Abstract:

Almost any magnetic property of a ferromagnetic material can be modulated to some extent by an electrical current. Major mechanisms for such modulation include the Spin Hall Effect, Ordinary Hall effect, and spin-dependent scatterings across interfaces.

When spin accumulation is induced in a nanomagnet by an electrical current, it initiates magnetization precession, and when sufficiently large, it can even trigger magnetization reversal. This phenomenon is known as the spin-orbit torque (SOT) effect. The SOT effect is used as a data recording mechanism for magnetic memory. By utilizing SOT magnetization reversal, information encoded in electrical data is stored in memory through the orientation of the nanomagnet in two opposite directions.

 

---

Magnetic parameters, which are modulated by an electrical current:

magnetic field, which is induced by the spin accumulation; Anisotropy field H_anis; Strength of spin- orbit interaction Energy of perpendicular magnetic anisotropy (PMA) E_anis;Coercive field H_c;Spin polarization;Logarithm of magnetization switching time; Logarithm of Retention time; Delta Δ;Hall angle;size of nucleation domain for magnetization switching

 

There is both a linear and quadratic dependence on electrical current for each of those parameters.

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

---

---

Content

click on the chapter for the shortcut

(). Origin of Spin-Orbit Torque in short

()Two method of magnetization reversal by spin- polarized electrons

() 3 mechanisms of the magnetization reversal

() Mechanisms of creation of Spin accumulation by an electrical current

() 3-terminal MTJ memory

() Non- existing "field-like" torque

() Limitations and Risks of usage of a Torque- based description of spin dynamics

() Violation of T- symmetry from the non- existing "field- like" torque

() Wrong path: Incorrect introduction "damp-like" torque and non-existent "field-like" torque

(3). Magnetic properties of a ferromagnetic metal affected by an electrical current

(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 H_anis and PMA energy

(measurement 4) SOT modulation of coercive field H_c

(measurement 5) SOT modulation of delta Δ and retention time

(measurement 6) SOT modulation of of effective magnetization M_eff and effective size of nucleation domain

(measurement 7) SOT modulation of Hall angle

(measurement 8) SOT modulation of spin polarization

(). Measurement method using 2d harmonic lock-in technique (unrecommended)

() Five mechanisms contribute to the 2nd harmonic signal

(contribution 1 to 2nd harmonic signal): Magnetization precession: Occurs due to the torque exerted by spin-accumulated electrons.

(contribution 2 to 2nd harmonic signal) Magnetization tilt resulting from the in-plane magnetic field generated by spin-accumulated electrons.

(contribution 3 to 2nd harmonic signal) Magnetization tilt resulting from the Oersted magnetic field created by electrical current.

(contribution 4 to 2nd harmonic signal) Modulation of anisotropy field which again leads to modulation of magnetization tilt.

(contribution 5 to 2nd harmonic signal) Modulation of spin polarization of existing spin- polarized conduction electrons resulting in the modulation of the Inverse Spin Hall effect.

() 2nd harmonic measurement as a vivid example of hype and fake research

() Why one should not use the 2nd harmonic method

() Is the 2nd harmonic measurement considered as an incorrect or misleading measurement?

()Does the 2nd harmonic measurement accurately estimate the damp-like and field-like torque?

() Is it possible to separate the damp-like and field-like torques by examining the 2nd harmonic signal under an external magnetic field applied along and perpendicular to the electrical current?

() Arguments behind incorrect interpretations of 2nd- harmonic measurement

() Incorrect method of separation of "damp-like" and "field-like" torques

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

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

() Mathematics behind incorrect interpretation of 2nd- harmonic measurements

() Contribution of a modulation of anisotropy field to 2nd- harmonic data

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

(9). Current-induced magnetization reversal in FeBTb

---

Questions & Answers

() about necessity to apply an in-plane magnetic field to achieve magnetization reversal

(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

 

.........

---

Two method of magnetization reversal by spin- polarized electrons

To initiate spin precession or magnetization reversal, the spin-polarized conduction electrons must either be injected into the nanomagnet through drifting from another material via an electrical current or be generated within the nanomagnet itself.

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

In this case, a current of spin-polarized electrons flows from one material to another. Consequently, the spin-polarized electrons from one material are transported to and accumulate within the second material. The presence of these spin-accumulated electrons exerts a torque on the magnetization of the second material, causing it to reverse and align with the direction of the spin polarization of the injected electrons.

