Magnetic Susceptibility of Bloch Electrons in a Dielectric Formulation

Both the diagonal and the off-diagonal parts of the magnetic susceptibility tensor are calculated by examining the limit, ω→0 and q →0, of the frequency and wave-vector dependent dielectric tensor, ε i j ( q ω). It is shown that the diagonal part reduces to the expression obtained by Hebborn and Sondheimer. Gauge-invariance of the formalism is made explicit.