  We report the observation of spin glass state in the double perovskite oxide
Sr$_{2}$FeCoO$_{6}$ prepared through sol-gel technique. Initial structural
studies using x rays reveal that the compound crystallizes in tetragonal $I
4/m$ structure with lattice parameters, $a$ = 5.4609(2) \AA and $c$ = 7.7113(7)
\AA. The temperature dependent powder x ray studies reveal no structural phase
transition in the temperature range 10 -- 300 K. However, the unit cell volume
shows an anomaly coinciding with the magnetic transition temperature thereby
suggesting a close connection between lattice and magnetism. Neutron
diffraction studies and subsequent bond valence sums analysis show that in
Sr$_{2}$FeCoO$_{6}$, the $B$ site is randomly occupied by Fe and Co in the
mixed valence states of Fe$^{3+}$/Fe$^{4+}$ and Co$^{3+}$/Co$^{4+}$. The random
occupancy and mixed valence sets the stage for inhomogeneous magnetic exchange
interactions and in turn, for the spin glass like state in this double
perovskite which is observed as an irreversibility in temperature dependent dc
magnetization at $T_f\sim$ 75 K. Thermal hysteresis observed in the
magnetization profile of Sr$_{2}$FeCoO$_{6}$ is indicative of the mixed
magnetic phases present. The dynamic magnetic susceptibility displays
characteristic frequency dependence and confirms the spin glass nature of this
material. Dynamical scaling analysis of $\chi'(T)$ yields a critical
temperature $T_{ct}$ = 75.14(8) K and an exponent $z\nu$ = 6.2(2) typical for
spin glasses. The signature of presence of mixed magnetic interactions is
obtained from the thermal hysteresis in magnetization of Sr$_{2}$FeCoO$_{6}$.
Combining the neutron and magnetization results of Sr$_2$FeCoO$_6$, we deduce
the spin states of Fe to be in low spin while that of Co to be in low spin and
intermediate spin.
