magnetization switching here.

The electrical current induces the spin-transfer torque (it is the mechanism of the current induced magnetization reversal in a MTJ). Under influence of the spin-transfer torque, the domain wall of the nucleation domain for magnetization switching may may. As a result,

(influence 3) Change of the spin polarization

See details on spin polarization here and here.

The electrical current creates the spin polarized electrons, which added to "already-existed" spin-polarized electrons. Depending on the polarity of the electrical current, the spin direction of "newly-created" spin-polarized electrons is either along or opposite to the spin direction of the "already-existed" spin-polarized electrons. As a result, the total spin polarization either decrease or increases for two opposite directions of the electrical current.

This influence makes current-dependent all magnetic properties, which depend on the spin polarization.

(influence 4) Change of the PMA energy

See details on thermally -activated magnetization switching here.

For a reason, which has not been understood yet, the PMA energy EPMA is changed by the electrical current. It leads to current-dependency of anisotropy field Hanis, coercive field Hc and delta Δ.


 

Transformation of Hysteresis loop due SOT effect

The position of loop is shifted due to current, but width and height of the loop are constant.
The x-axis is applied out-plane magnetic field. Click on image to enlarge it.

Magnetic parameters affected by SOT effect

creation of damping -like torque

This SOT effect is similar to the effect produced by an usual magnetic filed HDL , which is applied perpendicularly to the electrical current and perpendicularly to the magnetization.

The direction of the magnetic field HFL depends on the magnetization direction. When magnetization rotates along the z-axis. The magnetic field HDL rotates as well.

 

creation of field-like torque

This SOT effect is similar to the effect produced by an usual magnetic filed HFL , which is applied along the electrical current.

The magnetic field HFL does not depend on the magnetization direction.

 

modulation of the anisotropy field Hanis and the energy of perpendicular magnetic anisotropy EPMA

The bias current generates a spin-polarized electrons. The spin-polarized electrons at may affect the magnetization near film interface and consequently the the strength of the perpendicular magnetic anisotropy (PMA)

 

modulation of coercive field

Change of magnetization switching time under current due to SOT

dependence is opposite for spin-down to up and spin-down to up switching

switching from spin-down to spin-up

switching from spin-up to spin-down

switching time increases under a negative current and decreases under a positive current switching time increases under a positive current and decreases under a negative current
The magnetization switching time at a different current density. Sample ud30 Volt53B Ta(2.5):FeCoB(1):MgO Nanowire width: 1000 nm, length 200 nm. Measurements date is 10. 2018
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Under a bias current, the hysteresis loop are shifted from its center position (See Fig). It looks similar as an additional magnetic field applied perpendicularly to the film.

The switching field from spin-up to down state became different from switching field from spin-down to up state

modulation of delta Δ and retention time

The Δ and retention time characterize stability of the magnetization against a thermally- activated reversal.

The modulation of the Δ changes the probability thermally-activated magnetization switching

modulation of effective magnetization Meff and effective size of nucleation domain

The Meff is magnetization of first magnetic domain (nucleation domain), which triggers the magnetization reversal.

The bias current may move domain wall due to the spin-transfer torque. As a result the size of the nucleation domain becomes smaller or larger. Consequently, the Meff becomes smaller or larger.

modulation of the Hall angle

The Hall angle or the Hall resistance depends on the magnetization of the ferromagnetic metal, spin-polarization of the conduction electrons and the strength of the spin-orbit (SO) interaction. The bias current generates a spin-polarized electrons. As a result, the spin polarization of electron gas and its distribution across film changes. It causes the change of the Hall angle.

 


Measurement of SOT

Experiment

Fig.2 Anomalous Hall Effect is used for all SOT measurements
Click on image to enlarge it.

All SOT measurements were done using the Anomalous Hall Effect (AHE).

Fabrication of FeB, FeCoB and FeTbB nanomagnets connected to a Hall probe

The FeB, FeCoB and FeTbB films were grown on a Si/SiO2 substrate by sputtering. A Ta layer was used as a non-magnetic adhesion layer. The thickness of the Ta was between 2 and 10 nanometers and wafers of different Ta thickness were tested. A nanowire of different width between 100 and 1000 nm with a Hall probe was fabricated by the argon milling. The width of the Hall probe is 50 nm. The FeB and FeCoB layers were etched out from top of the nanowire except a small region of the nanomagnet, which was aligned to the Hall probe. The nanomagnets of different lengths between 100 nm to 1000 nm were fabricated.

 

 

 

 


Major obstacle of a SOT measurement is the heating

The SOT becomes substantial at the current of about 10-100 mA/um2. The heating of nanowire is substantial at this current. It is hard to remove the heating even when a pulse mode is used. For example, in my standard measurements an electrical pulse of 300 ms following 5 s cooling is used. However, there is still a substantial heating in this pulse mode (see below).

In any SOT measurements the sample heating should be taking into account.