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

In this scenario, spin-polarized electrons are generated within the ferromagnetic material, often near the material's boundary, by an electrical current. These spin-accumulated electrons induce a torque on the magnetization, leading to magnetization precession and eventual reversal. The spin direction of the accumulated electrons varies with the direction of the current. Consequently, 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 torques

(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. click here for more details   click here for more details   click here for more details
click on image to enlarge it

 

 

---

Mechanisms of creation of Spin accumulation by an electrical current

 

 

Mechanisms of creation of Spin accumulation by an electrical current
(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 click here for more details   click here for more details   click here for more details
click on image to enlarge it

 

 

---

 

3-terminal MTJ memory

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

 

---

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 E_PMA is changed by the electrical current. It leads to current-dependency of anisotropy field H_anis, coercive field H_c and delta Δ.

---

 

 

 

 

 

 

---

Non- existing "field-like" torque

(Wrong path): In order to explain rather- complex measurement data of the 2nd harmonic method (see below) and the symmetrical & asymmetrical contributions to FMR resonance, the "damp-like" torque and the "field-like" torque wn order to explain the rather complex measurement data of the 2nd harmonic method and the symmetrical and asymmetrical contributions to FMR resonance, the introduction of two independent torques—the "damp-like" torque and the "field-like" torque—was made in violation of several conservation laws.

Limitations and Risks of usage of a Torque- based description of spin dynamics

(fact): Torque is a concept in classical mechanics used to describe the dynamics of interactions between objects. However, the torque concept does not have a direct counterpart in quantum mechanics.

(fact): Quantum mechanics describe the dynamics of interactions between objects through transitions between quantum states. The spin dynamics, as a quantum phenomenon, is described by transitions between a lower energy spin-up quantum state and a higher energy spin-down quantum state. (see here)

(fact): The spin precession and the damping of the spin precession are intrinsic properties of the broken- symmetry.

(warning): The introduction and prolonged use of the non-existent "field-like" torque underscore the limitations and risks associated with relying solely on torque-based descriptions of spin dynamics.

(The torque as a subject of the Classical Physics to resolve problem of Quantum Mechanic):

The torque is a subject of the Classical Mechanics describing how a force changes rotation of an object. The spin does not describe any rotation (See here). In the Quantum Mechanic, the orbital moment describes the object rotation (See here). The spin describes the properties of the broken time inverse symmetry, according to which the spin can either precess or align along or opposite to an external magnetic field. Any introduction of the classical torque should fit to the fundamental properties of the time inverse symmetry

 

---

Violation of T- symmetry from the non- existing "field- like" torque

(important note): The conservation of time-inversion symmetry, or T-symmetry, ranks among the most stringent conservation laws in our universe, akin in its stringency to the law of energy conservation.

 

 

(T-symmetry and its conservation ) :

In nature, there exist reversible and irreversible processes, for which the T- symmetry is different. For instance, processes like light propagation along a path or spin precession are reversible, meaning that reversing the flow of time does not alter their behavior. Conversely, phenomena such as light absorption or spin damping are irreversible. Reversing the direction of time flow fundamentally changes the nature of these effects; for instance, light absorption becomes light amplification.

As a result, reversible processes are symmetrical against time reversal, while irreversible processes are asymmetrical.

The "damp-like torque" respects T-symmetry

as it reverses its polarity when time is reversed.

both magnetization M and electrical current reverse their polarity when time is reversed.

The "field-like torque" violates T-symmetry

as it does not reverse its polarity when time is reversed.

both magnetization M and electrical current reverse their polarity when time is reversed.

 

---

 

 

---

Magnetic properties of a ferromagnetic metal affected by an electrical current

 

 

creation of torque

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

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

 

creation of

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

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

modulation of the anisotropy field H_anis and the energy of perpendicular magnetic anisotropy E_PMA

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

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 M_eff and effective size of nucleation domain

The M_eff 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 M_eff 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.

 

---

1st type of SOT effect: current-induced in- plane magnetic field

incorrectly associated with "Damp -like" torque

 

This SOT effect is similar to the effect produced by an usual magnetic filed H_DL , 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?

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

2nd type of SOT effect: current-induced in- plane magnetic field incorrectly associated with "Field-like" torque

 

This SOT effect is similar to the effect produced by an usual magnetic filed H_FL , 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?

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 H_FL gives the field offset for such measurement (See right Fig). From a linear fitting of measured dependence, the H_FL 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 H_FL on the current is rather linear. All FeB and FeCoB samples, which I have measured by Nov. 2018, shows the same sign (positive) of H_FL.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

 

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

 

 

 

 

 

 

 

 

 

 

 

 

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.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample distribution of ΔHc

Measured sample distribution of the current- modulation of the coercive field ΔHc in FeB and FeCoB samples.

Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

---

5th type of SOT effect: modulation of delta Δ and retention time

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

6th type of SOT effect: modulation of effective magnetization M_eff and effective size of nucleation domain

 

 

 

 

 

 

 

 

 

 

 

 

 

---

7th type of SOT effect: SOT modulation of the Hall angle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

8th type of SOT effect: The SOT modulation of spin polarization

 

 

 

 

 

 

---

Measurement Technique

My Measurement Technique of current dependences of magnetic properties of ferromagnetic metal

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.

 

 

 

 

 

---

obstacle for of a measurement current- dependences of magnetic properties is 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.

---

 

 

---

Incorrect partition of torque into ""damp-like" torque" and "field-like" torque

 

What is the "damp-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 H_ext and the magnitude is the smallest (equals to 0), when the spin is parallel to H_ext.

 

 

 

 

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

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

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

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

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

 

 

 

most probable direction of the "damp-like" torque is H_damp,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 H_damp,x aligns the magnetization along this field

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

 

 

How H_damp,x , H_damp,y and H_damp,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.

 

 

 

 

 

 

 

---

Measurement method using 2d harmonic lock-in technique

in short: 2nd harmonic method

highly unrecommended: (reason 1): Incorrect and oversimplified interpretation of this method is frequently used

highly unrecommended: (reason 2): Its data is influenced by five independent effects. The correct interpretation of its measurements requires complementary measurements.

(fact): The shortcomings of the 2nd harmonic method are evident and readily verifiable through experimental investigation.

also some explainations about the 2nd harmonic method are here

(measurement procedure)

A low- frequency (50-500 Hz) AC voltage is applied at ends to a ferromagnetic wire and the second harmonic of the Hall voltage is measured by a lock-in amplifier.

(What physical property does the measured 2nd harmonic correspond to?)

(answer:) Modulation of magnetization direction by an electrical current

The presence of the 2nd harmonic of the Hall voltage arises from proportionality of the Hall angle to both the electrical current and the perpendicular component of magnetization resulting in frequency beating those two modulated components.Therefore, the 2nd harmonic signal is directly proportional to the degree of magnetization modulation induced by the current.

 

---

Five mechanisms contribute to the modulation of the perpendicular component of magnetization by electrical current and , therefore, to the 2nd harmonic signal:

There are at least five contributions to the 2nd harmonic signal, each of which can be independently and individually measured. The properties and behavior of each contribution are distinct and complex due to the diverse physics underlying each contribution

---

 

(contribution 1 to 2nd harmonic signal): Magnetization precession: Occurs due to the torque exerted by spin-accumulated electrons.

(reason why): The larger precession angle results in a smaller perpendicular component of magnetization.

(how to measure):

method 1: measurement of RF oscillations (current- induced FMR).

method 2: From current- dependence of Hall angle.

 

 

(experimental fact): The measured Hall angle clearly reduces under a larger electrical current. This is because a larger current increases the precession angle, subsequently reducing the perpendicular components of magnetization, which in turn leads to a reduction in the Hall angle. (Right graph ). Therefore, this effect contributes to the data of the 2nd harmonic measurement.

 

 

 

 

 

 

 

 

 

---

 

(contribution 2 to 2nd harmonic signal) Magnetization tilt resulting from the in-plane magnetic field generated by spin-accumulated electrons.

(reason why): Spin-polarized conduction electrons become accumulated at the edges of a metallic wire as a result of the Spin Hall effect when an electrical current passes through the wire. This accumulation generates a magnetic field attributed to the spins. The spins of these electrons, along with their magnetic field, lie in-plane and are perpendicular to the direction of magnetization. Consequently, the magnetic field induces a tilt in the magnetization towards the in-plane direction. Given that the level of spin accumulation correlates with the current, the degree of tilt is proportionate to the current, fulfilling the conditions necessary for contributing to the 2nd harmonic signal.

(how to measure): The magnetic field generated by the spin accumulation can be reliably and precisely measured using the method described here, in this paper (here or here) and in this paper (here or here)

(additional data): The method measures and tracks the spin precession and alignment of these spin-polarized electrons towards the easy axis. See Fig. 1(c) in this paper (here or here)

(experimental fact): The measured in-plane magnetic field, which is created by spin accamulation, evidently varies with the electrical current. As the electrical current increases, the spin accumulation also increases. This larger spin accumulation results in a correspondingly larger in-plane magnetic field, which consequently tilts the magnetization at a greater angle. This tilting effect reduces the perpendicular components of magnetization and subsequently decreases the Hall angle. Therefore, this effect contributes to the data of the 2nd harmonic measurement.

