Magnetic susceptibility of tetrahedrally coordinated solids

We derive a general expression for the magnetic susceptibility ($\chi$) of intrinsic semiconductors in the Bloch representation using finite-temperature Green's-function formalism. It is shown that terms of the same order have been missed in the earlier theories of $\chi$. In order to apply our theory to tetrahedral semiconductors, we construct a basis set for the valence bands which is a linear combination of the $s{p}^3$ hybrids forming a bond in which their relative phase factors (heretofore neglected) have been properly included. We also construct a basis set for the conduction bands which are orthogonal to the valence-band functions. We construct Wannier functions for the valence bands from our Bloch functions and show that the bond orbitals used in the earlier chemical-bond theories are not the proper choice for the Wannier functions of the valence band. We use our basis functions in our general expression to obtain an expression for $\chi$ of tetrahedral semiconductors. Our expression for $\chi$ is origin independent and is free from any "scaling" parameter, unlike the earlier theories. A novel feature of our result is that our expressions for Van Vleck-type susceptibility is proportional to the overlap integral and tends to zero in the "no bonding" limit. We calculate $\chi$ of elemental and III-V tetrahedral semiconductors, and there is good agreement with experimental results.