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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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Area of Science:

  • Physics
  • Nanoscience
  • Electrical Engineering

Background:

  • Phase coupling is crucial for synchronized behavior in coupled auto-oscillators.
  • Spin-torque vortex nano-oscillators offer a platform for studying nonlinear dynamics.

Purpose of the Study:

  • To experimentally investigate phase coupling between two dipolarly coupled spin-torque vortex nano-oscillators.
  • To determine the coupling strength and phase shift between the oscillators.

Main Methods:

  • Utilized an external microwave field to probe phase coupling.
  • Employed phase locking of one oscillator to the external source.
  • Analyzed coupled phase equations to understand frequency pulling phenomena.

Main Results:

  • Observed frequency pulling on the second oscillator when the first was phase-locked.
  • Demonstrated that frequency pulling arises from both oscillator-oscillator and source-oscillator couplings.
  • Successfully determined the coupling strength and phase shift between the two nano-oscillators.

Conclusions:

  • The experimental approach provides a method to quantify coupling in nano-oscillator systems.
  • Understanding phase coupling is vital for designing and implementing large interacting oscillator networks.
  • This work offers key parameters for advancing the development of synchronized nano-oscillator systems.