  We study the artificial molecular states formed in laterally coupled double
semiconductor nanorings by systems containing one, two and three electrons. An
interplay of the interring tunneling and the electron-electron interaction is
described and its consequences for the magnetization and charging properties of
the system are determined. It is shown that both the magnetic dipole moment
generated by the double ring structure and the chemical potential of the system
as function of the external magnetic field strongly depend on the number of
electrons and the interring barrier thickness. Both the magnetization and
chemical potentials exhibit cusps at the magnetic fields inducing ground-state
parity and / or spin transformations. The symmetry transformations are
discussed for various tunnel coupling strengths: from rings coupled only
electrostatically to the limit of coalesced rings. We find that in the
ground-states for rings of different radii the magnetic field transfers the
electron charge from one ring to the other. The calculations are performed with
the configuration interaction method based on an approach of Gaussian functions
centered on a rectangular array of points covering the studied structure.
Electron-electron correlation is also discussed.
