  The structural analogue of iron-based superconductors the BaMn$_2$P$_2$ and
BaMn$_2$As$_2$ compounds under hydrostatic pressure upto 140 GPa were studied
within the framework of DFT+U. The transition from an antiferromagnetic (AFM)
insulator to an antiferromagnetic metal is observed under pressure of 6.4 GPa
for BaMn$_2$P$_2$ and 8.3 GPa for BaMn$_2$As$_2$. This second order phase
transition to the AFM metallic state provides an appropriate normal state for
possible superconductivity in these materials. Moreover, a further increase in
pressure leads to a series of first order magnetostructural phase transitions
between different antiferromagnetic phases, then to a ferromagnetic metal and
finally to a nonmagnetic metal. In case of doping these compounds could
potentially be a superconductors under pressure (above 6-8 GPa) with critical
temperature growing under pressure.
