Note:
For a positive magnetogyric ratio, produces population excess (polarization) in the direction of \(\boldsymbol{B_{0}}\). The population difference between the spin state can be expressed as \[\frac{N_i}{N} = \frac{e^{-{\varepsilon}_{i}/kT}}{\sum _{j=1}^{M}{e}^{-{\varepsilon}_{j}/kT}}\] where \(T\) is the thermodynamic temperature, \(k\) is the Boltzmann constant, \(N_{\rm{i}}\) is the number of spins in excited state \(i\), \(N\) is the total number of spins and \(\varepsilon_{i}\) and \(\varepsilon_{j}\) are the energies of states \(i\) and \(j\) respectively, and \(M\) is the number of possible energy levels.