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Spin–Spin Coupling Constant: Overview

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...

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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...

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Robust Mutual Synchronization in Long Spin Hall Nano-oscillator Chains.

Akash Kumar^1,2,3, Himanshu Fulara⁴, Roman Khymyn¹

¹Physics Department, University of Gothenburg, 412 96 Gothenburg, Sweden.

|July 14, 2023

Summary

Mutual synchronization of spintronic nano-oscillators significantly enhances signal quality. Increasing oscillator numbers in chains boosts peak power quadratically, enabling advanced computing applications.

Keywords:

Mutual synchronization Spin Hall effect Spin Hall nano-oscillators Spintronic oscillators

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Area of Science:

Spintronics
Condensed Matter Physics
Nano-engineering

Background:

Spintronic nano-oscillators offer potential for high-quality signal generation.
Mutual synchronization of multiple oscillators can enhance performance metrics like coherence and power.
Applications in unconventional computing necessitate robust and scalable synchronized oscillator systems.

Purpose of the Study:

To investigate the effect of serially connecting spin Hall nano-oscillators on their synchronization properties.
To explore the scalability of mutual synchronization in nano-oscillator chains.
To quantify the improvements in coherence and peak power with increasing numbers of synchronized oscillators.

Main Methods:

Fabrication of spin Hall nano-oscillator chains with up to 50 serially connected nanoconstrictions using W/NiFe, W/CoFeB/MgO, and NiFe/Pt material stacks.
Experimental demonstration of mutual synchronization in these chains.
Characterization of synchronization robustness, operating frequency, line width, quality factor, and peak power.

Main Results:

Achieved robust and complete mutual synchronization of 21 nanoconstrictions at 10 GHz.
Demonstrated line widths <134 kHz and quality factors >79,000 for synchronized chains.
Observed a quadratic increase in peak power with the number of synchronized oscillators, reaching 400-fold enhancement in long chains.
Found that while synchronization persists in chains >21, it becomes less robust, with signal quality plateauing.

Conclusions:

Mutual synchronization of serially connected spintronic nano-oscillators effectively boosts coherence and peak power.
The number of synchronized oscillators in a chain is critical for performance gains, with optimal performance observed up to 21 units.
Longer chains show diminishing returns in signal quality and robustness, indicating limitations in scalability beyond a certain point.