  We study the effects of both a repulsive and an attractive three body
interaction potential on a spin-1 ultracold Bose gas using mean field approach
(MFA). For an antiferromagnetic (AF) inter- action, we have found the existence
of the odd-even asymmetry in the Mott insulating (MI) lobes in presence of both
the repulsive two and three body interactions. In case of a purely three body
repulsive interaction, the higher order MI lobes stabilize against the
superfluid phase. However, the spin nematic (singlet) formation is restricted
upto the first (second) MI lobes for the former one, while there is neither any
asymmetry nor spin nematic (singlet) formation is observed for the later case.
The results are confirmed after carefully scrutinizing the spin eigen value and
spin nematic order parameter for both the cases. On the other hand, for an
attractive three body interaction, the third MI lobe is predominantly affected,
where it completely engulfs the second and the fourth MI lobes at large values
of the interaction strength. Albeit no significant change is observed beyond
the fourth MI lobe. In the ferromagnetic case, the phase diagram shows similar
features as that of a scalar Bose gas. We have compared our results on the MFA
phase diagrams for both types of the interaction potential via a perturbation
expansion in both the cases.
