Dr. Vadym Zayets

Abstract:

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6. Explaination video

 

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Basic measurement methods of nanomagnet
(method 1)   (method 2)   (method 3) Measurement of Anomalous Hall effect (AHE) & Inverse Spin Hall effect (ISHE)   Measurement of PMA strength & anisotropy field & magnetic field induced by a spin accumulation   Measurement of Coercive field     (how and what is measured): An external magnetic field is applied along easy axis (along magnetization) and the the Hall angle is measured.   (how and what is measured): An external magnetic field is applied perpendicularly to the easy axis (perpendicularly to magnetization) and the angle of the magnetization tilting is measured using a Hall measurement..   (how and what is measured): An external magnetic field is applied opposite to the magnetization direction and the time, after magnetization reverses its direction to be along the external magnetic field, is measured. (physics beyond measurements) External magnetic field Hz is applied along the magnetic easy axis and, therefore, along the magnetization M (shown as green ball) of nanomagnet. Since Hz is applied along M, the magnetization direction is not changing and, therefore, the corresponded Anomalous Hall effect (AHE) is not influenced by the external magnetic field Hz. In contrast, the spins of spin- unpolarized conduction electrons are aligned along Hz . As a result, the number of spin- polarized electrons increases. It cause of a larger contribution of the Inverse Spin Hall effect (ISHE) and therefore an increase of the Hall angle vs. Hz.   (physics beyond measurements) ( mechanism 1) When an external magnetic field H|| is applied perpendicularly to the magnetization and along magnetic hard axis, the magnetization tilts towards the magnetic field.. The stronger perpendicular Magnetic Anisotropy (PMA) is, the stronger field is needed to tilt the magnetization. The magnetic field, at which the magnetization turns completely in-plane (along magnetic hard axis), is called the anisotropy field Hani The Hani is a measure of the strength of the perpendicular magnetic anisotropy (PMA). (mechanism 2) In the case when there is an additional magnetic field H(SO), which is induced by the spin accumulated electrons, at a fixed external magnetic field the tilting angle to the left and to the right is different. When scanning external magnetic field Hext from left to right, the data becomes non- symmetrical with respect to Hext=0, because of H(SO). Estimation of symmetry offset gives H(SO).   (physics beyond measurements) There is an energy barrier between two stable states for magnetization of a nanomagnet. The magnetization switches between the states only by assistance of a thermal fluctuation of an energy higher the barrier height. The probability of the thermal fluctuation is exponentially proportional to its energy. The magnetic field reduces the energy barrier. As a result, the switching time exponentially proportional to the magnetic field. The measurement of the switching time vs. external magnetic field gives all parameters of the thermally- activated magnetization switching (e.g. coercive field). (what is measured) (parameter 1) Hall angle of Anomalous Hall effect (AHE); (parameter 2) Hall angle of Inverse spin Hall effect (ISHE) (parameter 3) Spin polarization; (parameter 4) Intrinsic magnetic field inside the nanomagnet.   (what is measured) (parameter 1) anisotropy field; (parameter 2) magnitude and angle of magnetic field, which is induced by spin- accumulated electrons; (parameter 3) coefficient of spin- orbit interaction kSO for bulk and interfaces of nanomagnet; (parameter 4) oscillations of anisotropy field or the same the dependence of coefficient of spin- orbit interaction kSO on an external magnetic field ;   (what is measured) (parameter 1) coercive field; (parameter 2) retention time; (parameter 3) size of nucleation domain; (parameter 4) parameter delta; detailed explanation of method 1 is here   detailed explanation of measurement of anisotropy field is here and a measurement of spin- accumulation- induced magnetic field is here.   detailed explanation of method 3 is here short explanation of method 1 is below   short explanation of method 2 is below   short explanation of method 3 is below
click on image to enlarge it

 

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(method 1): Measurement of Anomalous Hall effect (AHE) and Inverse Spin Hall effect (ISHE)

