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# Spin Hamiltonians

rename
Updated
2009-03-12 00:09

## Spin Hamiltonians

Spin Hamiltonians are energy expressions used to interpret NMR (Nuclear Magnetic Resonance), ESR (Electron Spin Resonance), EPR (Electron Paramagnetic Resonance), and ENDOR spectra. They are also useful in the fields of Spintronics and Quantum Computing.

Symbol | Explanation |
---|---|

H | Overall Spin Hamiltonian,generally a Hermitian matrix |

h J S_{1}• S_{2} | Isotropic Exchange Interactionbetween two electron spins |

h A S • I | Isotropic Hyperfine Couplingbetween an electron spin and a nuclear spin |

h [A_{<FONT FACE="Symbol">^</FONT>}(S_{x} I_{x} + S_{y} I_{y}) + A_{||} S_{z} I_{z}] | Axial Hyperfine Couplingbetween an electron spin and a nuclear spin |

h (A_{x} S_{x} I_{x} + A_{y} S_{y} I_{y} + A_{z} S_{z} I_{z}) | Rhombic Hyperfine Couplingbetween an electron spin and a nuclear spin |

g μ_{B} B • S | Isotropic Electron Zeeman Effectfor an electron spin in a magnetic field |

μ_{B} [g_{<FONT FACE="Symbol">^</FONT>}(S_{x} B_{x} + S_{y} B_{y}) + g_{||} S_{z} B_{z}] | Axial Electron Zeeman Effectfor an electron spin in a magnetic field |

μ_{B} (g_{x} S_{x} B_{x} + g_{y} S_{y} B_{y} + g_{z} S_{z} B_{z}) | Rhombic Electron Zeeman Effectfor an electron spin in a magnetic field |

-g_{N} μ_{B} B • I | Nuclear Zeeman Effectfor a nuclear spin in a magnetic field |

μ_{0}/(4 π R^{3})[μ_{1}• μ_{2} - 3(μ_{1}• r)(μ_{2}• r)] | Dipole-Dipole Interactionbetween two electron magnetic moments a distance R apart where r is the unit vector between them |

h J I_{1}• I_{2} | J-Coupling or Spin-Spin Couplingbetween two nuclear spins |

Quadrupole Couplingdue to a nuclear spin I>1/2 | |

Zero-Field Splittingdue to an electron spin S>1/2 | |

Spin-Orbit Couplingbetween an electron spin and an angular momentum | |

Russell-Saunders Couplingbetween an electron spin and an angular momentum | |