Dr. Vadym Zayets

Ferromagnetic resonance (FMR) is a spectroscopic technique in which a microwave is absorbed by a ferromagnetic material when its frequency matches the Larmor precession of the material's magnetization. The magnetization precession is driven by the oscillating magnetic field of the microwave. However, because the precession of the magnetization is not synchronized with the oscillating magnetic field, the precession angle remains small during FMR. Although the magnetic field exerts a torque on the magnetization, the lack of synchronization causes the torque to periodically reverse polarity, resulting in an overall small net torque. Consequently, FMR does not lead to magnetization reversal or even a significant increase in the precession angle, even under high-power microwave excitation.

In contrast, Parametric Magnetization Reversal achieves full synchronization between the phase and frequency of the oscillating magnetic field and the magnetization precession. This synchronization ensures that the torque induced by the oscillating field is consistently applied in the same direction, leading to a significantly larger precession angle, which can ultimately result in magnetization reversal. The synchronization is typically achieved through a feedback loop, often involving the magnetoresistance of the ferromagnetic material.

 

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FMR vs. Optical Quantum Transition. Similarities and Differences.

Similar to the optical transition, Ferromagnetic resonance (FMR) describes the dynamics of spin transitions between energy levels: from the lower-energy state, where the spin is aligned parallel to the external magnetic field, to the higher-energy state, where the spin is antiparallel to the external field.

 

Similarities:

(similarity 1) Both optical transitions and ferromagnetic resonance (FMR) describe an electron transition between lower and higher energy levels.

(similarity 2) In both cases, the transition occurs only through the interaction with another particle, such as a photon.

Differences:

 

(difference 1) Field to Induce the Transition:

Optical transitions are induced by the oscillating electric field of an electromagnetic wave.

In contrast, FMR is induced by the oscillating magnetic field of an electromagnetic wave.

(difference 2) Nature of the Transition:

In an optical transition, an actual electron moves from one energy level to another. The electron’s symmetry changes, and the number of electrons occupying a given energy level is altered after the transition.

In contrast, during FMR or parametric magnetization reversal, individual electrons do not physically transition between energy levels. Instead, the lower- and higher-energy components of the entire spin system redistribute. Due to strong exchange interactions, all electron spins remain parallel to each other both during and after the transition. The outcome of the transition is a coherent precession of the entire spin system.

(difference 32) Dependence on Phase of electromagnetic wave:

Spin transitions in FMR and parametric reversal are highly dependent on phase matching between the spin precession and the electromagnetic wave. A 180-degree phase shift can completely reverse the nature of the transition: what was previously spin pumping (excitation from a lower to a higher energy level) becomes spin damping (relaxation from a higher to a lower energy level).

In contrast, optical transitions do not depend on the phase of the electromagnetic wave. The wave always induces a transition from the lower to the upper energy level, independently of phase of the electromagnetic wave. (For further details, see discussions on Rabi oscillations and stimulated optical transitions below.)

Optical transition	Spin transition (FMR)
induced by oscillating electric field	induced by oscillating magnetic field
The oscillating electric field interacts with the electron's charge, thereby modulating both its energy and wavefunction. As a result, an electron initially occupying the ground state E0​ acquires a small wavefunction component corresponding to the excited state E1​. This interaction facilitates the electron's transition from energy level E0​ to E1​.	Since spin is fundamentally associated with time-reversal symmetry (T-symmetry), a spin transition that reverses the spin direction requires an external field that itself breaks T-symmetry and directly interacts with the already broken T-symmetry of the electron. A magnetic field applied perpendicular to the spin meets these conditions, as it exerts a torque that tilts the spins, thereby enabling spin transitions.
The magnetic field of an electromagnetic wave is significantly weaker than its electric field, following the relation H=E/c. As a result, its influence on optical transitions is negligible compared to that of the electric field.	In contrast, an electric field cannot induce spin transitions because it does not directly interact with the electron spin.
click on image to enlarge it	click on image to enlarge it

 

 

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Only possible direction of the spin precession

(Key Fact): Unidirectionality of Spin Precession

Spin precession can occur only in one direction—specifically, clockwise with respect to the external magnetic field. This is a fundamental consequence of the time-space symmetry, which dictates the dynamic how the locally broken time-reversal symmetry (T-symmetry) of an electron, which is described by the electron spin, behaves within a globally broken T-symmetry, as defined by the external magnetic field.

Under no circumstances can the spin precess in the opposite (counterclockwise) direction.

Only possible direction of the spin precession
Only- possible clockwise precession of the spin Non-existing counterclockwise precession of the spin When viewed along the direction of the external magnetic field H—in this case, along the z-axis—the spin precession follows a clockwise trajectory. Under no circumstances can the spin precess in the opposite (counterclockwise) direction. Spin precession can occur only in one direction: clockwise with respect to the external magnetic field.
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(fact): Direction of Spin Precession in the Landau-Lifshitz Equation

In the Landau-Lifshitz equation, the direction of spin precession is uniquely determined by the negative sign of the first term on the left-hand side. This sign fixes the precession direction and is a fundamental aspect of the equation's description of spin dynamics.

 

 

 

 

 

 

 

 

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Reversal of precession direction under reversal of magnetic field

The direction of spin precession is unambiguously determined by the direction of the external magnetic field. When the magnetic field is reversed, the spin precession direction reverses accordingly.

Reversal of precession direction under reversal of magnetic field
(case 1) External magnetic field H is along z-axis. Small precession angle (case 2) H is opposite to z-axis. Small precession angle (case 3) H is opposite to z-axis. Large precession angle (larger than 90 degrees).
In all cases, the precession is clockwise direction with respect to the external magnetic field
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(Note about internal magnetic field):

The external magnetic field includes not only externally applied fields but also the magnetic field generated by the spin system itself. In a ferromagnet, this self-generated field is referred to as the internal magnetic field.

In the absence of any additional external magnetic field beyond the internal magnetic field, an interesting phenomenon occurs: when the precession angle exceeds 90 degrees, the polarity of the internal field reverses. This polarity reversal leads to a reversal of the spin precession direction (see below for further details).

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Precession Pumping by an Oscillating Magnetic Field

 

 

 

Precession Pumping/Damping by Circulary- polarized electroMagnetic Field
magnetic field rotation: clockwise magnetic field rotation: counter clockwise in-phase: in- antiphase: damping precession pumping precession damping When the magnetic field of an electromagnetic wave rotates in the same direction as the spin precession, the precession is amplified, and the precession angle increases. When the magnetic field of an electromagnetic wave rotates in the same direction as the spin precession but is out of phase (by 180°), it induces damping, leading to a decrease in the precession angle. no effect on precession   When the magnetic field of an electromagnetic wave rotates in the opposite direction to the spin precession, the rotating magnetic field has no effect on the precession. The rotating magnetic field influences spin precession only when its rotation direction matches that of the spin precession. The rotating magnetic field has no effect on spin precession only when its rotation direction is opposite to rotation of the spin precession.
The robustness of the one possible rotation direction for spin precession serves as strong evidence for the fundamental nature of the symmetrical origin of spin.
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Precession Pumping/Damping by Linearly- polarized electroMagnetic Field
in-phase: in- antiphase: precession pumping precession damping
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4 possible configuration for precession pumping by Linearly- polarized electroMagnetic Field
configuration 1 configuration 2 configuration 3 configuration 4
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Reversal of precession direction during magnetization reversal

 

 

 

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Precession Pumping vs. Precession Damping

 

 

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