Dr. Vadym Zayets

Abstract:

There is an intrinsic magnetic field with a nanomagnet with Perpendicular Magnetic Anisotropy. Its direction and magnitude is changed under applied external perpendicular magnetic field and under electrical current. Since this field influences the probability of the magnetization reversal, it is often called the "field- like torque" or "damp- like torque".

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Content

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1.SO in-plane magnetic field. Dependence on external magnetic field.

2. SO in-plane magnetic field. Dependence on current density

3. High -precision measurement method

4. Measurement method of 2nd harmonic. A rough measurement.

5.Data of Another sample. Smaller nanomagnet.

6. Comparison of smaller and larger nanomagnets. Current Dependence

7.Subject of effect: Localized d- electrons or conduction electrons? What is changed: Anomalous Hall effect or Inverse Spin Hall effect?

8."Field- like torque"? "damp- like torque"? Real or just fancy words?

6. Explaination video

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(What kind of filed it is?) It is a magnetic field, which direction is in-plane of a nanomagnet. The direction and magnitude of this magnetic field are changed under an external magnetic field and depends on polarity and magnitude of electrical current flowing through the nanomagnet. The in-plane magnetic field also depends on the sample geometry.

 

(What is the origin of this magnetic field?) The origin of this in-plane magnetic field is the spin-orbit interaction.

In-plane magnetic field induced by spin- accamulation created by current
Current creates spin accamulation due to Spin Hall effect. The spin accamulation induces magentic field, which tilts the magnetization 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.
Blue ball shows the magnetization. Green balls show the spin accamulation
click on image to enlarge it

 

 

 

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Spin-Orbit in-plane magnetic field H_|| . Dependence on external magnetic field.

The field is call the in-plane SO field H_||.

(fact ) A nanomagnet with the Perpendicular Magnetic Anisotropy (PMA) has in-plane magnetic field H_||, which is about 30-50 Gauss without an external magnetic field.

(fact: origin ) The origin of this in-plane field is the spin-orbit interaction (SO) and the origin is similar to the origin of PMA. This fact can be concluded from linear increase of the in-plane magnetic field under a large perpendicular magnetic field H_z (See Fig.1c below). Such dependence is very similar to the dependence of the anisotropy field on an external magnetic field (See here). Similarly, there is an oscillating feature for H_z<2 kG. The H_|| reaches about 100 Gauss under external magnetic field H_z= 7 kGauss

(fact: discontinuity at H_z =0) The in-plane magnetic field H_|| sharply changes its magnitude and direction at H_z =0.

(fact: dependence on demagnetization field) The in-plane magnetic field H_|| depends on shape and sizes of the nanomagnet, which implies that the H_|| depends on the demagnetization magnetic field.

(fact: interfacial origin ) The in-plane magnetic field H_|| depends substantially on polarity of external magnetic field . Such polarity non-symmetry can be created by a geometrical non- symmetry. There is only one non- symmetry of the measured nanomagnet: different materials at top and bottom interfaces. It implies the in-plane magnetic field H_|| is created at the interfaces (similar to PMA)

 

 

The following data is for a larger nanomagnet. Data for a smaller nanomagnet see below

Measurement of SO in-plane magnetic field H||. Dependence on an external magnetic field Hz

Fig1a. Experimental setup Fig1b. Component along x-axis Fig1c. Component along y-axis External magnetic field Hz is applied perpendicularly to the nanomagnet. Direction and amplitude of spin-orbit in-plane magnetic field H|| is measured Fig1b. It is a nearly-strait line with a negative slope. There is a step at Hz=0 The dependence is non- linear. There is a step at Hz=0. There is a substantial dependence on polarity of Hz.       Fig1c. total amplitude Fig1d. angle with respect to x- axis Fig1e. 2D map of H|| Amplitude linearly increases with H|| at a larger Hz. The dependence is non-linear at smaller Hz.. Angle is around 45 deg for negative Hz and around 90+45 deg for positive Hz Parametric plot of the SO magnetic field. The parameter is the external magnetic field Hz. A vector from axis center to the line corresponds the direction and magnitude of H||.