How to distinguish effects from the SOT from the effects from heating?

A. The SOT effect is linearly proportional to current, but heating ~I2, at a relatively-small current the SOT dominates, but at a higher current the heating dominates.

How to minimize the influence of the heating?

1) Sweep polarity of current

Usually (but not always) the SOT changes its polarity when the polarity of current is reversed. The heating does not dependent on the current polarity

2) use a narrower and shorter nanowire.

The dissipation of heating is more effective in this case.


Measurement method of "field -like" torque HFL

Dependence of in-plane component of magnetization on in-plane plane magnetic field. The magnetic field is applied in-plane and along the current. HFL is the the offset magnetic field, which is proportional to the current. The HFL is evaluated by linear fitting of the dependence, which measured in Hall configuration.
Click on image to enlarge it

Method to measure "damp-like" torque and "field-like" torque

This method is similar to the method of measurement of anisotropy field Hanis (See here). In this measurement the in-plane component of the magnetization is measured as a function of an external magnetic field Hext. The dependence is linear (See here). Therefore, it can be measured with a high precision. The anisotropy field Hanis is defined as the in-plane magnetic field, at which initially-perpendicular magnetization turns completely into the in-plane direction.

Under a sufficient bias current, additionally to Hext., there are two more additional magnetic fields: 1) effective field of "field-like" torque HFL in direction of current and 2) effective field of "damp-like" torque HDL in direction perpendicularly to the current. Therefore, the magnetization experiences two magnetic field:

In-plane magnetic field along bias current (the x-axis) Htotal,x=Hext,x+HFL ,

In-plane magnetic field perpendicularly to bias current (the y-axis) Htotal,y=Hext,y+HDL ,

 

As a result, the dependence M vs Hext is shifted on HFL (Hext is applied along x-axis) or HDL (Hext is applied along y-axis). From the shift the HFL are HDL are evaluated.

Note: The same measurements can be done by two method

Method 1. The direct measurement using a nano voltmeter (See Fig.2 above)

Method 2. The 2nd-harmonic measurement using a lock-in amplifier (See here)

Both measurements give the same values of HFL and HDL and nearly the measurement precision. However, the usage of the direct measurement is preferable for the following reasons. From the direct measurement, the dependence of HFL and HDL on bias current can be evaluated. From measured dependence of M vs H, the contributions of the "field-like" and "damp-like" torque can be separated in the case when they are in the same direction. In contrast to the 2nd-harmonic measurement, in the direct measurement the undesired contribution due to sample heating can be removed.

I use AHE measurement to evaluate the in-plane component of the magnetization. The tunnel magneto-resistance (TMR) of magnetic tunnel junction (MTJ) can be used as well (See here).

1st type of SOT effect: "Damp -like" torque

"Damping-like" torque

The electrical current creates a magnetic field HDL, which is directed along current and perpendicularly to the magnetization M.. Due to HDL, the magnetization M is inclined to the front direction. When external magnetic field Hext is applied, the magnetization M turns in-plane. Following M, HDL turns as well. From measurements of magnetization M vs Hext, HDL can be evaluated.

Click on image to enlarge it

 

This SOT effect is similar to the effect produced by an usual magnetic filed HDL , which is applied perpendicularly to the electrical current and perpendicularly to the magnetization.

The "damping-like" torque is described as

where the effective magnetic field of the "damping-like" torque is defined as

(See Landau–Lifshitz equation)

 

 

 

How to measure it?

Measurement method of "damping -like" torque HDL

Dependence of in-plane component of magnetization on in-plane plane magnetic field. The magnetic field is applied in-plane and perpendicularly to the current. The center of line is shifted, but its ends are at the same position. The HDL is the the offset magnetic field, which is proportional to the current. The HDL is evaluated by linear fitting of the dependence, which measured in Hall configuration.
Click on image to enlarge it

It can be measured by the same measurement, which is used to measure the anisotropy field (See here). The in-plane component of magnetization is measured as a function of in-plane magnetic field. The in-plane magnetic field, which is applied perpendicularly to the electrical current.

The HDL gives the field offset for such measurement (See right Fig). From a linear fitting of measured dependence, the HDL is evaluated.

In the case of the "damp-like" torque the dependence M vs H is not linear. Even in the case the fitting gives a high precision.

 

Effective magnetic field HDL of the "damping -like" torque

Slope: -0.21811 Oe/(mA/um2)

Slope: -0.3371 Oe/(mA/um2)

as Nov. 2018
Sample R64A Volt58B Ta(5):FeCoB(1):MgO Sample: L58B Volt58A . It is the same wafer as the left one, but device position on the wafer is different

Measured sample distribution of the current- modulation of the effective field HDL of "damp- like" torque in FeB and FeCoB samples.

Measurements date is 10. 2018
Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

What is the "damp-like" torque?

