  With the proposed Hund's rule correlation picture, i.e. the fluctuating Fe
local moments with the As-bridged antiferromagnetic superexchange interactions,
the exceptional collapsed tetragonal phase and related phase transitions
observed in CaFe$_2$As$_2$ are well understood. With the same framework, a
pressure-temperature phase diagram is predicted for BaFe$_2$As$_2$ as well, in
which a paramagnetic tetragonal and a collinear antiferromagnetic orthorhombic
structures to nonmagnetic tetragonal structure transitions take place around
4-8 GPa and 10-15 GPa respectively, and a nonmagnetic tetragonal to a
nonmagnetic collapsed tetragonal structure transition takes place over 26 GPa.
Our study helps better understand the complex correlation among crystal
structure, magnetism, and electronic structure in pnictides, a precondition to
understand the superconductivity in pnictides.
