Periodic spin polarization of small quantum dots

We demonstrate, using spin density functional theory, that a quantum dot in a weak transverse magnetic field undergoes spontaneous spin polarization which fluctuates periodically with field strength B. The fluctuations are related to anti-crossing of developing Landau levels at the Fermi surface. For electron number N even, a crossing of two levels is sufficient to cause an instability to spontaneous polarization. For N odd, a simultaneous crossing of three or more levels is required. Such multiple crossings are characteristic of a circularly parabolic potential. Our calculations show that the realistic confining potential of a dot, calculated self-consistently in 3D, is sufficiently close to parabolicity for the multiple crossings to persist.