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 ℎ𝜈=𝑔𝜇𝐵𝐵 and then release it to the lattice system one way, where h: Planck constant, ν: frequency, g: g-value, μB: 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 𝜔c, relaxes with velocity of 𝜅𝑐=𝜔𝑐 / 𝑄𝑢 , which is inversely proportional to unloaded Q value of the cavity. On the other hand, spins do precess with an angular frequency of 𝜔𝑚= 𝛾𝑒 𝐵𝑚 under the static magnetic field 𝐵𝑚.
When the resonant condition of 𝜔𝑐 = 𝜔𝑚 is satisfied, excited electron spins that absorbed microwave energy relax with the velocity of 𝛾𝑚 (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 𝑔𝑚. The coupling constant 𝑔𝑚 is expressed as
where 𝜂𝑚𝑠𝑞𝑟𝑡 is the square root of the filling factor of the cavity, 𝛾𝑒 is gyromagnetic ratio of the electron, ℏ is reduced Planck constant (h/2π), 𝜇0 is vacuum permeability, 𝑉𝑐 is the volume of the cavity, N is number of magnetic ions, and S is spin quantum number.