(Distinguished feature): How to recognize and distinguish the spin accumulation from other contributions:

(undeniable fact): Distinguished feature of spin accumulation is the precession of its spin and alignment of its spin along the total magnetic field. Any contribution which does not have these features is not related to the spin accumulation.

contribution 2 to 2nd harmonic signal: magnetic field generated by spin-accumulated electrons
Why it contributes to 2nd harmonic signal:
As electrical current increases, spin accumulation increases. This larger spin accumulation results in a correspondingly larger in-plane magnetic field, which consequently tilts the magnetization at a greater angle. It makes the perpendicular components of magnetization smaller. It makes the Hall angle smaller.
Direct measurement: Current creates spin accumulation due to the Spin Hall effect. The spin accumulation induces a magnetic field, which tilts the magnetization Blue ball shows the magnetization. Green balls show the spin accumulation component along current component perpendicular to current See more details about this measurement here and here Sample Volt 54a\R42C SOT.. The measured in-plane magnetic field, which is created by spin accamulation, evidently varies with the electrical current.
click on image to enlarge it

 

 

 

---

(contribution 3 to 2nd harmonic signal) Magnetization tilt resulting from the Oersted magnetic field created by electrical current.

(reason why): The conventional Oersted magnetic field, which is created by an electrical current, circulates around a wire and tilts the magnetization. Given that a portion of the current passes beneath the nanomagnet via the non-magnetic metal, it affects the magnetization of the ferromagnetic metal.

(how to measure): The magnetic field generated by the spin accumulation can be reliably and precisely measured using the method in this paper (here or here) (the same measurement method as for contribution 2)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

 

(contribution 4 to 2nd harmonic signal) Modulation of anisotropy field which again leads to modulation of magnetization tilt.

(reason why): When an external magnetic field is applied perpendicular to the easy axis (in the in-plane direction), the magnetization tilts towards the in-plane direction. The degree of tilting is directly proportional to the strength of the anisotropy field. Consequently, when the electrical current modulates the anisotropy field, it also modulates the tilt angle. Therefore, this mechanism contributes to the 2nd harmonic measurement.

(how to measure): The method for precise measurement of the anisotropy field is detailed here and here and here and in this paper. The modulation of the anisotropy field induced by an electrical current is indeed significant.

(mechanism): The anisotropy field is influenced by the spin-accumulated electrons, but in this case their spin direction is aligned along the easy axis (perpendicular- to- plane). Furthermore, the modulation of the spin-orbit interaction by the electrical current also contributes to the modulation of the anisotropy field.

(additional data): This measurement method also enables a measurement of the strength of spin-orbit interaction and its modulation by the electrical current. See here and this paper

contribution 4 to 2nd harmonic signal: Modulation of anisotropy field
Why it contributes to 2nd harmonic signal:
A larger current makes the precession angle larger. It makes the perpendicular components of magnetization smaller. It makes the Hall angle smaller.
Reason why Direct measurement: Reason why anisotropy field contribute to the 2nd harmonic signal (fact) Contribution exists only when an external in-plane magnetic field H|| is applied The magnetization tilting angle depends on both external in-plane magnetic field and anisotropy field. The electrical current, which flows through the FeB nanomagnet, modulates the anisotropy field of the nanomagnet. As a result, the magnetization tilting angle is modulated by the electrical current. This modulation contributes to the 2nd harmonic signal   Single- layer nanomagnet Anisotropy field Anisotropy field Hanis as a function of external magnetic field Hz applied along the easy axis under a different density of electrical current. The anisotropy field linearly depends on the current density. The change of anisotropy field is opposite for the opposite current direction.   Hanis - Hz Slope of this graph is proportional to the coefficient kSOof spin orbit interaction. Both the slope and offset depends on the current. sample VOLT 57B (see here for more details) Ta(5 nm)/ FeCoB( x=0.5 1.1 nm) Multi- layer nanomagnet Anisotropy field Anisotropy field Hanis as a function of external magnetic field Hz applied along the easy axis under a different density of electrical current.The anisotropy field depends on the square of the current density. The change of anisotropy field is the same for the opposite current direction.   Hanis - Hz Slope of this graph is proportional to the coefficient kSOof spin orbit interaction. Both the slope and offset depends on the current. sample Volt45B W(3) [FeB(0.55) W(0.5)]5 FeB(0.55)   (fact) The anisotropy field is substantially modulated by an electrical current.
See more details about this measurement here and here and here
click on image to enlarge it

 

 

---

 

(contribution 5 to 2nd harmonic signal) Modulation of spin polarization of existing spin- polarized conduction electrons resulting in the modulation of the Inverse Spin Hall effect.

