  Using density functional theory (DFT) based electronic structure
calculations, the effects of morphology of semiconducting nano structures on
the magnetic interaction between two magnetic dopant atoms as well as a
possibility of tuning band gaps have been studied in case of the bi-doped
(ZnO)$_{24}$ nano structures with the impurity dopant atoms of the 3$d$ late
transition metals (TM) - Mn, Fe, Co, Ni and Cu. To explore the morphology
effect, three different structures of the host (ZnO)$_{24}$ nano-system having
different degrees of spatial confinement, have been considered : a two
dimensional (2D) nanosheet, an one dimensional (1D) nanotube and a finite
cage-shaped nanocluster. The present study employs hybrid density functional
theory to accurately describe the electronic structure of all the systems. It
is shown here that the magnetic coupling between the two dopant atoms, remains
mostly anti-ferromagnetic in course of changing the morphology from the sheet
geometry to the cage-shaped geometry of the host systems, except for the case
of energetically most stable bi-Mn doping, which shows a transition from
ferromagnetic to anti-ferromagnetic coupling with decreasing aspect ratio of
the host system. The effect of the shape change, however, has a significant
effect on the overall band gap variations of both the pristine as well as all
the bi-doped systems, irrespective of the nature of the dopant atoms and
provides a means for easy tunability of their optoelectronic properties.
