  Perpendicular magnetic anisotropy of the new ferromagnetic semiconductor
(Ba,K)(Zn,Mn)$_{2}$As$_{2}$ is studied by angle-dependent x-ray magnetic
circular dichroism measurements. The large magnetic anisotropy with the
anisotropy field of 0.85 T is deduced by fitting the Stoner-Wohlfarth model to
the magnetic-field-angle dependence of the projected magnetic moment.
Transverse XMCD spectra highlights the anisotropic distribution of Mn 3$d$
electrons, where the $d_{xz}$ and $d_{yz}$ orbitals are less populated than the
$d_{xy}$ state because of the $D_{2d}$ splitting arising from the elongated
MnAs$_{4}$ tetrahedra. It is suggested that the magnetic anisotropy originates
from the degeneracy lifting of $p$-$d_{xz}$, $d_{yz}$ hybridized states at the
Fermi level and resulting energy gain due to spin-orbit coupling when spins are
aligned along the $z$ direction.