(reason why): There are two primary contributions to the measured Hall voltage: the Anomalous Hall effect (AMR) and the Inverse Spin Hall effect (ISHE). The AMR accounts for the lateral deviation of the electrical current caused by the spins of localized electrons, whereas the ISHE involves the lateral deviation of the electrical current due to the spins of spin-polarized conduction electrons. As an electrical current alters the quantity of spin-polarized conduction electrons within a ferromagnetic metal, it modulates the ISHE and consequently the Hall angle. Therefore, this mechanism contributes to the 2nd harmonic measurement.

(how to measure): The spin polarization in a ferromagnetic nanomagnet is measured by the method described in this paper (here or here) or in this page and here. The modulation of spin polarization by an electrical current is substantial.

(mechanism): The conduction electrons in a ferromagnetic metal are spin- polarized even in the absence of an electrical current. However, when an electrical current is applied, it introduces additional spin-polarized electrons, which interact with the pre-existing spin-polarized electrons. Consequently, the average quantity of spin-polarized electrons becomes modulated by the electrical current.

 

 

 

 

 

 

 

 

 

 

---

 

(this is important) : It is evident that the simple single data from the 2nd harmonic alone cannot discern the contribution of each of these 5 intricate effects.

There are known measurement methods, which allow measurement of each contribution separately. It is imperative to use those measurement methods. Only then can the signal of the 2nd harmonic be accurately reconstructed and explained. Otherwise, all discussions on data of the 2nd harmonic measurement are very speculative.

(why one should not use the 2nd harmonic method):

I earnestly recommend utilizing those more reliable measurement techniques and reconstructing the 2nd harmonic signal independently. Doing so will lead to a clear realization of the limitations associated with 2nd harmonic measurements. I assure, once one has conducted such experiments, he/she will cease relying on 2nd harmonic measurements.

(why one should not use the 2nd harmonic method):

Continued reliance on the flawed and speculative interpretation of 2nd harmonic measurements could adversely affect the reputation of one's research. It is crucial to abandon this method in favor of more accurate approaches.The problems associated with 2nd harmonic measurements is a well-established fact known to many research groups.

---

Is the 2nd harmonic measurement considered as an incorrect or misleading measurement?

No, the 2nd harmonic measurement is a valid and useful method. It measures a change in magnetization direction induced by an electrical current. However, its oversimplified interpretation of this measurement, which relies solely on simplified notions of "damp-like" and "field-like" torques, is incorrect. Rather, five complex mechanisms contribute to the measured 2nd harmonic signal. Additional measurements are necessary to distinguish and understand each of these contributions. Therefore, interpretations based solely on the 2nd harmonic measurement tend to be speculative and may not fully capture the underlying physics.

Does the 2nd harmonic measurement accurately estimate the damp-like and field-like torques?

Absolutely not.

While the 2nd harmonic measurement does capture the contribution proportional to the angle of magnetization precession, and magnetization precession is induced by the torque and the precession angle is proportional to the strength of the torque, it also includes four additional contributions of similar, if not larger, magnitudes. Consequently, isolating the contribution directly proportional to magnetization precession from the 2nd harmonic signal is nearly impossible.

Is it possible to separate the damp-like and field-like torques by examining the 2nd harmonic signal under an external magnetic field applied along and perpendicular to the electrical current?

(note): symmetrical and asymmetrical dependences of 2nd- harmonic signal on external magnetic field is the only argument for such separation. (See below)

Absolutely not.

Regardless of the torque's origin, any torque acting on the magnetization results in an increase in the precession angle. A larger precession angle corresponds to a larger torque, irrespective of its origin. Even if it were feasible to isolate and quantify the current-induced change in the precession angle from the 2nd harmonic signal, distinguishing contributions from individual torques would be exceedingly challenging due to their identical effects on precession.

Furthermore, the application of an external magnetic field tilts the magnetization and complicates the precession, as described by the Kittel formula.

 

---

2nd harmonic measurement as a vivid example of hype and fake research.

2nd harmonic measurement is an excellent example of a hyped and fake research, because it encapsulates all the known features of such misleading research.

 

Known features of hype and fake research and their implications in 2nd harmonic measurements include:

(feature 1 of hype and fake research): Fake research often originates from a genuine and accurate measurement, yet its interpretation is wholly incorrect. The incorrect interpretation is supported, because it allows constant reporting of mysterious and unexplainable results. Consequently, it facilitates numerous publications on the subject, inflates research indexes, and perpetuates a steady influx of government funding into such research topics.

(implementation in 2nd harmonic measurement): The 2nd harmonic measurement accurately evaluates the current-induced change in the perpendicular component of magnetization. The measurement itself is entirely correct. However, the provided explanation, which relies on the damp-like torque and field-like torque, is incorrect and absolutely unjustified.

(feature 2 of hype and fake research): The utilization of sophisticated terminology, fancy- sound names and terms, often bearing little or no correlation with the research topic, is a distinct feature of hype and fake research. These fancy words are employed to impress non-scientific individuals and bureaucratic figures within the scientific community, as well as to render the research topic more mysterious, unreachable and inaccessible to "simple" people.

(implementation in 2nd harmonic measurement): The terms "damp-like torque" and "field-like torque" are used for the incorrect explanation of the 2nd harmonic measurement. This flawed interpretation frequently leads to the discovery of purportedly new effects, distinguished only by their elaborate fancy names, which typically consist of combinations of words such as "spin," "torque," "current," "Hall," "enormous," "gigantic," and so on.

The existence of the field-like torque contradicts several conservation laws of quantum mechanics, rendering it a non-existent concept (see above). While the damp-like torque may have some applicability, it is not without limitations. Torque itself is not a subject of quantum mechanics; instead, quantum dynamics are typically described through quantum transitions. However, despite these limitations, the damp-like torque can still be employed within certain bounds.

(feature 3 of hype and fake research): Another distinguishing feature is that the majority of researchers are aware of the fraudulent nature of fake and hyped research. Despite this awareness, many researchers willingly acknowledge the existence of such deceptive studies and align their own interests with them. Simultaneously, there exists a correct explanation, supported by robust experimental and theoretical evidence. However, as long as the fraudulent research continues to yield benefits, it persists, often suppressing the correct explanation.

(implementation in 2nd harmonic measurement): A clear and straightforward correct explanation of the 2nd harmonic signal has been well-established since 2016. Direct measurements of each contribution to the 2nd harmonic signal have been documented in published papers and presented at top-rated conferences on Magnetism (such as MMM and Intermag). Despite the widespread awareness among researchers in the field regarding the fraudulent nature of the explanation rooted in "damp-like torque" and "field-like torque," publications and conference presentations based on this false interpretation continue to surface periodically up to the present day (2024).

(feature 4 of hype and fake research): Clear and understandable explanations pose the greatest threat to fake and hyped research. Such research deliberately avoids straightforward explanations at all costs. Instead, it employs tactics to evade the discussion of simple and easily understandable facts, while promoting complex, difficult-to-understand, and challenging-to-verify effects. These effects are often portrayed as well-known and self-evident, purportedly requiring no further explanation, justification, or proof.

(implementation in 2nd harmonic measurement): The faked interpretation of the 2nd harmonic measurement emphasizes that the 2nd harmonic data directly corresponds to the strength of the damp-like torque and field-like torque, presenting it as an indisputable fact beyond questioning or doubt. However, any specifics regarding why this is considered factual or what precisely constitutes the measured value corresponding to a torque remain elusive. Whether it pertains to the magnetic field utilized in torque descriptions within the Landau-Lifshitz equation, the angle of spin precession, or the alteration of anisotropy field (See more details here) , existing explanations are riddled with numerous complex and often incorrect details, seemingly designed to obfuscate rather than clarify the matter.

(feature 5 of hype and fake research): Usage of circle citation. Circular citation is a notable characteristic of fake research, employed to obscure a straightforward explanation. When the necessity for an explanation becomes unavoidable, citations are utilized, suggesting that the comprehensive explanation can be found in the referenced paper. However, upon scrutiny of the cited paper, it often diverges slightly from the previous topic, lacking the required explanation. Instead, it refers to yet another paper, which may be even more detached from the original subject. Consequently, the needed explanation remains elusive, seemingly resolved only through a chain of referenced papers.

(implementation in 2nd harmonic measurement): The circle citation is very popular in this fake research. The circle citation is often used when it is necessary to provide a simple sentence or two to justify the use of a specific formula or the discovery of a purportedly "new" torque or spin effect. Instead a citation to an article that supposedly explains everything is used. However, upon inspection of the cited article, one often finds either a tangential mention of the claim without substantive proof or a further citation, perpetuating the cycle of vague references.