In-plane spin-orbit magnetic field H|| vs. external perpendicular magnetic field Hz.

sample Volt 54a nanomagnet R42C. Size 3000nm x 3000nm. See more details about sample here.

Click on image to enlarge it

 

 

 

 

 

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Spin-Orbit in-plane magnetic field H_||. Dependence on current density .

 

(fact ) There is an in-plane magnetic field H_||, in a nanomagnet, which is linearly proportional to the electron current flowing in a nanomagnet. At current density of 100 mA/ μm² (a very high density), the in-plane current- dependent SO field is about 40-70 Gauss

(fact ) Both the magnitude and the direction of the in-plane current- dependent SO field also depends on direction of the externally- applied perpendicular magnetic field H_z. Its component along current (x- component) reverses its polarity when H_z is reversed. Its magnitude is nearly a constant with a weak oscillations. The component perpendicular to current (y- component) has a maximum at H_z=0 and decays at larger H_z. The y- component does not change polarity.

(fact ) Dependencies of in- plane magnetic field on external magnetic field and on electron current seems to be always perpendicular each other (See Fig.7 and Fig.2f). For example, the direction of a change of H_||, when the current increases, is about perpendicular to the direction change due to a change of H_z. It implies both dependencies have the same origin.

(fact ) The dependence of H_|| on current density is perfectly linear (See Fig.3) even at a higher current without visible ~I² dependence . At current density of 100 mA/ μm² the nanomagnet is heated up to 70-80 C. As following Curie-Weiss law (See here), the magnetization (the total spin of localized electrons) reduced for about 3-4 %. The measured parameters for the same nanomagnet, which is linearly depends on the total spin of the localized electrons (e.g. the coercive field, the anisotropy field, Anomalous Hall effect), follow ~I² and are reduced about 3-4 %. It implies that the current-induced in-plane magnetic field H_|| is not proportional and is not influenced by the total magnetic moment of localized electrons. It can be either proportional to Oersted Field induced by the current or the total spin of the conduction electron due to the Spin Hall effect.

component along current component perpendicular to current

Sample Volt 54a\R42C SOT. Click here to check all data

Click on image to enlarge it

 

 

The following data is for a larger nanomagnet. Data for a smaller nanomagnet see below

Measurement of SO in-plane magnetic field H||. Dependence on current density

Fig. 2a. Experimental setup Fig 2b. Component along x-axis Fig.2c Component along y-axis The light- blue arrow shows the in-plane SO magnetic field H|| created by the external magnetic field Hz. The red arrow shows H||,j created by the electrical current. Both fields H|| and H||,j are nearly perpendicular to each other. The x-component of H|| reverses its polarity when Hz is reversed. The magnitude of H|| is nearly constant with a weak oscillations. The x-component of H|| decays when Hz increases.       Fig.2d. component along x-axis Fig.2e component along x-axis Fig.2f. 2D map of H||

The current dependence of In-plane spin-orbit magnetic field H||

sample Volt 54a nanomagnet R42C. Size 3000 nm x 3000 nm. See more details about sample here.

Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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High- precision measurement of SO in-plane magnetic field

Developed by Zayets in 2019

See description of the method here

High- precision measurement of SO in-plane magnetic field
External magnetic field H|| is applied in-plane and perpendicularly to the magnetization (along a hard axis). As a result, the magnetization turns towards the magnetic field. The dependence of M|| vs. H|| is linear. However, the line does not pass through the axis center and there is an offset magnetic field Hoff . This offset magnetic field Hoff is the intrinsic in-plane magnetic field, which is aimed for the measurement in this method.
(what is measured) In- plane magnetic field, which might be induced by an electrical current or PMA. The in-plane magnetic field is measured as the offset magnetic field Hoff for the H|| scan.
Hoff is the measured the SO in-plane magnetic field!!!
Note. I have developed this measurement method in 2019-2020
Click on image to enlarge it

 

 

Main idea of the measurement method:

