Abstract:

Parametric magnetization reversal occurs when the magnetization direction is modulated by an external parameter, for example, by electrical current flowing through the nanomagnet. The merit of the parametric reversal as a recording mechanism for a MRAM cell is the energy efficiency. The parametric reversal requires a substantially smaller energy required for a recorded data pulse than, for example, the mechanism of the spin injection (mechanism of spin transfer torque (STT) and mechanism of spin- orbit torque (SOT)).

When the external parameter is modulated at a frequency close the resonance frequency ω_L of the magnetization precession (Larmor frequency), a tiny modulation of magnetization direction is resonantly enhanced and leads to magnetization precession at a substantial angle and further to the magnetization reversal.

The most unique feature of the parametric mechanism is the ability to induce the magnetization precession and the magnetization reversal by a DC electrical current when there is no external parameter modulated at the precession frequency. This unique effect occurs only in a magneto-resistant structure when the electrical current is modulated by the magnetization precession and the modulated current, which parametrically enhances the same precession. There is a positive feedback loop, which is able to enhance the precession of a tiny thermal oscillation until a magnetization reversal occurs.

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page creation date: start April 2021-

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Content

(1) Main merit of parametric recording:) Lower recording energy

(1a) (Merit 1) of Parametric recording: Low-recording energy

(2) The mechanisms of the parametric magnetization reversal

(video:) Magnetization reversal: parametric reversal vs. reversal due to spin-transfer

(video:) Conference presentation video

(video 1) Spin orbit Torque, Parametric Mechanism of Magnetization reversal (Intermag 2021);
(video 2) Comparison of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet (TMRC 2021)
(video 3) Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet( Joint MMM-INTERMAG 2022)

 

 

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details about this mechanism of the parametric magnetization reversal can be found here V. Zayets arXiv:2104.13008 (2021), V.Zayets IEEE Transactions on Magnetics (2021)V.Zayets. arXiv:2111.05438 (2021)

(Part 1 is here): General principles of Parametric mechanism of Magnetization Reversal.
(Part 2 is here): Parameter of parametric resonance: Current- induced magnetic field.
(Part 3 is here): Parameter of parametric resonance: Anisotropy field.
(Part 4 is here): Parameter of parametric resonance: Amount of spin injection.

 

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(Main merit of parametric recording:) Lower recording energy

 

 

(recording energy) A data bit in a memory cell are stored by means of two stable states of minimal energy. There is an energy barrier between the stable states.

This is a general rule for any memory. Examples of memory types:

(MRAM cell): The recorded parameter is magnetization direction of a nanomagnet. Bit "1" corresponds to the spin-up direction and bit "0" corresponds to the spin-down direction. The energy barrier corresponds to the energy barrier between two stable opposite magnetization directions.

(DRAM cell): The recorded parameter is a charge of a capacitor. Bit "1" corresponds to a charge accumulated at a capacitor (floating gate). Bit "0" corresponds to uncharged capacitor. The energy barrier corresponds to the height of the tunnel barrier between the floating gate and the emitter- collector channel.

 

 

Why the parametric recording is more efficient?

In order to record a data by a conventional recording method, the data pulse should supply energy higher than energy barrier between two stable state of the memory cell. In contrast, in the case of parametric recording the energy of the data pulse higher than the energy barrier is not required and a data pulse of a substantially smaller is able to record data.

For example, in case MRAM memory the data pulse should provide a magnetic torque larger than the damping torque during time of the magnetization precession and reversal. In contrast, for the parametric magnetization reversal the magnetic torque 10 time smaller than the damping torque is usually sufficient. When the parametric recording is optimized, the timing for the reversal is nearly the same as in the case of the conventional recording.

 

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What is the parametric recording and the parametric magnetization reversal?

It is a type of magnetization reversal when one of magnetic parameters of a nanomagnet is modulated at a frequency close to the precession frequency of the nanomagnet. The amplitude of the modulation might be a very small, but the frequency and the phase of the modulation must be well- matched to the magnetization precession.

What are the conditions for the parametric reversal?

(condition 1): A magnetic parameter of a nanomagnet should be modulated by an electric current flowing through the nanomagnet

(condition 2): The magnetization precession of the nanomagnet should nodulate the electric current due to magneto- resistance.

 

 

 

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(Merit 1) of Parametric recording: Low-recording energy

(Merit 1) of Parametric recording: Low-recording energy
Direct recording   Parametric recording   (energy-> hard push) Under a hard push, a lot of energy is supplied to the electron, so it overcomes the barrier and jump into another stable state. However, a substantial amount of energy is wasted in the process.   (energy-> soft push) Under a soft push at an optimum moment,it is possible to climb over the barrier spending a minimal required energy. (spin injection) Direct magnetization reversal requires an injection of a large amount of the spin- polarized electrons into the nanomagnet. As a result, the threshold current for a magnetization reversal is high.   (spin injection) Direct Parametric magnetization reversal required a substantially smaller amount of spin polarized electrons. Additional merit is that the parametric reversal does not require the spin injection deep inside of the nanomagnet. A spin accumulation at nanomagnet interface is sufficient for the magnetization reversal. (swing: hard push) In principle, it is possible to turn around by one hard push. However, it is very energy-ineffective. It requires a large force, a large energy is lost.   (swing: soft push) When a soft push is done resonancely and in the right time, the turn around can be achieved with a small spending energy and a small applied force.
(energy barrier): There is an energy barrier between two stable states of the nanomagnet (memory), which corresponds to the stored data of "0" and "1". The height of the barrier should be at least 100 kT. Otherwise, a random thermal fluctuation may flip the magnetization, which leads to the loss of the stored data.
click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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The mechanisms of the parametric magnetization reversal

For an efficient parametric enhancement, the frequency and phase matching between the pump and oscillator are important. In order to achieve the matching, the external control of the pumping parameters and the feedback tuning should be achieved. In the studied case of the current- induced magnetization reversal, it means that the magnetization direction should be modulated by the electron current, which flows through the nanomagnet. According to this requirement, there are three mechanisms of parametric magnetization reversal

The type of the parametric mechanism is defined according to the magnetic parameter , which is modulated by the electrical current

(condition for the parametric resonance): dependence of the magnetization tilt on the electron current

For an efficient parametric enhancement, the frequency and phase matching between the pump and oscillator are important. In order to achieve the matching, the external control of the pumping parameters and the feedback tuning should be achieved. In the studied case of the current- induced magnetization reversal, it means that the magnetization direction should be modulated by the electron current, which flows through the nanomagnet.. According to this requirement, three mechanisms of the parametric magnetization reversal have been proposed.

(mechanism 1) modulated parameter: the magnetic field H^(CI) induced by the accumulated spin-polarized conduction electrons

Details of this mechanism are described on the current page

 

For the 1st parametric mechanism, the modulated parameter is the magnetic field, which is induced by the spin- accumulated electrons. This magnetic filed tilts the magnetization from its equilibrium direction. Since the amount of the spin accumulation is proportional to the electron current, the magnetization tilt is also proportional to the current as required for the parametric resonance.

The electron current creates a spin accumulation at boundary of the nanomagnet due to the Spin Hall effect. The magnetic field due to spin (magnetic moment) of these accumulated electrons affects the nanomagnet magnetization and is the current-modulated parameter of this mechanism. This magnetic field, which is generated by an electrical current, is the parameter of the parametric mechanism 1.

(note) This mechanism does not require an in-plane external magnetic field. A perpendicular-to-plane external field may be used to optimize the reversal efficiency.

(mechanism 2) modulated parameter: the anisotropy field H_ani

Details of this mechanism are described on this page. Details about the anisotropy field H_ani is here

For the second parametric mechanism, the modulated parameter is the anisotropy field. When a bias external magnetic field is applied perpendicularly to the nanomagnet easy magnetic axis, a change of the anisotropy field causes the change of the magnetization tilting angle. There are two efficient methods for a modulation of the anisotropy field. The first method is a modulation by electrical current due to spin accumulation created by the Spin Hall effect. The second mechanism is the modulation by a gate voltage due to the voltage-controlled magnetic anisotropy (VCMA) effect . In a magnetic tunnel junction (MTJ), the current is proportional to the applied voltage. Therefore, for both methods the magnetization tilt is proportional to the current.

