Interaction Contribution to the Magnetization of Quantum Dots

We calculate the interaction contribution to the orbital magnetism of ballistic quantum dots. By developing a semiclassical approach, we evaluate both the first-order and higher-order Hartree-Fock contributions for an ensemble of square quantum dots, motivated by the experiment of Lévy, et al. In contrast to the diffusive ring case, the higher-order contributions do not simply renormalize the first-order one. The temperature dependence resulting from the higher-order calculation is much weaker than that of either the first-order interaction contribution or the non-interacting contribution. Most interestingly, this contribution to the susceptibility can change sign as a function of temperature--- from paramagnetic to diamagnetic--- for certain reasonable parameters.