Theory of magnetic susceptibility of graphite intercalation compounds

The orbital magnetic susceptibility (${\ensuremath{\chi}}_{or}^{c}$) of graphite intercalation compounds is calculated for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ using a tight-binding model for the $\ensuremath{\pi}$-electron energy bands and the compact expression for ${\ensuremath{\chi}}_{or}^{c}$ derived by Fukuyama, which includes both intraband and interband terms. The results are presented as an approximate analytic expression for ${\ensuremath{\chi}}_{or}^{c}$ as a function of Fermi level $\ensuremath{\mu}$ ($0<\ensuremath{\mu}\ensuremath{\lesssim}3$ eV) and temperature. For $\frac{\ensuremath{\mu}}{{k}_{B}T}\ensuremath{\ll}1$ the susceptibility is large and diamagnetic (due to interband transitions), while for ${k}_{B}T\ensuremath{\ll}\ensuremath{\mu}\ensuremath{\lesssim}3$ eV, ${\ensuremath{\chi}}_{or}^{c}$ is paramagnetic (mainly due to intraband transitions) in contrast to the usual Landau-Peierls diamagnetism of conduction electrons in parabolic bands. Furthermore, ${\ensuremath{\chi}}_{or}^{c}$ is shown to be a sensitive function of $\ensuremath{\mu}$ and hence of the conduction-electron charge distribution in each graphite layer. We show that this theory accounts for the main features of the experimental data (stage and temperature dependence of ${\ensuremath{\chi}}_{or}^{c}$) and suggest that measurements of the stage dependence of ${\ensuremath{\chi}}_{or}^{c}$ can be used to estimate the $c$-axis screening length in graphite intercalation compounds.