Pressure-induced charge orders and their postulated coupling to magnetism in hexagonal multiferroic LuFe₂O₄

Hexagonal LuFe₂O₄ is a promising charge order (CO) driven multiferroic material with high charge and spin-ordering temperatures. The coexisting charge and spin orders on Fe³⁺/Fe²⁺ sites result in magnetoelectric behaviors, but the coupling mechanism between the charge and spin orders remains elusive. Here, by tuning external pressure, we reveal three charge-ordered phases with suggested correlation to magnetic orders in LuFe₂O₄: (i) a centrosymmetric incommensurate three-dimensional CO with ferrimagnetism, (ii) a non-centrosymmetric incommensurate quasi-two-dimensional CO with ferrimagnetism, and (iii) a centrosymmetric commensurate CO with antiferromagnetism. Experimental in situ single-crystal X-ray diffraction and X-ray magnetic circular dichroism measurements combined with density functional theory calculations suggest that the charge density redistribution caused by pressure-induced compression in the frustrated double-layer [Fe₂O₄] cluster is responsible for the correlated spin-charge phase transitions. The pressure-enhanced effective Coulomb interactions among Fe-Fe bonds drive the frustrated (1/3, 1/3) CO to a less frustrated (1/4, 1/4) CO, which induces the ferrimagnetic to antiferromagnetic transition. Our results not only elucidate the coupling mechanism among charge, spin, and lattice degrees of freedom in LuFe₂O₄, but also provide a new way to tune the spin-charge orders in a highly controlled manner.