  Density functional theory (DFT) calculations are performed to predict the
structural, electronic and magnetic properties of electrically neutral or
charged few-atomic-layer (AL) oxides whose parent systems are based on polar
perovskite $KTaO_{3}$. Their properties vary greatly with the number of ALs
($n_{AL}$) and the stoichiometric ratio. In the few-AL limit ($n_{AL}\leqslant
14$), the even AL (EL) systems with chemical formula $(KTaO_{3})_{n}$ are
semiconductors, while the odd AL (OL) systems with formula
($K_{n+1}Ta_{n}O_{3n+1}$ or $K_{n}Ta_{n+1}O_{3n+2}$) are half-metal except for
the unique $KTa_{2}O_{5}$ case which is a semiconductor due to the large
Peierls distortions. After reaching certain critical thickness ($n_{AL}>14$),
the EL systems show ferromagnetic surface states, while ferromagnetism
disappears in the OL systems. These predictions from fundamental complexity of
polar perovskite when approaching the two-dimensional (2D) limit may be helpful
for interpreting experimental observations later.
