Thermal Equilibrium and Spin Relaxation

For a sample in thermodynamic equilibrium containing N spin systems (5 = 1/2) in a magnetic field, there is a population difference between the two m, levels arising from each S = Ijl system the diflference follows the Boltzmann distribution. 

Under normal conditions there is a slight excess population in the lower (/ = —1/2) level. Absorption of microwave energy by the sample induces transitions from the Ws = —1/2 to the m, = +1/2 level. To maintain steady-state conditions, electrons promoted to the excited state must lose energy and return to the lower level otherwise, saturation would occur and no resonance absorption would be observed. This is similar to the situation in NMR spectroscopy. 

Unpaired electrons can interact with other magnetic dipoles in the system. Such interactions do not dissipate energy and hence do not directly contribute to returning the spin systems to equilibrium. However, the spin-lattice transition may be enhanced if the interaction with the magnetic dipoles brings the excess energy to a position for transfer to the lattice. A variety of dipoles are frequently part of an unpaired electron s environment for example, other unpaired electrons, magnetic nuclei of the lattice, and various electronic and impurity dipoles. Since dipolar interactions decrease with the cube of the separation, i.e., ai = many 

Ez = the Zeeman-interaction energy of the electron with the external magnetic field ( 1 cm ) 

Esf = the hyperfine interaction energy—the energy of coupling betwren 

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