  We present the results of structural and magnetic phase comparisons of the
iron oxychalcogenides La$_{2}$O$_{2}$Fe$_{2}$O$M$$_{2}$ ($M$ = S, Se). Elastic
neutron scattering reveals that $M$ = S and Se have similar nuclear structures
at room and low temperatures. We find that both materials obtain
antiferromagnetic ordering at a Neel temperature $T_{N}$ 90.1 $\pm$ 0.16 K and
107.2 $\pm$ 0.06 K for $M$= Se and S, respectively. The magnetic arrangements
of $M$ = S, Se are obtained through Rietveld refinement. We find the order
parameter exponent $\beta$ to be 0.129 $\pm$ 0.006 for $M$ = Se and 0.133 $\pm$
0.007 for $M$ = S. Each of these values is near the Ising symmetry value of
1/8. This suggests that although lattice and electronic structural
modifications result from chalcogen exchange, the nature of the magnetic
interactions is similar in these materials.
