Competition of three-dimensional magnetic phases in Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$: A structural perspective*

The crystalline and magnetic structures of Ca$_2$Ru$_{1-x}$Fe$_x$O$_4$ have been studied using neutron and X-ray diffraction. The Fe-doping reduces the Ru-O bond length in both apical and planar directions. The smaller Ru(Fe)O$_6$ octahedron leads to its reduced distortion. The $Pbca$ space group is maintained in all the Fe-dopings, so is the octahedral flattening. Two competing antiferromagnetic orders, $A$- and $B$-centered phases have been observed. The Fe-doping-relaxed crystal structure prefers the latter to the former. The absence of the two-dimensional antiferromagnetic critical fluctuations above the magnetic transition temperature and the three-dimensional magnetic correlation below the transition, together with the anomalous lattice response, point to an important role of orbital degree of freedom in driving the magnetic phase competition.