Effective magnetic field of "damp-like" and "anti damp-like" torque

damp-like torque

anti damp-like torque

The damp-like torque align the spin along the external magnetic field. The anti damp-like torque align the spin opposite to the external magnetic field.
Red arrow shows the spin (the magnetization). Blue arrow show the magnetic field Hext. Green arrow shows the effective magnetic field of the damp Hdamp (anti damp Hanti damp) torque.
Click on image to enlarge it

 

 

Difference between "damp-like" torque and "field-like" torque

 

 

 

 

Properties of effective magnetic field of "damp-like" torque

Its direction changes, when the spin direction (magnetization direction) changes.

Its magnitude changes, when the spin direction (magnetization direction) changes. The magnitude is the largest, when the spin is perpendicular to Hext and the magnitude is the smallest (equals to 0), when the spin is parallel to Hext.

 

 

 

 

What is the direction of the "damp-like" torque?

3 components of the "damp-like" torque can be distinguished. They are labeled as Hdamp,x , Hdamp,y and Hdamp,z.

Since the direction and magnitude of the effective magnetic field of "damp-like" torque changes when the magnetization direction is changed, the following definition is used:

Hdamp,x aligns magnetization along the x-axis (along bias current)

Hdamp,y aligns magnetization along the y-axis. (in-plane and perpendicularly to bias current)

Hdamp,z aligns magnetization along the z-axis. (perpendicularly to plane)

 

Direction of effective magnetic field of "damp-like" torque

magnetization rotates in yz- plane

magnetization rotates in xz- plane

Hdamp,x and Hdamp,z change their magnitude. Hdamp,y changes its direction Hdamp,y and Hdamp,z change their magnitude. Hdamp,x changes its direction

Red Arrow :M is the magnetization (the spin).
Gold Arrow: Hdamp,x is magnetic field of damping towards the x-axis
Blue Arrow: Hdamp,y is magnetic field of damping towards the y-axis
Green Arrow: Hdamp,z is magnetic field of damping towards the z-axis

Click on image to enlarge it

most probable direction of the "damp-like" torque is Hdamp,x

It is because of the following reason: The bias current breaks the time-reversal symmetry along the x-axis. Similarly, the time-reversal symmetry breaks in this direction, when a magnetic field is applied along the x-axis. Then, damp-like" torque is Hdamp,x aligns the magnetization along this field

Note: The existence of Hdamp,y and Hdamp,z is also allowed by the symmetry.

 

 

How Hdamp,x , Hdamp,y and Hdamp,z change their magnitude and direction when magnetization is rotated in the yz-plane and the xz-plane

It is important because from measurements of such rotation both is "field-like" torque and "damp-like" torque are evaluated.

 

 

 

 

 

 

 


2nd type of SOT effect: "Field-like" torque

"Field like" torque

The electrical current creates a magnetic field HFL, which is directed along current. Due to HFL, the magnetization M is inclined to the right direction. When external magnetic field Hext is applied, the magnetization M turns fully in-plane at a smaller field Hext= Hanisotropy - HFL,in the left direction. The magnetization M turns field in-plane at a larger field Hext= Hanisotropy + HFL,in the right direction. Measuring the difference between two field, HFL can be evaluated
Click on image to enlarge it

 

This SOT effect is similar to the effect produced by an usual magnetic filed HFL , which is applied along the electrical current.

The "field-like" torque is described as

where the effective magnetic field of the "field-like" torque is defined as

 

 

 

 

 

How to measure it?

Measurement method of "field -like" torque HFL

Dependence of in-plane component of magnetization on in-plane plane magnetic field. The magnetic field is applied in-plane and along the current. HFL is the the offset magnetic field, which is proportional to the current. The HFL is evaluated by linear fitting of the dependence, which measured in Hall configuration.
Click on image to enlarge it

It can be measured by the same measurement, which is used to measure the anisotropy field (See here). The in-plane component of magnetization is measured as a function of in-plane magnetic field. The in-plane magnetic field is applied along the electrical current.

The HFL gives the field offset for such measurement (See right Fig). From a linear fitting of measured dependence, the HFL is evaluated.

The Hall measurement is used to evaluate the in-plane component of the magnetization. The TMR can be used as well (See here).

 

The dependence of HFL on the current is rather linear. All FeB and FeCoB samples, which I have measured by Nov. 2018, shows the same sign (positive) of HFL.

