Paramagnetic-diamagnetic interplay in quantum dots fornon-zero temperatures

Abstract

In the usual Fock and Darwin formalism with a parabolic potentialcharacterized by the confining energyϵ0 = ℏω0≈3.4 meV, but including explicitlyalso the Zeeman coupling between spin and magnetic field, we studythe combined orbital and spin magnetic properties of quantum dots ina two-dimensional electron gas with the parameters for GaAs, for N = 1 and N>>1 electrons on the dot.For N = 1 the magnetization M(T,B) consists of a paramagnetic spincontribution and a diamagnetic orbital contribution, which dominatein a non-trivial way at low temperatures and fields and at hightemperatures and fields respectively.For N>>1, where orbital and spin effects are intrinsicallycoupled in a subtle way and cannot be separated, we find in asimplified Hartree approximation that at N = m2, i.e. for ahalf-filled last shell, M(T,B,N) is parallel (antiparallel) to themagnetic field, if temperatures and fields are low enough (highenough), whereas for N≠m2 the magnetization oscillates withB and N as a T-dependent periodic function of the variablex: = {(N)1/2eB}/({2m*cω0}), with T-independent periodΔx = 1 (where m* = 0.067 m0 is the small effective mass ofGaAs, while m0 is the electron mass).Correspondingly, by an adiabatic demagnetization process,which need only be fast enough with respect to the slow transient time of the magnetic properties of the dot, thetemperature of the dot diminishes or increases with decreasingmagnetic field, and in some cases we obtain quite pronouncedeffects.