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Spin Hamiltonians

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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.

 

SymbolExplanation
HOverall Spin Hamiltonian,
generally a Hermitian matrix
h J S1S2Isotropic Exchange Interaction
between two electron spins
h A SIIsotropic Hyperfine Coupling
between an electron spin and a nuclear spin
h [A<FONT FACE="Symbol">^</FONT>(Sx Ix + Sy Iy) + A|| Sz Iz]Axial Hyperfine Coupling
between an electron spin and a nuclear spin
h (Ax Sx Ix + Ay Sy Iy + Az Sz Iz)Rhombic Hyperfine Coupling
between an electron spin and a nuclear spin
g μB BSIsotropic Electron Zeeman Effect
for an electron spin in a magnetic field
μB [g<FONT FACE="Symbol">^</FONT>(Sx Bx + Sy By) + g|| Sz Bz]Axial Electron Zeeman Effect
for an electron spin in a magnetic field
μB (gx Sx Bx + gy Sy By + gz Sz Bz)Rhombic Electron Zeeman Effect
for an electron spin in a magnetic field
-gN μB BINuclear Zeeman Effect
for a nuclear spin in a magnetic field
μ0/(4 π R3)[μ1μ2 - 3(μ1r)(μ2r)]Dipole-Dipole Interaction
between two electron magnetic moments
a distance R apart
where r is the unit vector between them
h J I1I2J-Coupling or Spin-Spin Coupling
between two nuclear spins
Quadrupole Coupling
due to a nuclear spin I>1/2
Zero-Field Splitting
due to an electron spin S>1/2
Spin-Orbit Coupling
between an electron spin and an angular momentum
Russell-Saunders Coupling
between an electron spin and an angular momentum
memorize

References:

C. P. Slichter's "Principles of Magnetic Resonance", 3rd Edition, 1996
http://books.google.com/books?id=zgnrRkaIhFoC
J. A. Weil and J. R. Bolton's "Electron Paramagnetic Resonance", 2nd Edition, 2006
http://books.google.com/books?id=qjLpMw9ZgPIC