Spin Hamiltonians

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 S1• S2	Isotropic Exchange Interaction between two electron spins
h A S • I	Isotropic 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 B • S	Isotropic 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 B • I	Nuclear Zeeman Effect for a nuclear spin in a magnetic field
μ0/(4 π R3)[μ1• μ2 - 3(μ1• r)(μ2• r)]	Dipole-Dipole Interaction between two electron magnetic moments a distance R apart where r is the unit vector between them
h J I1• I2	J-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
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See also: