Water, vacancies, and competing exchange interactions in Prussian blue analogues: a neutron diffraction study of field and dehydration-driven magnetic transitions
We report a neutron diffraction study of the structural and magnetic properties of a family of ferro- and ferrimagnetic Prussian blue analogues (PBAs), $A_4$[Fe(CN)$_6$]$_{2.7}$ ($A$ = Co, Mn, Ni), Rb$_2$Ni$_4$[Fe(CN)$_6$]$_{3.3}$, and Mn$_4$[Cr(CN)$_6$]$_{2.7}$, as a function of temperature (2--450~K) and applied magnetic field. All bimetallic compounds of the Fm$\overline{3}$m family exhibit a broad diffuse feature at low scattering angle, which we identify, through comparison with the cation-stabilized Rb$_2$NiFe framework, as an intrinsic signature of correlated vacancies and their associated interstitial water. High-temperature diffraction reveals a continuous crossover from positive to negative thermal expansion in CoFe and MnFe upon dehydration, while NiFe remains structurally robust up to 450~K. At low temperature, all compounds order in a collinear ferrimagnetic state with propagation vector $\mathbf{k}=(0,0,0)$, except MnFe, which adopts a partially frustrated magnetic structure with $\mathbf{k}=(1,0,0)$. A moderate magnetic field of $B_c = 1.3$~T drives a spin reorientation in MnFe toward the collinear $\mathbf{k}=(0,0,0)$ ferrimagnetic state common to the other compounds; the same transition is independently induced by dehydration. A minimal Heisenberg model shows that this transition results from a near-compensation between antiferromagnetic Mn--Fe coupling and a geometrically frustrated antiferromagnetic Mn--Mn interaction on the face-centered-cubic Mn sublattice, placing MnFe in the vicinity of a magnetic compensation point. These results resolve a longstanding ambiguity in the interpretation of the Fe $K$-edge XMCD response of MnFe-based PBAs, and establish water content as a key parameter controlling both the structural and magnetic stability of this family of materials, with direct relevance to their use as battery electrodes.