A magnetic parameter, which depends symmetrically on an applied in- plane magnetic field H_ext, is measured. Due to existence of the intrinsic magnetic field the measured data is shifted with respect to the axis center H_ext,. Adding the offset field H_off as a parameter, the data symmetrized with respect to a reversal of (H_ext,+H_off). The minimum square difference between data (H_ext,+H_off) and data(-(H_ext,+H_off)) gives the required intrinsic magnetic field H_||

(in short: how measurement is done) :

The Hall angle α_Hall is measured under a scan in-plane magnetic field H_||. The measurement is not symmetric with respect to a reversal of H_|| due to the intrinsic magnetic field. The intrinsic magnetic field is evaluated from the shift of the measured dependence of α_Hall vs. H_||.

 

(The measurement behind the proposed measurement method): Measurement of Anisotropy filed H_a (See here and here)

In an equilibrium the magnetization direction is along the easy axis. When an external magnetic field is applied perpendicular to the easy axis, the magnetization is inclined toward the field. The magnetic field, at which the magnetization is fully turns along the field and perpendicularly to the easy axis (along the hard axis), is called the anisotropy field H_a. In the case of a nanomagnet with perpendicular magnetic anisotropy (PMA), the external magnetic field is applied in the in-plane direction. The feature of the PMA is that the in-plane component of the magnetization M_|| linearly depends on an external in-plane magnetic field H_||:

The measured Hall angle α_Hall is proportional to the perpendicular component of the magnetization:

and therefore the dependence is non-linear with respect to H_||:

For the proposed high- precision measurement, the specific dependence of α_Hall vs H_|| is not important. It is only important that the dependence is symmetrical with respect to a polarity reversal of H_||. As a result, a shift of the symmetry point due to the intrinsic magnetic field can be easy evaluated.

 

 

 

 

 

 

 

 

 

 

 

 

High- precision measurement procedure:

 

In order to evaluated a symmetry shift of the measured dependence of α_Hall vs H_||. , the dependence of α_Hall vs |H_||+H_off| is analyzed, where H_off is a fitting parameter. There are two curves corresponding to the positive and negative part of the dependence. The scanning of H_off and minimizing the square difference between curves give the value of the intrinsic magnetic field.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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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.

also some explainations about the 2nd harmonic method are here

 

 

 

 

(measurement procedure)

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

 

Why there is a second harmonic?

The AC current creates intrinsic in-plane magnetic field, which makes the the magnetization wabble with the same frequency. The Hall voltage is modulated by both the AC current and modulated magnetization. The frequency beating gives the 2nd harmonic.

 

Detailed calculation

When an AC voltage V_ω

is applied to a nanowire, there is an AC current j_ω which induces in spin-orbit magnetic field H_||,ω (See fig. 2 above) as

where ζ and κ are constants. κ= ζ/R, where R is the nanowire resistance.

The total in-plane magnetic field is

where H_||,0 is the sum of the externally applied magnetic filed and spin-orbit intrinsic in-filed, which is proportional to an external perpendicular magnetic field (See Fig.1).

Any type of in-plane magnetic field forces the magnetization to turn slightly into its direction. The the in-plane component of the magnetization M_|| is linearly proportional to an in-plane magnetic field H_||(See here and here):

When a current flows perpendicularly to a the magnetization, there is a Hall voltage due the Anomalous Hall effect, which is proportional to the electrical current, perpendicular component of the magnetization M_⊥ is and the Hall angle α_Hall :

where w and L is nanowire width and length. The perpendicular component of the magnetization M_⊥can be calculated from Eq.(11.4) as

Assuming

Eq.(11.6) can be simplified as

Substitution of Eq.(11.8) into (11.5) gives the Hall voltage as

It has a DC-component V_Hall,DC

and 1st harmonic -component V_Hall,ω

2nd harmonic -component V_Hall,ω

where α_Hall is the Hall angle of a ferromagnetic metal, w,L,R are width,length and resistance of nanowire, V is amplitude of AC voltage, H_a is the anisotropy filed, which should be measured by this experiment, H_||,0 is total in-plane magnetic field, which includes the external filed and SO field (See fig.1), ζ is proportionately coefficient of current- generated SO field and current density.