For full details see here

method 1: measurement of Inverse- Spin Hall effect and spin polarization
Experiment: Measurement of Hall angle αHE in FeB nanomagnet under external magnetic field Hz. The FeB nanomagnet is fabricated on top of Ta nanowire. The Hall voltage is measured by a pair of the Hall probe. The blue balls shows the conduction electrons in the FeB, the arrows show their spin direction. In absence of magnetic field Hz. only a few spins are aligned perpendicularly to plane. These conduction electrons are called spin-polarized. Spins of other (spin-unpolarized electrons) are equally distributed in all directions. When magnetic field Hz is applied, the spins of the spin- unpolarized electrons are aligned along Hz. The larger Hz is, the more spins are aligned. As a result, the number of spin-polarized electrons becomes larger. The Hall voltage (its ISHE contribution) is linearly proportional to the number of spin-polarized electrons or the spin polarization. Therefore, the Hall voltage (and αHE) increases when magnetic field increases.
Measurement: The spin polarization is evaluated from a non-linear increase of αHE in external magnetic field. The measured hysteresis loop of can be divided into 3 contributions: AHE (~ constant), OHE (~H) and ISHE (~non-linear vs H). Since the dependence of the spin polarization on the magnetic field is known, the polarization s evaluated from fitting of non-linear part.
Note. I have developed this measurement method in 2019-2020
click on image to enlarge it

 

(main idea of the measurement): AHE, ISHE and ordinary Hall effect (OHE) are separated and measured individually by measuring the dependence of the Hall angle α_Hall on externally- applied perpendicular magnetic field H_z. AHE is a constant vs H_z. OHE is linearly proportional to H_z and ISHE non- linearly depends on H_z. As a result, AHE and OHE do not contribute to second derivative d²α_Hall /dH_z² and the 2d derivative is only proportional to ISHE. AHE does not contribute to 1st derivative dα_Hall /dH_z. Therefore, comparison of α_Hall and dα_Hall /dH_z gives AHE.

(measurement method 1): Measurement of Hall angle vs magnetic field applied along magnetization
External magnetic field Hz is applied along magnetization M (shown as green ball) of nanomagnet. Since Hz is applied along M, the magnetization and corresponded Anomalous Hall effect (AHE) are not influenced by the magnetic field Hz. In contrast, the spins of conduction electrons are aligned along Hz . As a result, the number of spin- polarized electrons increases. It cause of a larger contribution of the Inverse Spin Hall effect (ISHE) and therefore an increase of the Hall angle vs. Hz.
(what is measured) The increase of the Hall angle vs. increasing magnetic field applied along magnetization
(which parameters are evaluated) AHE, ISHE, spin polarization of conduction electrons.
Click on image to enlarge it

What are the main challenge of the measurement method 1? Why it was not used before?

A. Main problem of this measurement method is the static magnetic domains. When magnetic field applied, magnetic wall of magnetic domain is moving and the total magnetization of the sample changes substantially. The change of α_Hall due to the magnetization change during the domain movement is substantially larger than the α_Hall change due to magnetic- field dependence of OHE and ISHE. As a result, it is hard to separate AHE,ISHE and OHE.

Main challenge of this measurement method is to avoid the static magnetic domains. Simple solution is use a sample of a small size ( a nanomagnet), which does not have any static domains.

The fabrication of a nanomagnet is rather recent technology, which is the reason why this measurement method has not been used before.

Why there is no static domains in a small sample (a nanomagnet)?

A. The static domains are formed when the energy of magnetostatic interaction between domains of opposite magnetization exceeds the formation energy of a domain wall (the exchange energy). The magnetostatic energy is proportional to the domain area. When the nanomagnet area becomes smaller, the magnetostatic energy is not sufficient for a static domain to form and there is no static domain.

(measurement method 1): transformation of hysteresis loop for AHE and ISHE evaluation
measured hysteresis loop of αHall vs Hz absolute value of αHall vs absolute value of Hz
Color lines show different parts of the loop. Scan of Hz from a negative to positive value: ( before M switching): light- blue line; (after M switching): blue line. Scan of Hz from a positive to negative value: ( before M switching): green line; (after M switching): red line.
In absence of a magnetic domain, all 4 lines follows the same path in 3d graph
Analysis and fitting are done for a curve, which is an average of these 4 lines.
The coincidence of the 4 lines is an indication on the absence of static magnetic domains
Fig.11. Click on image to enlarge it

In the case of FeCoB nanomagnet, the single- domain magnetization reversal occurs in nanomagnet with diameter smaller than 50 nm. Does it mean that the method 1 can be used only for such small nanomagnet?

A. No. The method 1 can for a moderate size nanomagnets as well. E.g. size 3um x 3 um mostly is OK for a FeCoB nanomagnet.

There are nucleation domains in the nanomagnet of a moderate size. The nucleation domain is unstable and its domain wall is always expand. As sooner as a nucleation domain is formed, it expands over the whole nanomagnet. The nucleation domain has no influence on the measurement method 1.

 

 

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My presentation on this topic no MMM 2020 conference

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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I am strongly against a fake and "highlight" research