 

Effective magnetic field HFL of the "field like" torque induced by SOT

Slope: 0.22093 Oe/(mA/um2)

Slope: 0.42035 Oe/(mA/um2)

as Nov. 2018
Sample R64A Volt58B Ta(5):FeCoB(1):MgO Sample: L58B Volt58A . It is the same wafer as the left one, but device position on the wafer is different Measured sample distribution of the current- modulation of the effective field HFL of "field- like" torque in FeB and FeCoB samples.
Measurements date is 10. 2018
Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


3d type of SOT effect: SOT modulation of anisotropy field Hanis and PMA energy

Change of anisotropy field Hanis & PMA energy due to the SOT effect

case 1: SOT modulation of Hanis

case 2: nearly no SOT modulation

Current- (SOT-) induced change of Hanis Sample distribution of ΔHanis

Due to SOT effect, the Hanis increases at a negative current and decreases at a positive current. Additionally, the electrical current heats the sample. The heating causes the decreases of Hanis. Since SOT effect is linearly proportional to current, but heating ~I2, at a small negative current the Hani increases, but at a higher current effect of the heating dominates. Under a higher current the heating is stronger and temperature increase. When T increase, Hanis sharply decreases (see here). The decrease is symmetrical for opposite polarities of current. The of anisotropy field Hanis for two opposite directions of current as function of current as Nov. 2018
Sample R64A Volt58B Ta(5):FeCoB(1):MgO Sample: L58B Volt58A . It is the same wafer as the left one, but device position on the wafer is different Sample: ud49 Volt53, Ta(2.5) FeCoB(1):MgO, wire width 400 nm, nanomagnet length 500 nm Measured sample distribution of the current- modulation of the anisotropy field ΔHanis in FeB and FeCoB samples.
Measurements date is 10. 2018
Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measurement method of anisotropy field

Dependence of in-plane component of magnetization on in-plane plane magnetic field. The slope depends on the electrical current. The anisotropy field is evaluated from the slope of the line.
Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 


 

4th type of SOT effect:SOT modulation of the coercive field

Change of coercive field due to the SOT effect (case 1:stronger heating)

Transformation of Hysteresis loop due SOT effect. The position of loop is shifted due to current, but width and height of the loop are constant.

Switching fields (coercive field) between spin-down to up and spin-up to down states. At a positive current, the coercive field of spin-down to up switching is larger. At a negative current, the coercive field of spin-up to down switching is larger. Such dependence is due to the SOT effect. For both current polarities, the coercive field decrease when the bias current increases. It is due to heating and the temperature rise.

 

Difference of switching fields between spin-down to up and spin-up to down states. The dependence is linear.
Data was measured using method described here, which gives measurement precision of coercive field better than 0.1 Oe.
Sample Ta(5)/FeB(0.9)/ MgO(6)/ Ta(1)/Ru(5) (Volt55 free44). Measurements date is 06. 2018
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When current increases, two effects occur:

1.Heating

Even though the measurements of the coercive field are done in pulse mode, it is difficult completely avoid heating.

Due to the heating coercive field decreases. However, the decrease of the switching field between spin-down to up and switching field between spin-up to down states are absolutely identical and symmetrical (See here)

2. SOT effect

 

The coercive field was measured using method described here, which gives measurement precision of coercive field better than 0.1 Oe.

Change of coercive field due to the SOT effect (case 2: weaker heating)

Coercive field for the magnetization switching from spin-down to spin-up and spin-up to spin-down. Due to heating coercive field decreases. Due to SOT effect, the coercive field increases for spin-down to spin-up at a negative current and for spin-down to spin-up at a positive current. Since SOT effect is linearly proportional to current, but heating ~I2, only at a small current the Hc increases, but at a higher current effect of the heating dominates.

The difference of the coercivity field when polarity of the current reversed. The dependence is opposite for the magnetization switching from spin-down to spin-up and spin-up to spin-down.

Difference of switching fields between spin-down to up and spin-up to down states. The dependence is linear.
Sample ud30 Volt53B Ta(2.5):FeCoB(1):MgO Nanowire width: 1000 nm, length 200 nm.
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Sample distribution of ΔHc

Measured sample distribution of the current- modulation of the coercive field ΔHc in FeB and FeCoB samples.
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5th type of SOT effect: modulation of delta Δ and retention time

modulation of delta Δ

modulation of retention time

modulation of delta Δ is nearly the same for magnetization switching from spin-down to up and from spin-up to down modulation of retention time is nearly the same for magnetization switching from spin-down to up and from spin-up to down
Sample ud30 Volt53B Ta(2.5):FeCoB(1):MgO Nanowire width: 1000 nm, length 200 nm
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6th type of SOT effect: modulation of effective magnetization Meff and effective size of nucleation domain

modulation of effective size of nucleation domain

Sample ud30 Volt53B Ta(2.5):FeCoB(1):MgO Nanowire width: 1000 nm, length 200 nm Sample: ud49 Volt53, Ta(2.5) FeCoB(1):MgO, wire width 400 nm, nanomagnet length 500 nm
Dependence of size of nucleation domain on the electrical current. The black line shows for the case of magnetization switching from spin-down to spin-up state. The red line show for the case of switching from spin-up to spin-down state.
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7th type of SOT effect: SOT modulation of the Hall angle

