High-entropy magnetism of murunskite

Murunskite (K$_2$FeCu$_3$S$_4$) is a bridging compound between the only two known families of high-temperature superconductors. It is a semiconductor like the parent compounds of cuprates, yet isostructural to metallic iron-pnictides. Moreover, like both families, it has an antiferromagnetic (AF)-like response with an ordered phase occurring below $\approx$ 100 K. Through comprehensive neutron, M\"ossbauer, and XPS measurements on single crystals, we unveil AF with a nearly commensurate quarter-zone wave vector. Intriguingly, the only identifiable magnetic atoms, iron, are randomly distributed over one-quarter of available crystallographic sites in 2D planes, while the remaining sites are occupied by closed-shell copper. Notably, any interpretation in terms of a spin-density wave is challenging, in contrast to the metallic iron-pnictides where Fermi-surface nesting can occur. Our findings align with a disordered-alloy picture featuring magnetic interactions up to second neighbors. Moreover, in the paramagnetic state, iron ions are either in Fe$^{3+}$ or Fe$^{2+}$ oxidation states, associated with two distinct paramagnetic sites identified by M\"ossbauer spectroscopy. Upon decreasing the temperature below the appearance of magnetic interactions, these two signals merge completely into a third, implying an orbital transition. It completes the cascade of (local) transitions that transform iron atoms from fully orbitally and magnetically disordered to homogeneously ordered in inverse space, but still randomly distributed in real space.