(feature 6 of hype and fake research): Giving unrealistic promises, which nobody intends to keep. A significant portion of any presentation or paper related to fake and hyped research comprises numerous unrealistic promises, which nobody actually intends to fulfill. These often include science-fiction-like narratives, akin to Star Wars tales, depicting how the purported "fake research" will revolutionize the human race. These narratives typically lack any form of scientific evidence or justification. Moreover, the projected timelines for the realization of these promises are often exceedingly distant, spanning millions of years, rendering them effectively unverifiable. The primary target audience for such promises is often science bureaucrats whose scientific understanding is drawn largely from movies like Star Wars and similar science fiction films. These individuals are easily swayed by fantastical claims and seldom demand scientific justifications for such science fiction promises.

(implementation in 2nd harmonic measurement): Any presentation or paper on this fake topic often makes promises of delivering a super memory with an exceptionally efficient recording mechanism, purportedly due to the utilization of super-effective field-like torque or damp-like torque. However, in reality, the measured data of the 2nd harmonic bears only a distant relation to the effectiveness of data recording in a magnetic memory.

 

---

Arguments behind incorrect interpretations of 2nd- harmonic measurement

 

 

(2nd harmonic measurement):

The Hall voltage is proportional to the current and the perpendicular components of magnetization. When current is modulated with frequency ω, the magnetization direction, the magnetization magnitude and spin-polarization of the conduction electrons are modulatedby a current at the same frequency ω. Due to the frequency beating , the Hall voltage is modulated with frequency 2ω. As a result, he 2d harmonic signal is linearly proportional to the magnetization direction, magnitude, and spin polarization of the conduction electrons

 

 

 

 

---

Accepted, but incorrect, Measurement methods of "damp-like" torque and "field-like" torque

It has been commonly accepted, albeit inaccurately, that the "damp-like" torque and "field-like" torque can be measured and distinguished from each other through the following techniques:

(technique 1): The 2nd harmonic-lock-in technique;

(technique 2): From ST-FMR measurements.

 

 

---

Incorrect method of separation of "damp-like" and "field-like" torques

 

(main (incorrect) idea behind used separation method): dependence & independence on magnetization reversal

There are only two existing torques, and their dependence on the magnetization direction differs significantly. This feature is used to separate them.

One type of torque 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 type of torque does depend on the magnetization direction of the ferromagnetic metal. Such torque is called the damp-like torque.

 

field-like torque

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

2. The magnetic field H_FL of the "field-like" torque is oriented along the current , meaning it lies in the in-plane direction along to the current.

damp-like torque

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

2. The magnetic field H_DL of the "damp-like" torque lies in the in-plane direction perpendicular to the current.

 

---

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

(old and incorrect interpretation):

1. "Field-like" torque

 

It can be evaluated from the symmetric 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

 

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

---

 

 

 

 

 

---

Mathematics behind incorrect interpretation of 2nd- harmonic measurements

Both the "damp-like" torque and "field-like" torque are associated with corresponding magnetic fields H_DL and H_FL, both of which are linearly proportional to the electrical current j.

(fact): The electrical current indeed generates a magnetic field, comprising three components that can be measured with high precision (see here). The first component is the conventional Oersted field, which circulates around the current. The second component is the magnetic field created by the spins of the spin-accumulated electrons. The third is related to magnetization. However, these magnetic fields do not produce any torque except when the conditions of the parametric resonance are satisfied.

Math of "damp-like" torque:

The "damp-like" torque is described as

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

(direction): The magnetic field H_DL of the "damp-like" torque is oriented perpendicular to both the current and the magnetization, meaning it lies in the in-plane direction perpendicular to the current.

(symmetry): The polarity of the magnetic field H_DL of the "damp-like" torque reverses when the magnetization is reversed.

Math of "field-like" torque:

 

The "field-like" torque is described as

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

(direction): The magnetic field H_FL of the "field-like" torque is oriented along the current , meaning it lies in the in-plane direction along to the current.

(symmetry): The polarity of the magnetic field H_FL of the "field-like" torque does not change when the magnetization is reversed.

