  We study the low-temperature properties of a classical Heisenberg model with
site-random interlayer couplings on the cubic lattice. This model is introduced
as a simplified effective model of Sr(Fe$_{1-x}$Mn$_{x}$)O$_2$, which was
recently synthesized. In this material, when $x=0.3$, $(\pi\pi\pi)$ and
$(\pi\pi0)$ mixed ordering is observed by neutron diffraction measurements. By
Monte Carlo simulations, we find an exotic bulk spin structure that explains
the experimentally obtained results. We name this spin structure the "random
fan-out state". The mean-field calculations provide an intuitive understanding
of this phase being induced by the site-random interlayer couplings. Since
Rietveld analysis assuming the random fan-out state agrees well with the
neutron diffraction pattern of Sr(Fe$_{0.7}$Mn$_{0.3}$)O$_2$, we conclude that
the random fan-out state is reasonable for the spin-ordering pattern of
Sr(Fe$_{0.7}$Mn$_{0.3}$)O$_2$ at the low-temperature phase.
