Purely orbital diamagnetic to paramagnetic fluctuation of quasi two-dimensional carriers under in-plane magnetic field

An external magnetic field, $H$, applied parallel to a quasi two-dimensional system modifies quantitatively and qualitatively the density of states. Using a self-consistent numerical approach, we study how this affects the entropy, $S$, the free energy, $F$, and the magnetization, $M$, for different sheet carrier concentrations, $N_s$. As a prototype system we employ III-V double quantum wells. We find that although $M$ is mainly in the opposite direction of $H$, the system is not linear. Surprisingly $\partial M / \partial H$ swings between negative and positive values, i.e., we predict an entirely orbital diamagnetic to paramagnetic fluctuation. This phenomenon is important compared to the ideal de Haas-van Alphen effect i.e. the corresponding phenomenon under perpendicular magnetic field.