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