Dr. Vadym Zayets

(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.

Current-modulated anisotropy field H_ani

origin of current dependence of anisotropy field: spin accumulation at interface
(important): spin direction of accumulated conduction electrons is along the spin direction of nanomagnet magnetization
An electric current, which flow through the nanomagnet, creates spin accumulation of spin-polarized conduction electrons (green balls) due to the Spin Hall effect and Ordinary Hall effect (See here). the magnetic field due to the current- induced spin accumulation is perpendicular to the spin of localized electrons (blue ball). As a result, the spin of localized electrons (magnetization) is tilted towards the in-plane direction.
(fact) Anisotropy field increases when an external magnetic field is applied perpendicularly to the plane (See here)
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(key properties for parametric magnetization reversal) Ability to change the magnetization direction by an electrical current. This is achieved by using two properties:

(key property 1 ): Dependence of the anisotropy field H_ani on electrical current flowing through the nanomagnet; (alternative property 1): Dependence of the anisotropy field H_ani on a gate voltage applied to the nanomagnet. (key property 2 ): Dependence of magnetization angle with respect to the magnetic easy axis on the anisotropy field H_ani in the case when an external in-plane magnetic field is applied perpendicularly to the easy axis;

(RF modulated current: parametric resonance)The RF current modulates the H_ani. When frequency and phase of the modulation of the anisotropy field H_ani is in the resonance with the magnetization precession, there is an enhancement of magnetization oscillations, which leads to the magnetization reversal (See details below)

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(DC electrical current: positive feedback loop) Under a DC current a thermally- initiated magnetization oscillation is enhanced to a substantial magnetization precession and further to the magnetization reversal due to positive feedback loop. The positive feedback loop is: (1) a small magnetization precession---> (2) modulation of the magneto- resistance ---> (3) modulation of electrical current ---> (4) modulation of the anisotropy field H_ani---> (5) parametric enhancement of magnetization precession ---> (6) magnetization precession at a larger precession angle ---> (2) --->(3) ---> (4) ---> (5) --->(6) --> (2)

(origin of dependency of anisotropy field on electrical current): The perpendicular magnetic anisotropy (PMA) in a nanomagnet exists due to the unique magnetic properties (See here) of localized d-electrons at the nanomagnet interface. The spin- polarized conduction electrons are accumulated at boundary of the nanomagnet under an electrical current due to the Spin Hall effect. The spin accumulation affects the magnetic properties of the localized d-electrons, which leads to the change of the PMA strength and therefore to the modulation of H_ani.

(origin of dependency of anisotropy field on gate voltage): The gate voltage affects the magnetic properties of the localized d-electrons at the nanomagnet interface, which leads to the change of the PMA strength and therefore to the modulation of H_ani. This effect is called the Voltage Controlled Magnetic Anisotropy (VCMA). See here for details

(high- precision measurement of the anisotropy field) (see here)

How does it work?

How does the modulation of PMA and anisotropy field leads to parametric magnetization reversal?

(explanation in short)

(point 1: magnetization tilting angle vs. PMA strength):In an equilibrium, the magnetization of a nanomagnet is perpendicular- to- plane. When an external in-plan magnetic field is applied, the magnetization is tilted towards the external field. The tilting angle depends on the field strength and the strength of the PMA. The tilting angle is larger when the in-plane field is larger and the PMA strength is smaller.

(point 2: modulation of magnetization tilting angle):When the PMA strength is modulated either by a current or by a gate voltage, the magnetization tilting angle is changing following the modulation strength.

(point 3: parametric resonance):When the frequency and phase of the modulation of the magnetization angle are in the resonance with the magnetization precession, the magnetization precession angle resonancely increases, which eventually leads to the magnetization reversal.

Two mechanisms of modulation of anisotropy field: (1) current; (2) gate voltages

Similarity of two mechanisms:

(similarity 1): strength of Perpendicular Magnetic Anisotropy (PMA) and therefore anisotropy field H_ani are modulated in both mechanisms

(similarity 2): External in-plane magnetic field H_|| is required in both mechanisms

Difference between two mechanisms:

(difference 1): an electrical current flows for mechanism 1. The current flow is not required for the second mechanism.

(difference 2) both mechanisms can be used as a par metric recording for MRAM. However, mechanism 1 can be used in a 3-terminal MRAM, but mechanism 2 can be used in

Modulation of Perpendicular magnetic anisotropy and as a result Hani
Blue ball shows the magnetization of FeB nanomagnet. Under external magnetic field H|| the magnetization is tilted towards the field. The tilted angle is determined by the strength of the Perpendicular Magnetic Anisotropy of the nanomagnet. The magnetization titled angle is proportional to the ration of the in-plane magnetic field H|| and anisotropy field Hani. When the anisotropy field Hani is modulated, the titled angle is modulated as well.
mechanism 1: modulation Hani by a current   mechanism 2: mudulation of Hani by a gate voltage   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 is used for the parametric magnetization reversal..   A gate voltage is applied a top of FeB nanomagnet with the MgO as a gate isolator. Even when the MgO gate is thick (>10 nm) and there is no current flow through the nanomagnet, the gate voltage affect the nanomagnet top interface and therefore changes interface-induced PMA. As a result, the magnetization tilting angle is modulated by the gate voltage. This modulation is used for the parametric magnetization reversal.
Measurements
mechanism 1: dependence of Hani on current j   mechanism 2: dependence of Hani on gate voltage         sample: Volt40B R21A (See sample details here)   sample Volt54A L74C (See sample details here)
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mechanism 1: Dependence of the anisotropy field on current

mechanism 1: dependence of Hani on current j		mechanism 2: dependence of Hani on gate voltage
		sample
sample: Volt40B R21A (See here)

Origin

Application:

Importance of an external in-plane magnetization field for the magnetization reversal by this mechanism

with offset field Hext: modulation of M angle   without offset field Hext: no modulation of M angle

In both cases

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Gate

mechanism 2: dependence of Hani on gate voltage
		sample
		sample Volt54A L74C (See sample details here)

Spin Transfer Torque 2-terminal MRAM cell
Fig.1a. Under applied voltage, the spin- polarized conduction electrons flows from the "pin" layer to "free" layer creating the spin-torque. When the spin torque is sufficient, the magnetization of the "free" layer is reversed and is data is recorded.

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