RIGOROUS MAGNETIC SUSCEPTIBILITY FOR A MAGNETIC BREAKDOWN MODEL

The exact diamagnetic susceptibility is calculated as a function of the magnetic field for a magnetic breakdown model which has been previously presented. The susceptibility is obtained by numerically evaluating the appropriate derivative of the Helmholtz free energy using the exact eigenvalues of the model Hamiltonian. The susceptibility calculated by this method includes the contributions from both the zero-field diamagnetism and the de Haas-van Alphen effect. The periodicities in the susceptibility are related to the semiclassical electron orbits corresponding to this model: for low magnetic fields the periods are determined by two closed orbits, one within the other; for high fields a single period is observed corresponding to the broken down case of two identical intersecting elliptical orbits. The behavior in the transition region is compatible with the expression for the breakdown probability derived by several authors. An approximate calculation of the oscillatory part of the diamagnetism is also carried out using the semiclassical method of Falicov and Stachowiak. When the influence of the energy gap on the orbit geometry is taken into account, their method yields results which are in good agreement with the exact susceptibility. Evaluation of the steady diamagnetism for the model using the expression for the susceptibility derived by Wannier and Upadhyaya yields results which are in agreement with the numerical calculations and, in addition, exhibits anomalous features of the zerofield diamagnetism in the neighborhood of critical points of the Fermi surface. © 1969.