Most metals are paramagnetic because metals have a lot of unpaired electrons. While carbon is a nonmetal, because graphite has a lot of unsaturated bonds, those pi electrons can move freely just like metals. As a result, graphite should be a good paramagnet. Yet graphite is one of the best diamagnets and the only material that can be levitated by permanent magnets under room temperature. So what causes the large diamagnetism of graphite?
1 Answer1
The magnetic susceptibility in metal includes two kinds of contribution: the Pauli paramagnetism$\chi_{s}>0$ comes from the spin, the Landau diamagnetism$\chi_{orb}<0$ comes from the orbital motion. For a free electron gas with$E=p^2/2m$,$\chi_{orb}=-\chi_s/3$, so usually the metal is paramagnetic; however, the lattice introduces complex electronic structures, and this is not always true. Roughly speaking, when consider only intra-band contribution$\chi_{orb}/{\chi_s} \propto (m/m_*)^2$ where$m_*$ is the effective mass (see,e.g. Aschroft& Mermin, Solid State Physics, Eq(31.73)) and graphite has a very small effective mass for which$\chi_{orb}$ is very large. For single-layer graphene, the band has Dirac cones and the effective mass is even zero (in the clean and non-interacting limit). In graphite/graphene, the interband effect will also affect$\chi_{orb}$. Nonetheless, graphite has a very large$\chi_{orb}$ which surpasses$\chi_s$, and it is diamagnetic. Similar phenomena occur in bismuth, where diamagnetism was first observed. It also has a Dirac-like band and is one of the strongest diamagnets (if we do not take the perfect diamagnetism in superconductors into consideration).
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