Paramagnetic-diamagnetic interplay in quantum dots for non-zero temperatures

In the usual Fock and Darwin formalism with a parabolic potential character ized by the confining energy is an element of (0) = h omega (0) approximate to 3.4 meV, but including explicitly also the Zeeman coupling between spin and magnetic field, we study the combined orbital and spin magnetic proper ties of quantum dots in a two-dimensional electron gas with the parameters for GaAs, for N = 1 and N much greater than I electrons on the dot. For N = 1 the magnetization M(T, B) consists of a paramagnetic spin contrib ution and a diamagnetic orbital contribution, which dominate in a nontrivia l way at low temperatures and fields and at high temperatures and fields re spectively. For N much greater than 1, where orbital and spin effects are intrinsically coupled in a subtle way and cannot be separated, we find in a simplified H artree approximation that at N = m(2), i.e. for a half-filled last shell, M (T, B, N) is parallel (antiparallel) to the magnetic field, if temperatures and fields are low enough thigh enough), whereas for N P m2 the magnetizat ion oscillates with B and N as a T-dependent periodic function of the varia ble x root NeB/(2m*c omega (0)), with T-independent period Deltax = 1 (wher e m* = 0.067 m(0) is the small effective mass of GaAs, while mo is the elec tron mass). Correspondingly, by an adiabatic demagnetization process, which need only b e fast enough with respect to the slow transient time of the magnetic prope rties of the dot, the temperature of the dot diminishes or increases with d ecreasing magnetic field, and in some cases we obtain quite pronounced effe cts.