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Peer-reviewedCC BY 4.0Royal Society Open Science

Spectral theory of spin relaxation

  • Timothy Field1
  1. 1Electrical & Computer Engineering and Mathematics & Statistics, McMaster University , Hamilton, Ontario, Canada
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Abstract

A dynamical theory of spin relaxation previously formulated in terms of stochastic differential equations is extended beyond the extreme narrowed approximation to incorporate temporal correlation in the driving random magnetic fields. An analysis of spin–spin relaxation in this case is provided, which is non-perturbative in the random field and yields an exact solution to the spin dynamical equations for axial (longitudinal) field fluctuations. We provide a real-time dynamical derivation that leads to a generalized class of spin spectra that are essentially non-Lorentzian for all finite field parameters. A spectral-moment analysis and novel parameter-extraction scheme lead to distinct notions of observable relaxation timescales compared with the standard characteristic exponential. The Lorentzian case is recovered as the extreme narrowed limit.

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Cite

BibTeXRIS
BibTeX
@article{field2026spectral,
  title = {{Spectral theory of spin relaxation}},
  author = {Timothy Field},
  journal = {Royal Society Open Science},
  year = {2026},
  month = nov,
  doi = {10.1098/rsos.260478},
  url = {https://royalsocietypublishing.org/rsos/article/13/11/260478/484066/Spectral-theory-of-spin-relaxationSpectral-theory},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Spectral theory of spin relaxation
AU  - Timothy Field
PY  - 2026
DA  - 2026/11/04
JO  - Royal Society Open Science
DO  - 10.1098/rsos.260478
UR  - https://royalsocietypublishing.org/rsos/article/13/11/260478/484066/Spectral-theory-of-spin-relaxationSpectral-theory
AB  - A dynamical theory of spin relaxation previously formulated in terms of stochastic differential equations is extended beyond the extreme narrowed approximation to incorporate temporal correlation in the driving random magnetic fields. An analysis of spin–spin relaxation in this case is provided, which is non-perturbative in the random field and yields an exact solution to the spin dynamical equations for axial (longitudinal) field fluctuations. We provide a real-time dynamical derivation that leads to a generalized class of spin spectra that are essentially non-Lorentzian for all finite field parameters. A spectral-moment analysis and novel parameter-extraction scheme lead to distinct notions of observable relaxation timescales compared with the standard characteristic exponential. The Lorentzian case is recovered as the extreme narrowed limit.
SN  - 2054-5703
ER  -