A conventional ESR spectrometer uses a cavity for microwave irradiation and detection of ESR absorption. On the resonance state, it can be considered as a model that spins absorb energy of โ๐=๐๐๐ต๐ต and then release it to the lattice system one way, where h: Planck constant, ฮฝ: frequency, g: g-value, ฮผB: Bohr magneton, and B: magnetic flux density.
However, the interaction between photon of microwave and spins of electrons is a little more complex in fact.
Figure 1 is a modelized drawing that expresses energy flow of microwave photon and spins. The cavity resonates with angular frequency ๐c, relaxes with velocity of ๐
๐=๐๐ / ๐๐ข , which is inversely proportional to unloaded Q value of the cavity. On the other hand, spins do precess with an angular frequency of ๐๐= ๐พ๐ ๐ต๐ under the static magnetic field ๐ต๐.
When the resonant condition of ๐๐ = ๐๐ is satisfied, excited electron spins that absorbed microwave energy relax with the velocity of ๐พ๐ (half width: half width at half maximum (HWHM)), which corresponds to spectral line width. At this time, photon and electron spins exchange energy with a coupling constant ๐๐. The coupling constant ๐๐ is expressed as[1]
ๆฐๅผ
where ๐๐๐ ๐๐๐ก is the square root of the filling factor of the cavity, ๐พ๐ is gyromagnetic ratio of the electron, โ is reduced Planck constant (h/2ฯ), ๐0 is vacuum permeability, ๐๐ is the volume of the cavity, N is number of magnetic ions, and S is spin quantum number.