  Atomic, electronic, and magnetic structure of LaSrCo$_{1/2}$Fe$_{1/2}$O$_4$
mixed-metal Ruddlesden-Popper oxide is investigated theoretically using
self-consistent ACBN0 DFT + $U$ approach. We show that the electronic and
magnetic properties strongly depend on the distribution of transition-metal and
La/Sr ions in the lattice. Fe-Fe exchange is found to be antiferromagnetic,
whereas Co-Co and Fe-Co exchange is ferromagnetic. We find that Co spin states
depend on the distribution in both La/Sr and transition-metal ions. The most
energetically favorable configuration is ferromagnetic, whereas the majority of
metastable configurations are antiferromagnetic. LaSrCo$_{1/2}$Fe$_{1/2}$O$_4$
was synthesized using spray-pyrolysis method. Magnetization measurements
revealed antiferromgnetic behavior, thus indicating presence of metastable
configurations in the synthesized material. In addition, we show that in
complex systems, such as mixed-metal Ruddlesden-Popper phases, Hubbard $U$
values have to be determined for each crystallographically non-equivalent site.
