Magnetic order in Co[Cr(CN)$_6$]$_{2/3}\cdot z$H$_2$O and its interplay with correlated vacancy order

Prussian blue analogues (PBAs) are versatile hybrid framework materials that often exhibit local and long-range departures from their cubic parent structure, influencing their functionality. Long-range magnetic order is common in PBAs, owing to magnetic interactions between transition metal ions via bridging cyanide ligands in the structure. Here we report the magnetic structure of cobalt (II) hexacyanochromate, Co[Cr(CN)$_6$]$_{2/3}\cdot z$H$_2$O, determined using neutron powder diffraction. No evidence for magnetostriction at the magnetic ordering temperature is observed in contrast to the reported behaviour of a related PBA. Following experimental characterisation of the magnetic order of this PBA, we employ a simple Monte Carlo model to gain a better understanding of the relationship between hexacyanometallate vacancy distributions and magnetic ordering behaviour in these materials. This model shows that magnetic ordering is robust to the extent and nature of vacancy correlations, with only minor effects noticeable in the critical region, suggesting that PBAs with the same composition but different vacancy correlations might be expected to show similar magnetic behaviour.