Magnetic ordering in quantum dots
Pientka, James M.
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This thesis explores different manifestations of the magnetic ordering in quantum dots. In the first part of the thesis we propose a model of magnetic polaron formation in semiconductor quantum dots doped with magnetic ions. A wetting layer serves as a reservoir of photo-generated holes, which can be trapped by the adjacent quantum dots. For certain hole densities, the temperature dependence of the magnetization induced by the trapped holes is reentrant: it disappears for some temperature range and reappears at higher temperatures. We demonstrate that this peculiar effect is not an artifact of the mean field approximation and persists after statistical spin fluctuations are accounted for. We predict fingerprints of reentrant magnetic polarons in photoluminescence spectra. In the second part of the thesis we investigate how changing the carrier occupancy in magnetically-doped quantum dots, from open to closed shells, leads to qualitatively different forms of carrier-mediated magnetic ordering. While it is common to study such nanoscale magnets within a mean field approximation, excluding the spin fluctuations can mask important phenomena and lead to spurious thermodynamic phase transitions in small magnetic systems. By employing coarse-grained, variational, and Monte Carlo methods on singly and doubly occupied quantum dots to include spin fluctuations, we evaluate the relevance of the mean field description and distinguish different finite-size scaling in nanoscale magnets. In the last part of the thesis we explore how semiconductor quantum dots doped with magnetic impurities provide an intriguing opportunity to explore the interplay of confinement, Coulomb and exchange interactions. Using exact diagonalization we study the ground state properties of a magnetic quantum dot with multiple occupancies. We show that the ground state not only depends on the orientation of the carrier and impurity spins, but is also very sensitive to the position of the magnetic impurities in the quantum dot. Our results reveal magnetic frustration and strongly correlated states, qualitatively different from the noninteracting limit.