SOT modulation of Hall angle

Difference of Hall for two opposite polarities of the bias current vs absolute value of current. The proximity of MgO modifies significantly
Sample: Ta(5):FeCoB ( 1 nm, x=0.3):MgO(7) Volt58A (L58B); nanowire width is 3000 nm, nanowire length is 25 um, length of um etched section is 3 um. For measurements of different magnetic properties of this sample click here
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8th type of SOT effect: The SOT modulation of spin polarization

Dependence of spin polarization on polarity of bias current (SOT effect)

Sample: FeB. Spin polarization as function of current density. At a higher current, the spin polarization decreases due to the sample heating. However, the decrease is different for opposite polarities of the current Sample: FeB. Change of the spin polarization under reversal of current direction Sample: FeCoB. Change of the spin polarization under reversal of current direction

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"damp-like" torque and "field-like" torque

The "damp-like" torque and "field-like" torque can be measured by following techniques:

1) from measurement of anisotropy field; 2) by 2f-lockin technique; 3) from ST-FMR measurements


 

Comparison between "damp-like" torque and "field-like" torque

Difference between "Damp-like" torque and "Field-like" torque

Evaluation of type of SOT effective field "Field-like" torque "Damp-like" torque
In-plane component of magnetization as a function of applied in-plane magnetic field. The green line shows the case when there is no the spin-orbit torque. The blue line shows the case when the torque is "field-like" type. The red line shows the case when the torque is "damp-like" type. The effective magnetic field HFL of the "field-like" torque does not depend on the magnetization direction. Independently on the magnetization direction, it is always directed along the current.

The effective magnetic field HDL of the "damp-like" torque. It is always perpendicular to the magnetization direction. When the magnetization turns, the he effective magnetic field HDL turns as well.

 

Click on image to enlarge it

 

There are two substantially different types of the Spin-Orbit Torque.

One type does not depend on the magnetization direction of the ferromagnetic metal. It is only depend on the direction of the current. Such torque is called the field-like torque. The second

The second type does depend on the magnetization direction of the ferromagnetic metal. Such torque is called the anti-damping torque.

Even without any current, there are spin-polarized conduction electrons in a ferromagnetic metal. All conduction electrons in a ferromagnetic metal can be divided into two groups: group of spin-polarized electrons and group of spin-unpolarized electrons (See here for details). As was mentioned above, the spin-dependent scatterings originate the Spin-Orbit Torque. Since the properties of the spin-unpolarized electrons does not depend on the magnetization direction, the scattering of these electrons creates the anti-damping torque.. Spin direction of spin-polarized conduction electrons is parallel to the magnetization (See here for details). Therefore, the scattering of the spin-polarized creates the field-like torque

The field-like torque

1.It does not depend on the magnetization direction of the ferromagnetic metal.

2. It is created due to scattering of the spin-unpolarized electrons

The anti-damping torque

1.It does depend on the magnetization direction of the ferromagnetic metal.

2. It is created due to scattering of the spin-polarized electrons

 

 


Influence of interface on SOT effect

Dependence of SOT on the interface material

not-etched part etched part
 
Backside Hall probe is connected to a nanomagnet. FeB is thicker in this region and top of FeB is covered by MgO. The Front side Hall probe is connected at side of a nanomagnet. FeB is thinner in this region and at its top covered by SiO2. The distance between two Hall pairs is 11 μm.  
Sample: Ta(5):FeCoB ( 1 nm, x=0.3):MgO(7) Volt58A (L58B); nanowire width is 3000 nm, nanowire length is 25 um, length of um etched section is 3 um. For measurements of different magnetic properties of this sample click here
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Measurements of the SO torque using 2d harmonic lock-in technique

Measurement of the Spin-orbit torque by 2d harmonic lock-in technique

asymmetric (even) component

symmetric (odd) component

it measures :(1) "field-like" torque, when the in-plane magnetic field is applied along the wire ( along electrical current); (2) "damp-like" torque, when the in-plane magnetic field is applied perpendicularly to the wire ( to electrical current); It measure
In this method the 2d harmonic of Hall voltage is measured as a function of an in-plane magnetic field
Click on image to enlarge it

 

The Hall voltage is proportional to the current, the perpendicular components of magnetization and the spin polarization of conduction electrons. When current is modulated with frequency ω, the magnetization direction, the magnetization magnitude and spin-polarization of the conduction electrons may be modulated due to the effect of the SO torque. As a result, the Hall voltage is modulated with frequency 2ω. Measuring this 2d harmonic the amplitude of the SO torque can be estimated.

 

What can be measured by the 2d harmonic lock-in technique?

1. "Field-like" torque

The direct measurements see here

It can be evaluated from the asymmetric (even) component of dependence of the 2d-harmonic voltage vs the in-plane magnetic field, when the magnetic field is applied along the current.

2. "Damp-like" torque

The direct measurements see here

It can be evaluated from the asymmetric (even) component of dependence of the 2d-harmonic voltage vs the in-plane magnetic field, when the magnetic field is applied perpendicularly the current.

