  We investigate theoretically spin and orbital pseudospin magnetic properties
of a molecular orbital in parabolic and elliptic double quantum dots (DQDs). In
our many body calculation we include intra- and inter-dot electron-electron
interactions, in addition to the intradot exchange interaction of `p' orbitals.
We find for parabolic DQDs that, except for the half or completely filled
molecular orbital, spins in different dots are ferromagnetically coupled while
orbital pseudospins are antiferromagnetically coupled. For elliptic DQDs spins
and pseudospins are either ferromagnetically or antiferromagnetically coupled,
depending on the number of electrons in the molecular orbital. We have
determined orbital pseudospin quantum numbers for the groundstates of elliptic
DQDs. An experiment is suggested to test the interplay between orbital
pseudospin and spin magnetism.
