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Interplay between charge-order, ferroelectricity and ferroelasticity: tungsten bronze structures as a playground for multiferroicity

Large electron-electron Coulomb-interactions in correlated systems can lead to a periodic arrangement of localized electrons, the so called "charge-order". The latter is here proposed as a driving force behind ferroelectricity in iron fluoride K0.6FeF3. By means of density functional theory, we propose different non-centrosymmetric d5/d6 charge-ordering patterns, each giving rise to polarization along different crystallographic axes and with different magnitudes. Accordingly, we introduce the concept of "ferroelectric anistropy" (peculiar to improper ferroelectrics with polarization induced by electronic degrees of freedom), denoting the small energy difference between competing charge-ordered states that might be stabilized upon electrical field-cooling. Moreover, we suggest a novel type of charge-order-induced ferroelasticity: first-principles simulations predict a monoclinic distortion to be driven by a specific charge-ordering pattern, which, in turn, unambiguously determines the direction of ferroelectric polarization. K0.6FeF3 therefore emerges as a prototypical compound, in which the intimately coupled electronic and structural degrees of freedom result in a manifest and peculiar multiferroicity.