3. Current-modulation of anisotropy field

The direct measurements see here

It can be evaluated from the symmetric (odd) component of dependence of the 2d-harmonic voltage vs the in-plane magnetic field. The result is the same whether the magnetic field applied along or perpendicularly to the current.

 

The fields of the the spin-orbit torque can be calculated from the following dependance of the 2d-harmonic voltage VHall,2ω vs applied in-plane magnetic field Hx :

where ΔHanis,ω is the current induced change of the anisotropy field Hanis; ΔHoff,ω is the effective magnetic field HFL,ω of the "field-like" torque, when Hx is applied along electrical current; and ΔHoff,ω is the effective magnetic field HDL,ω of the "damp-like" torque, when Hx is perpendicularly to the electrical current;

the odd and even components can be calculated as

Rwire is the is the ohmic resistance of the wire; RHall,0 is the is the Hall resistance, when a in-plane magnetic field is not applied ;

Hanisot is the anisotropy field, which can be measured directly (See here) with a high precision or from 1st harmonic with a moderate precision.

The Hanisot can be evaluated from the following dependance of the 1d-harmonic voltage VHall,ω vs applied in-plane magnetic field Hx :

 

for details description of 2d harmonic lock-in technique, click there to expand

 

The 2d harmonic lock-in technique measures the current- modulation of the effective magnetic field HDL of "damp- like" torque, the effective magnetic field HFL of "field- like" torque and the anisotropy field ΔHanis

Without electrical current, the in-plane component of the magnetization Mx depends on the applied external in-plane magnetic field Hx as (see here)

where Hanis is the anisotropy field

As was demonstrated above, the spin-orbit torque (SOT) produces the offset magnetic field ΔHoff and changes the anisotropy field Hanis on ΔHanis. As a result, the Eq.(4.1) is modified as

where ΔHoff equals to HFL when the in-plane magnetic field is applied along current and ΔHoff equals to HDL when the in-plane magnetic field is applied in-plane and perpendicularly to the current

In the case when

Eq.(4.2) can be simplified as

or

where

from (4.2) we have .

The z- component of the magnetization Mz can be calculated as

or

 

The Hall voltage is calculated as

when magnetization is not perpendicular to plane, the Hall voltage is calculated as

where Mz is the perpendicular-to-film component of magnetization, RHall,0 is the Hall resistance when the magnetization is perpendicular to the film (Mz =M).

When the current is modulated with frequency ω ,

both the ΔHoff and ΔHanis are modulated as well:

Using a trigonometric relation

and substituting Eqs (4.7) (4.10),(4.11) into Eqs. (4.7) gives the Hall voltage VHall,2ω of the 2d harmonic (the coefficient at cos(2ωt)) as

In a lock-in measurement it is convenient to use the reference voltage Vω rather than reference current Iω

2d harmonic

as a function of applied in-plane magnetic field.
Click on image to enlarge it

where Rwire is the resistance of metallic nanowire.

Substituting Eqs. (4.2) and (4.14) into Eq. (4.13) gives

or

The voltage of the second harmonic has two component. The first component is proportional to ΔHoff and is an odd function in the respect to Hx. The first component is proportional to ΔHanis and is an even function in the respect to Hx. Therefore, the voltage of the second harmonic can be calculated as

2d harmonic

as a function of applied in-plane magnetic field.
Click on image to enlarge it

Eq (4.17) can be written in a symmetrical form as

where

 


Measurement of anisotropy field from the 1st harmonic (not recommended)

1st harmonic

Perpendicular-to-plane component of magnetization as a function of applied in-plane magnetic field.
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When current is small, the ΔHoff and ΔHanis can be ignored. Than, the Hall voltage VHall,ω of 1st harmonic can be calculated from Eq.(4.9) as

substitution of Eq(4.1) into Eq.(4.20) gives the Hall voltage VHall,ω of 1st harmonic as

 

The ratio of voltage of 1st harmonic to the voltage of 1st harmonic can be calculated as

 

 

 

 

 

 

 

 

Measurement of anisotropy field Hanis

The arrow shows the direction and magnitude of the applied in-plane magnetic field. The ball shows the magnetization direction. Without magnetic field the magnetization is perpendicularly-to-plane. Under magnetic field, the magnetization turns toward magnetic field. The field, at which the magnetization turns completely in-plane, is called the anisotropy field. The dots of the right graph shows experimental data. Measurement date: May 2018.
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Current-induced magnetization reversal in FeBTb

Electrical current can induce spin torque or reduce the exchange interaction between localized electrons. This can change the direction of magnetization of a material.

Current-induced magnetization reversal in FeBTb film

 

Dependence on applied magnetic field

Coercive field significantly decreases when current density increases

click here or on image to enlarge it

Dependence on current density

magnetization is reversed by electrical current

click to enlarge

 

Two current-induced effects, which can lead to the current-induced magnetization reversal:

1) Current-induced Spin torque

2) Current-induced reduction of the exchange interaction between localized electrons.