(note) The 2nd harmonic depends on each the external in-plane magnetic field, the SO-type intrinsic magnetic field (See fig.1) and therefore external perpendicular magnetic field and the SO current-induced magnetic field (See fig.3)

(note) The 2nd harmonic, as a non-linear effect, is proportional to square of applied voltage V. As a result, in order to be detected it requires a substantial applied voltage (~1-5 V). The amplitude of the corresponding current is large and is about ~30-100 mA/ μm²

 

(golden mine) Since the 2nd harmonic measurement gives a complex result (See Eq.11.12), which depends on many parameters, and has several sharp changes and polarities changes (See Fig.1 and Fig.2) , this measurement has been a golden mine for the "faked" and "highlight" research. Maybe hundreds of papers have been published on this topic with many different fantasy stories, which have nothing to do with the reality.. It is a good example of a topic, around which the faked research is concentrated. In a case when an experimental result has no immediate clear explanation, it is a good chance to ignore all Laws of Physics and to start making the "Harry- Potter style" research stories.

 

 

 

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"Field- like torque"? "damp- like torque"? Real or just fancy words?

 

 

 

 

 

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Current- induced magnetization reversal

 

 

 

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Another sample. Smaller nanomagnet.

 

Dependence on an external magnetic field

 

Measurement of SO in-plane magnetic field H||. Dependence on an external magnetic field Hz

experimental setup component along x-axis component along y-axis External magnetic field Hz is applied perpendicularly to the nanomagnet. Direction and amplitude of spin-orbit in-plane magnetic field H|| is measured In comparison to a larger nanomagnet, a strait line is not clear, but the step becomes more pronounced. The dependence is nearly a constant at a negative field (different from a larger nanomagnet) and is non-linear at a negative field (similar to a bigger sample)       total amplitude angle with respect to x- axis 2D map of H|| In comparison to a larger nanomagnet, the linear increase starts at at a larger Hz. It is more clear in case of at a negative Hz Angle is around 45 deg for negative Hz and around 90+45 deg for positive Hz. In comparison with a larger sample, the dependence is nearly a constant at positive Hz.

In-plane spin-orbit magnetic field H|| vs. external perpendicular magnetic field Hz.

sample Volt 54B nanomagnet ud 66. Size 200 nm x 500 nm See more details about sample here.

Click on image to enlarge it

 

 

Dependence on current density

 

Measurement of SO in-plane magnetic field H||. Dependence on current density

experimental setup component along x-axis component along y-axis The light- blue arrow shows the in-plane SO magnetic field H|| created by the external magnetic field Hz. The red arrow shows H|| created by the electrical current. Both fields H|| are nearly perpendicular each other. it is very similar to a larger nanomagnet In contrast to a larger nanomagnet, the derivative increases again after initial decrease       component along x-axis angle with respect to y- axis 2D map of H||

In-plane spin-orbit magnetic field H|| vs. external perpendicular magnetic field Hz.

sample Volt 54B nanomagnet ud 66. Size 200 nm x 500 nm See more details about sample here.

Click on image to enlarge it

 

 

 

 

 

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Comparison of smaller and larger nanomagnets. Current Dependence

 

Fig.7	angle of dH||/dj	Comparison of angles of dH||/dj and H||	Difference of angles of dH||/dj and H||

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Subject of effect: Localized d- electrons or conduction electrons?

What is changed: Anomalous Hall effect or Inverse Spin Hall effect?

 

 

 

 

 

 

 

 

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"Field- like torque"? "damp- like torque"? Real or just fancy words?

What is the magnetic torque? At which condition it occurs?

Wiki definition of the torque see here

(field-like torque. Torque or not?): When electron spin is not aligned to an external magnetic field, there is a spin precession around the magnetic field. In classical physics assumes that the precession is caused by a torque, which is called the field- like torque. However, the quantum mechanic understands the spin precession as one stable states of the spin. The spin precession is the spin state when the electron energy is between spin-up and spin- down states, when the magnetic energy is the largest and smallest. Due to the spin conservation law, the angle of the spin precession can be changed only when interact with another particle, which has non-zero spin.

