  We have studied the atomic and magnetic structure of the dilute ferromagnetic
semiconductor system (Ba,K)(Zn,Mn)$_2$As$_2$ through atomic and magnetic pair
distribution function analysis of temperature-dependent x-ray and neutron total
scattering data. We detected a change in curvature of the temperature-dependent
unit cell volume of the average tetragonal crystallographic structure at a
temperature coinciding with the onset of ferromagnetic order. We also observed
the existence of a well-defined local orthorhombic structure on a short length
scale of $\lesssim 5$ \AA, resulting in a rather asymmetrical local environment
of the Mn and As ions. Finally, the magnetic PDF revealed ferromagnetic
alignment of Mn spins along the crystallographic $c$-axis, with robust
nearest-neighbor ferromagnetic correlations that exist even above the
ferromagnetic ordering temperature. We discuss these results in the context of
other experiments and theoretical studies on this system.
