Theory of the Magnetic Susceptibility of Graphite

Abstract

The theory of the magnetic susceptibility of graphite is presented in terms of a three-dimensional Wallace electron energy band structure. The experimentally observed variation with temperature is explained in a satisfactory manner, provided the interplane resonance integral occurring in the band approximation is given a value of about 0.5 ev. This is about five times larger than the previously used estimate and implies that a two-dimensional band approximation may be invalid in many cases. The inplane resonance integral is obtained by fitting the variation, with electron concentration, of the electrical resistivity of a graphite-bisulphate residue compound. In this way a value of 1.63 ev for this integral is obtained. It might be noted that these values enabled a better fit of the resistivity over the entire range of bisulphatization than could be obtained by a two-dimensional theory. On the other hand, the value thus obtained for the actual magnitude of the susceptibility is lower than that observed by a factor of about 40. The (room temperature) variation of the susceptibility of bromine graphite is then analyzed on the basis of the above theory, using the indicated values of the constants. In this way, a value is obtained for the percentage of the bromine which is ionized. This is found to be weakly dependent on the amount of bromine, varying between 18% at 0.3 atomic percent bromine to 13% at 0.8 atomic percent bromine. The experimental value has been found to vary slightly around 18%. This agreement is very good and indicates that the theory is valid in explaining relative variations of the susceptibility, even though there is difficulty in predicting the absolute magnitude. The latter is the only serious discrepancy found in the present work and has not yet been explained.