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Two-Variable Theory on Electron Spin Resonance

Updated: Jul 24, 2018

I began to study electron and nuclear magnetic resonance theory and experiment in 1986 at Monash University after teaching Physics for four years at SCNU in China. By 1990, my first paper in the field was published.


Ever since Bohr's atomic model was proposed to explain hydrogen absorption spectra, the resonance condition has been well known: the maximum absorption occurs when the gap between two energy levels equals to the photon energy. Nevertheless, when applying the resonance condition is applied to describe either electron or nuclear spin resonance phenomena, it remained obscure how to incorporate the magnetic field and photon frequency into the basic formula.


Since the 1940s, the formula for magnetic resonance had been described be one-variable, whilst the magnetic field and the photon frequency were considered exchangeable in every textbook. In fact, many authors are still unaware of such an obscure theoretical inconsistency.


When Prof. Pilbrow, my Ph.D. supervisor, draw my attention to this issue, I was busy in writing my thesis. A few weeks later, it occurred to me that the resonance condition is governed by the photon frequency whilst the the maximum absorption is actually determined by applied magnetic field. Thus, both electron and nuclear spin magnetic resonance should be described by two independent variables: magnetic field and photon frequency.


Implications of this revelation were studied and then published in Journal of Magnetic Resonance in 1990. In 1999, the work was selected into a specialist hand book edited by Poole and Farach.






In fact, the two-variable formulation for magnetic resonance provides a starting point to describe more sophisticated spin dynamics that involves spin-photon coupling in addition to electron-nucleon hyperfine coupling. In the study of spintron device for quantum computing, for example, the profile of the field-frequency dependence is apparently different as shown in this figure.

Hence, it could be argued that the exciting quantum entanglement between spins and photons might have been discovered if more researchers had learnt that the magnetic field and photon frequency should be treated as two independent variables.


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