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\section{Nuclear Schottky effect}  In the presence of a magnetic field, the energy levels of a nucleus with spin $I$ split into $2I+1$ levels. This effect --- known as the nuclear Zeeman effect --- leads to hyperfine splitting of energy levels when the nuclei are in a local magnetic field and a field and temperature dependent contribution to the specific heat. In closed form,   \begin{equation}  \label{eq:ClosedFormSolution}  c_N = R \left(\frac{x}{2I}\right)^2 \{\csch^2(\frac{x}{2I}) - 2(2I+1)^2 \csch^2[(2I+1)\frac{x}{2I}]\}  \end{equation}  The Zeeman splitting of the nuclear energy levels leads to a broad peak in the specific heat when $k_b T$ is on the order of the energy splitting $\mu H$, but because the energy splittings are small\footnote{the nuclear magneton is a factor of 1836.1 smaller than the Bohr magneton $\mu_B$}, only the high temperature $(\mu H/k_B T)^2$ tail of specific heat peak is seen. Assuming that the zero field field splitting (ZFS) is negligible in comparison to that from the applied field $H$, then \cite{Lounasmaa1974, Leyarovski_1988}, \begin{equation}  \label{eq:SchottkyTail}  c_N(T,H) = \frac{{\lambda}_N}{\mu_0}\left(\frac{H}{T}\right)^2 \textrm{ [J/ mol K]}