The electron spin interacts with the total magnetic field, which is a vector sum of all possible magnetic fields applied. The common magnetic fields are (1) external magnetic field (2) magnetic field of the spin- orbit interaction; (3) effective field of the exchange interaction.

 

Can a small magnetic field reverse the magnetization from one stable to another stable direction?

(note about intrinsic magnetic fields) An electron in a solid always experiences several magnetic fields (e.g. magnetic field of the spin- orbit interaction; effective field of the exchange interaction). The electron spin is aligned along a vector sum of all these magnetic fields. In a case a huge external magnetic field is applied, of course, the spin is along this field. In the reality, an external magnetic field or an intrinsically- generated field (e.g. by the Spin Hall effect) are smaller or comparable to the magnetic field, which the electron already experiences.

(note about thermally- activated switching) Details see here. At a non-zero temperature, the electron interacts with many non-zero-spin particles (e.g. a photon, a spin wave), the spin is transformed from those particles to electron, which causes a spin precession around the existed magnetic field. Since the spin precession of different electron is in different phases, overall all spin precessions looks like the spin swinging (See here). For example, the average spin-swinging angle in Fe is 12 deg. at room temperature(See here). The spin swinging is a statistical process and there is a probability of swinging angle larger than 90 degrees, after which the magnetization is reversed. This process is called the thermally- activated switching and it is strongly influenced by an external magnetic field (see here). However, this process has nothing to with a torque.

 

Comparison between different type of magnetic fields

(magnetic field 1) . magnetic field of exchange interaction: H_exchange~ 1500T=1.5 ×10⁷ Gauss =15,000,000 Gauss. (see here and here)

(note 1) The magnetic field H_exchange is huge, but it describes only the interaction between

(note 2) The exchange interaction is poorly described by the magnetic field H_exchange.

(note 3) The exchange interaction only fixes the alignment between spins. When such alignment is considered as one object (a magnetic domain) with a single spin, the H_exchange can be ignored.

(magnetic field 2) . magnetic field of the spin- orbit interaction : H_SO~ 1-10 kGauss=10³ -10⁴ Gauss

(note 1) The magnetic field H_SO is huge, but it describes only the interaction between

(note 2) The magnetic field H_SO depends on degree of breaking of symmetry of the orbital moment. As a result, the H_SO dependents on the direction of the electron spin with respect to orbital symmetry.

 

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Comparission between differrnt sample
soft FeB nanomagnet Hanis =2.5 kG HC =60 Oe hard FeB nanomagnet Hanis =7 kG HC =270 Oe hard FeCoB nanomagnet Hanis =5 kG HC =700 Oe sample Volt 54A nanomagnet R42C. Size 3000 nm x 3000 nm sample Volt 58A nanomagnet L65C. Size 3000 nm x 3000 nm sample Volt 57A nanomagnet R41C. Size 3000 nm x 3000 nm

 

 

 

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Method to measure the current-induced in- plane magnetic field

This method is similar to the method of measurement of anisotropy field H_anis (See here). In this measurement the in-plane component of the magnetization is measured as a function of an external magnetic field H_ext. The dependence is linear (See here). Therefore, it can be measured with a high precision. The anisotropy field H_anis 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 H_ext., there are two more additional magnetic fields: 1) effective field of "field-like" torque H_FL in direction of current and 2) effective field of "damp-like" torque H_DL in direction perpendicularly to the current. Therefore, the magnetization experiences two magnetic field:

In-plane magnetic field along bias current (the x-axis) H_total,x=H_ext,x+H_FL ,

In-plane magnetic field perpendicularly to bias current (the y-axis) H_total,y=H_ext,y+H_DL ,

 

As a result, the dependence M vs H_ext is shifted on H_FL (H_ext is applied along x-axis) or H_DL (H_ext is applied along y-axis). From the shift the H_FL are H_DL 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 H_FL and H_DL 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 H_FL and H_DL 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).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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High-precision measurement method

Developed by Zayets in 2019

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Video

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I am strongly against a fake and "highlight" research