 

---

 

Contribution of a modulation of anisotropy field to 2nd- harmonic data

Results:

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

where ΔH_anis,ω is the current induced change of the anisotropy field H_anis; ΔH_off,ω is the effective magnetic field H_FL,ω of the "field-like" torque, when H_x is applied along electrical current; and ΔH_off,ω is the effective magnetic field H_DL,ω of the "damp-like" torque, when H_x is perpendicularly to the electrical current;

the odd and even components can be calculated as

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

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

The H_anisot can be evaluated from the following dependance of the 1d-harmonic voltage V_Hall,ω vs applied in-plane magnetic field H_x :

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

 

---

 

 

 

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.

 

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.

It occurs in magnetic or non-magnetic metals in which there are substantial spin-dependent scatterings. Due to spin-dependent scatterings a spin-polarized current flows perpendicularly to the flow of spin- unpolarized drift current. The spin is accumulated at one side of a metallic wire and the spin is depleted at another side. The spin accumulation(depletion) may cause the spin torque at sides of the wire, which magnitude and direction is proportional to the drift current. The accumulated spin may  have different spin direction than the spin direction of the equilibrium spin polarization.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

---

Questions & Answers

---

(about necessity to apply an in-plane magnetic field to achieve magnetization reversal)

(Fan Yan, Wuhan University of Technology) Why is it necessary to apply an in-plane magnetic field(Hx) to achieve magnetization reversal in ferromagnetic layers? I have seen explanations mentioning that the breaking of symmetry through the application of a magnetic field to achieve field-free reversal. Could you elaborate on this symmetry aspect? Some explanations of SOT-induced magnetization reversal mention the necessity of an in-plane auxiliary field to facilitate domain switching, enabling the manipulation of domain size via spin currents (see attached figure Advanced Functional Materials, 2020, 30: 1909092). However, would this in-plane field still be necessary if the size of individual storage units within a device is smaller than the domain size? In such cases, does the explanation regarding domain switching through auxiliary fields remain valid?

(2024/04/26). There are several reasons why the application of an in-plane magnetic field (H_x) is necessary for achieving magnetization reversal, and these reasons depend on the specifics of the utilized magnetization reversal mechanism:

(magnetization reversal method 1) parametric magnetization reversal

This mechanism, functioning as a resonance mechanism, is highly effective and occurs at minimal current levels. However, it requires precise tuning and is only applicable in structures with magneto-resistance (MR). A larger MR is preferable, although even a small MR, such as AMR, can suffice for this resonance-based reversal. The key mechanism employed in parametric reversal involves the modulation of magnetization direction by electrical current. Whether H_x is required or not depends on the specific mechanism employed:

(Mechanism 1): In-plane magnetic field H_|| generated by spin accumulation due to the Spin Hall effect.

H_x is not necessary here because H_|| is perpendicular to magnetization M and tilts the magnetization.

(Mechanism 2): Modulation of anisotropy field H_ani by current.

H_x is required in this case. In equilibrium, the magnetization aligns along the easy axis, and modulation of H_ani does not tilt M. The application of H_x, however, tilts M, with the tilting angle dependent on H_ani . Therefore, modulation of H_ani results in a modulation of the magnetization tilting angle. See more here:

(magnetization reversal method 2) conventional reversal by an injection of a large amount of spins

 

(Case 1): Injected spin is opposite to magnetization.

H_x is not required.

(Case 2): Injected spin is perpendicular to magnetization.

H_x is required.

This scenario is applicable to nanomagnets with perpendicular magnetic anisotropy (PMA), where the injected spin direction is in-plane, as generated by the Spin Hall effect.

---

( about magnetic domains)

Regarding magnetic domains, it's important to note the distinction between static domains and nucleation domains. Nucleation domains are transient, unstable and exist briefly during magnetization reversal. In my studies of FeCoB nanomagnets ranging from 30 nm x 30 nm to 3000 nm x 3000 nm, static domains are rare. Nucleation domain sizes range from 30 nm to 80 nm, depending on nanomagnet quality. Measuring nucleation domain size is a relatively simple and well-established technique, detailed in this Web page

Under H_x, the size of the nucleation domain decreases rapidly, leading to a decrease in coercive field H_C and facilitating thermal-activated magnetization reversal. However, H_x also reduces overall thermal stability due to reduced nucleation domain size, making this method somewhat tricky.

H_x affects nucleation domain wall movement speed, impacting the speed but not the efficiency of magnetization reversal.

---

Your answer does not have a simple and short answer. In general, symmetry is important. In reality, the necessity or unnecessity of applying H_x for magnetization reversal depends largely on sample properties and the specific magnetization reversal mechanism employed.

 

 

---

(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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

---

(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
click on image to play it

 

 

 

 

 

 

 

 

 

---

 

I am strongly against a fake and "highlight" research