 

The anisotropy field characterized the strength of the perpendicular magnetic anisotropy (PMA) (see here). The anisotropic field, which is modulated by an electrical current, is the parameter of the parametric mechanism 2.

(note) This mechanism occurs only when a external in-plane magnetic field is applied. A perpendicular-to-plane external field is not required..

 

(mechanism 3) modulated parameter: spin injection

Details of this mechanism are described on this page.

For the third parametric mechanism, the modulated parameter is the amount of the spin injection. The nanomagnet magnetization can be reversed  directly by a substantial spin injection, which is the mechanism of the ST and SOT MRAM recording methods. However, utilizing the parametric resonance the magnetization reversal can be achieved at a substantially smaller amount of spin injection and, therefore, at a smaller recording current. The amount of the spin injection is proportional to current flowing through the MTJ.  The magnetization precession is proportional to the amount of the spin injection and, therefore, to the current  as required for the parametric resonance.

 

The spin-polarized conduction electrons can be drifted from the first region to the second region by an electrical current. In the case when the amount and direction of spin-polarized electrons are different in the 1st and 2nd regions, the electrical current changes the spin polarization in each region. This effect is called the spin injection (See here) . The spin injection breaks the equilibrium between the spin- polarized conduction electrons and localized d- electrons. This creates the torque, which moves the magnetization from its equilibrium position. The torque is called the spin torque. The current-induced spin torque is the parameter of the parametric mechanism 3.

Parametric resonance. Comparison of 3 mechanisms
Source: current-induced spin- accumulation Source: transfer of spin polarized electrons from another region Spin-polarized electrons are accumulated at nanomagnet boundaries due to the Spin Hall effect Spin- polarized electrons are transferred from one region (e.g. from "pin" layer) to another region (e.g. "free" layer) (mechanism 1:) current modulation of in-plane magnetic field   (mechanism 2:) current modulation of anisotropy field details of mechanism 1 are described here   details of mechanism 2 are described here   . Direction of the spin accumulation is perpendicular to the magnetization direction (magnetic easy axis)   .Direction of the spin accumulation is along the magnetization direction (magnetic easy axis) Magnetic field due to the spin accumulation tilts the magnetization towards in-plane direction. Additionally, the exchange interaction between spin- accumulated electrons and localized electrons also forces the magnetization to tilt toward the accumulated spin (towards the in-plane direction)   Magnetic field due to the spin accumulation enhances the perpendicular magnetic anisotropy (PMA). As a result, the anisotropy field of the nanomagnet is modulated by current (see here) (mechanism 3:) spin injection details of mechanism3 are described here injection of a tiny amount of spin-polarized electrons of different spin direction rotates the spin direction of a larger amount of existed spin polarized electrons towards spin direction of injected electrons click here to see details on spin injection
blue ball shows the magnetization of the nanomagnet (or the spin of localized d- electrons). Blue balls show the spins of conduction electrons, which are accumulated due to the electrical current j(shown as a green arrow).
Measurements:
(mechanism 1:) measurement of current modulation of in-plane magnetic field   (mechanism 2:) measurement of current modulation of anisotropy field   (mechanism 2b:) measurement of modulation of anisotropy field by gate voltage     Magnitude and angle of magnetic field H(CI), which is induced by   spin- accumulated electrons, measured at current density 10 mA/mm2 as a function of the magnetic field Hz, which is externally applied along the nanomagnet easy axis. The measured field angle is between the in-plane component of H(CI) and  to the direction of current j   Measured anisotropy field in FeCoB nanomagnet as a function of a current density flowing through the nanomagnet and external magnetic field Hz applied along easy magnetic axis (perpendicularly to plane)   Measured anisotropy field in FeCoB nanomagnet as a function of a gate voltage applied to the nanomagnet and external magnetic field Hz applied along easy magnetic axis (perpendicularly to plane) click on image to enlarge it   click on image to enlarge it   click on image to enlarge it. Sample Volt54A L74C (See sample details here)
click on image to enlarge it

 

 

 

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(video): Magnetization reversal: parametric reversal vs. reversal due to spin-transfer

(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 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:) 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:)   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

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Magnetization reversal by a DC current

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Video

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I am strongly against a fake and "highlight" research