Magnetic ordering in quantum dots: Open vs. closed shells

In magnetically-doped quantum dots changing the carrier occupancy, 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.