  With local density approximation + Hubbard $U$ (LDA+$U$) calculations, we
show that the ferromagnetic (FM) insulating state observed in tensile-strained
LaCoO$_3$ epitaxial thin films is most likely a mixture of low-spin (LS) and
high-spin (HS) Co, namely, a HS/LS mixture state. Compared with other FM
states, including the intermediate-spin (IS) state (\textit{metallic} within
LDA+$U$), which consists of IS Co only, and the insulating IS/LS mixture state,
the HS/LS state is the most favorable one. The FM order in HS/LS state is
stabilized via the superexchange interactions between adjacent LS and HS Co. We
also show that Co spin state can be identified by measuring the electric field
gradient (EFG) at Co nucleus via nuclear magnetic resonance (NMR) spectroscopy.