 

Both effects occur because of transfer of delocalized (conduction) spin-polarized electrons from a point to point, which alters  an equilibrium spin polarization in a material.

The spin torque occurs when the delocalized spin-polarized electrons are transferred from one material to another by a drift or a diffusion current. When spin-polarized delocalized electrons are injected, it is not only change magnitude of spin accumulation, but  also it changes spin direction of spin accumulated electrons. As result, the spin direction of localized and delocalized electrons becomes different. This induces the torque,  which may turn or reverse the spin direction of the localized electrons.

Note: At one place an electron gas may have only one spin direction of its spin accumulation. In the case when the electrons with a different spin direction is injected, the spins quickly relax and the spin accumulation of only one spin direction remains. The final spin direction is different from initial spin direction and from the injected spin direction. Details see here and here

 

 

 

The spin torque may change magnetization direction in a material because of the exchange interaction between localized and delocalized electrons.

 

 

 

There are several effects which can cause the current-induced spin torque:

1)The spin-transfer torque.

It occurs  because of transfer of spin-polarized electron from material to material by a drift or diffusive spin current. Example: the spin transfer between electrodes  in a MTJ or GMR junction. The polarity of the spin-transfer torque depends on mutual magnetization directions of the electrons.


2) The spin-orbit (SO) torque.


 

 

Current-induced magnetization reversal in FeBTb film

 

Negative bias

Coercive field significantly decreases when current density increases

click here or on image to enlarge it

Positive bias

magnetization is reversed by electrical current

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Current-induced magnetization reversal in FeBTb film

 

delocalized (conduction p- or s-) electrons

The spin-polarized delocalized electrons are accumulated at the left side of the wire and they are depleted at the right side. Since the delocalized spin-polarized electrons mediates the exchange interaction between localized electrons, the exchange interaction becomes weaker at right side and stronger at left side.

click here or on image to enlarge it

localized (d- or f-) electrons

When a weak magnetic field is applied opposite to the magnetization of the wire, it is not sufficient to reverse magnetization of the wire. When current flows through the wire, delocalized electrons are depleted at right right side of wire and the exchange interaction between localized electrons is reduced in this area. Because of reduced exchange interaction, the weak external magnetic field becomes sufficient to reverse magnetization of localized electrons at the right side. This reversal triggers the magnetization reversal in whole wire.

click here or on image to enlarge it

click here to see both side reversal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Questions & Answers


(about systematic errors of 2nd harmonic measurements)

Regarding 2nd harmonic method, I have to disagree with you. The technic is reliable if you manipulate it correctly, and like any experiment there is always the risk of an “artifact” effect not taken into account. I believe that we have reached today a conclusion on how to perform an analysis using 2nd harmonic and to take into account spurious effects..

The problem of the 2nd harmonic measurement is that it has too many independent contributions, such as

1. magnetization precession due to spin injection

2. magnetic field Hoff, which is induced by the spin accumulation

3. Current dependency of anisotropy field

4. PHE/AMR effect.

Three of them can be used for magnetization reversal by an electrical current.

The fact is that the 2nd harmonic measurement does not have enough data to describe its own measured data, because of a large number of different independent contributions. The new method, which I have developed, measures each contribution individually and independently of other contributions. Each contribution has a rich and interesting Physics, which can be individually optimized for an efficient magnetization reversal.

--------------------------------

The 2nd harmonic measurement has the similar tendency as the current dependency of the magnetic field Hoff, which is induced by the spin accumulation. Therefore, it is OK to use data of the 2nd harmonic measurement in a publication, in which different tendencies are studied and discussed, and in which some systematic error is not a big issue. However, for a technology optimization, the use of a direct and more reliable measurement is better.


 

(about field- like torque) (from Sreyas Satheesh) I had some serious doubts regarding the field like torque terms. You had mentioned the field-like field to be independent of the magnetization direction and to be directed along the direction of the current. However, in some of the works, I had found it to be orthogonal to the direction of the current. Ref: 1)Garello, K. et al. Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures. Nature Nanotech. 8, 587–593 (2013). 2)Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189–193 (2011).

(about torque & spin dynamic & Quantum mechanic)

There is only one torque, which is damping (or anti damping torque) of the Landau-Lifshitz equation. The introduction of any possible torque of different types or a different direction violates the rules of the Quantum Mechanics.

The spin is a pure quantum- mechanical object and the torque is the object of classical physics. Therefore, strictly-speaking it is incorrect to use the torque for a description of the spin dynamics. However, it is still possible to use the torque for the spin dynamics, when the torque closely mimics and well- approximates all features of the quantum-mechanical dynamics of the spin. The reason for the use of the torque is to simplify the description and understanding of the spin dynamics. However, in contrast to the classic mechanic, in which the torque may have any direction and magnitude, the quantum- mechanical rules limit the torque to only one possible direction and make the torque strength dependent on the spin precession angle.

