  Cosmological simulations show that dark matter halos surrounding baryonic
disks have a wide range of angular momenta, measured by the spin parameter
($\lambda$). In this study, we bring out the importance of inner angular
momentum($<$30 kpc), measured in terms of the halo spin parameter, on the
secular evolution of the bar using N-body simulations. We have varied the halo
spin parameter $\lambda$ from 0 to 0.1 for co-rotating (prograde) spinning
halos and one counter-rotating (retrograde) halo spin ($\lambda$=-0.1) with
respect to the disk. We report that as the halo spin increases, the buckling is
also triggered earlier and is followed by a second buckling phase in high-spin
halo models. The timescale for the second buckling is significantly longer than
the first buckling. We find that bar strength does not reduce significantly
after the buckling in all of our models, which provides new insights about the
role of inner halo angular momentum, unlike previous studies. Also, the buckled
bar can still transfer significant angular momentum to the halo in the secular
evolution phase, but it reduces with increasing halo spin. In the secular
evolution phase, the bar strength increases and saturates to nearly equal
values for all the models irrespective of halo spin and the sense of rotation
with respect to the disk. The final boxy/peanut shape is more pronounced
($\sim$20 $\%$) in high spin halos having higher angular momentum in the inner
region compared to non-rotating halos. We explain our results with angular
momentum exchanges between the disk and halo.
