Charge Ordering and Incommensurate Modulations in the Metamagnetic Layered Manganese Oxysulfide Sr₂MnO₂Cu_3.5S₃

Sr₂MnO₂Cu_3.5S₃ contains mixed-valent Mn ions Mn^2+/3+ in axially elongated MnO₄S₂ octahedra connected via apical sulfide anions to copper-deficient antifluorite-type Cu_4-δS₃ layers where δ ∼ 0.5. Copper deficiency is charge-compensated by oxidation of Mn 3d states resulting in mixed-valency. The compound is tetragonal in P4/mmm at ambient temperatures (a = 4.016345(1) Å, c = 11.40708(5) Å). Below 190 K, superlattice reflections in diffraction data and an increase in resistivity, signal checkerboard charge-ordering of Mn²⁺ and Mn³⁺. The superstructure approximates to a √2a × √2a × 2c expansion of the room temperature cell in space group P4₂/nmc. However, satellite reflections signal a (3 + 2)D incommensurate modulation of Cu site occupancies in the Cu-deficient sulfide layers coupled with displacements of the sulfur positions; overall the superstructure below 190 K requires description in superspace group P4₂/nmc(a,0,0)0000(0,a,0)00s0. Analysis of total scattering measurements along with pair distribution functions supports the charge-ordered low temperature model and reveals local order of distinct Mn sites within the higher-temperature charge-disordered regime. Below T_N = 27 K, long-range magnetic ordering is A-type antiferromagnetic with distinct moments for Mn²⁺ and Mn³⁺ ions directed perpendicular to the MnO₂ planes and ordered ferromagnetically. Long-range antiferromagnetic order results from interlayer antiferromagnetic coupling. A metamagnetic transition at 1.1 T corresponds to a change to long-range interlayer ferromagnetic ordering via a spin-reorientation of magnetic moments and is associated with a slight decrease in the charge separation between the Mn sublattices, consistent with observations on mixed-valent perovskite and Ruddlesden-Popper-type oxide manganites.