The spin dynamics, as any quantum mechanical process, is described by a transition between quantum levels. In the case of the spin, the lower-energy level corresponds to spin direction along the magnetic field (spin-up) and the lower-energy level corresponds to spin direction opposite to the magnetic field (spin-down) . Only possible other quantum states of the spin are the states, whose energy is between the spin-up and spin-down levels and which corresponds to the spin precession at a different spin precession angle.

For example, in an equilibrium the spin is in the spun-up state and there is no spin precession. When there is an injection of spin-down electrons, both the spin-up and spin-down quantum states are partially filled, which corresponds to the spin precession. The spin precession is larger when there are more spin-down electrons. This quantum mechanical process can be described rather well and reasonably correctly by the damping torque (or anti-damping torque) of the Landau-Lifshitz (LL) equation.

(about Field-Like torque)

Except for the transition between the spin-up and spin-down quantum levels, which is described by the damping torque of LL Eqs, I do not see any other options for a possible quantum spin dynamic and, therefore, any possibility for introduction of the other torque. For example, another possible mechanism of the spin reversal, the parametric magnetization reversal, when the magnetization direction is modulated in the resonance with spin precession, is also described by the transition between the spin-up and spin-down quantum levels and, therefore, the same anti-damping torque of LL Eqs. You can find more explanations about this in this video (click here)

There is no such thing as the field-like torque. However, there is a magnetic field, which is induced by spin-accumulated electrons. Since the spin accumulation is created by the current, this magnetic field can be modulated by current and can be used for the parametric magnetization reversal. One of the in-plane components of this magnetic field is incorrectly associated with the damp-like torque and another in-plane component is incorrectly associated with the field-like torque. The reason for that is the symmetry of the 2nd harmonic measurement with respect to the magnetization reversal. More details about this magnetic field and its measurement you can find in this video (click here).

Two papers, which you have mentioned, are two important papers, in which the field-like torque was introduced based on the 2nd harmonic measurement. However, the problem of the 2nd harmonic measurement is that it is influenced by too many parameters and the data of measurement of the 2nd harmonic alone is not sufficient to explain the changes of all those parameters. Now the direct measurements have clarified the situation. You can find the explanation about it in the mentioned video.

In the two mentioned papers, the puzzling data of the 2nd harmonic measurement was explained by the introduction of the field-like torque. It is a great, but incorrect idea. It is a very natural way of the development of science. Some great, but incorrect models may exist until new data clarifies the situation.

 

 

 


Video

Parametric magnetization reversal.

Spin- orbit torque

Conference presentation. Intermag 2021

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(video): Measurement of coefficient of spin- orbit interaction, anisotropy field in a nanomagnet and magnetic field created by a spin accumulation.

(Part 6): Magnetic field Hoff created by spin accumulation. Origin and properties

 

(Part 7): Dependency of Hani & Hoff on electrical current (SOT effect) & gate voltage (VCMA effect)

 

(Part 8a): Magnetization reversal by electrical current & Gate voltage. Parametric reversal

 

(Part 8b): Magnetization reversal due to modulation of Hani or Hoff by electrical current or Gate voltage.

     
(short content 1:) the origin and properties the magnetic field created by spin accumulation, Hoff   (short content 1:)  the reason why the spin accumulation makes Hani and Hoff dependent on the electrical current.
  (short content 1:)  the possibilities of magnetization reversal  utilizing the measured effects of current modulation of Hani & Hoff.
  (short content 1:)  required conditions for the parametric magnetization reversal using the current modulation of Hani or using the current modulation of Hoff required conditions for the parametric magnetization reversal using the current modulation of Hani or using the current modulation of Hoff
(short content 2:) dependence of Hoff on the strength of the spin-orbit interaction. The reason why Hoff is larger in a multilayer nanomagnet and smaller in a single-layer nanomagnet   (short content 2:)   the experimental data of the current dependency of Hani and Hoff .   (short content 2:)  quantum- mechanical description of the spin- transfer torque
  (short content 2:)  ( inefficient parametric resonance 1): FMR measurement; ( inefficient parametric resonance 2):  microwave-assisted hard-disk recording
(short content 3:)  dependency of direction and magnitude of Hoff on the external magnetic field.   (short content 3:)    the experimental data of the gate- voltage dependency  of Hani (VCMA effect)
  (short content 3:)  the reason  why the parametric mechanism of the magnetization reversal is much more efficient than the spin-transfer-torque mechanism   (short content 3:)  the parametric magnetization reversal using a gate voltage (VCMA reversal).
Other parts of this video set is here
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I am strongly against a fake and "highlight" research

 

 

I truly appreciate your comments, feedbacks and questions

I will try to answer your questions as soon as possible

 

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