conventional displacive-type ferroelectricity in a 3D space, e.g., relative shifts of the transition-metal cation or lone-pair ions, geometric ferroelectricity does not require strong hybridization between the transition-metal and oxygen ions. [7][8][9][10] This removes the constraint of d 0 -ness of the transition-metal ion, thereby allowing magnetism to coexist with ferroelectricity. In addition, while the soft-phonon mode at the Brillouin zone-center manifests displacive ferroelectricity, [11,12] the collective distortion of the 2D network results in zone-boundary soft-phonon modes for geometric ferroelectrics. [3] What about in 1D networks? Spatial inversion symmetry breaking can be intuitively envisioned in 1D chain networks as well, especially with an MO 4 tetrahedral unit. An MO 4 tetrahedron has one of the lowest symmetries among the MO x polyhedra and can form corner-shared 1D chains within crystals (Table 1). More interestingly, a collective distortion of the 1D network can introduce an unconventional polar state resulting from both the displacement of ions and the rotation of the tetrahedra.Ferroelectricity occurs in crystals with broken spatial inversion symmetry. In conventional perovskite oxides, concerted ionic displacements within a 3D network of transition-metal-oxygen polyhedra (MO x ) manifest spontaneous polarization. Meanwhile, some 2D networks of MO x foster geometric ferroelectricity with magnetism, owing to the distortion of the polyhedra. Because of the fundamentally different mechanism of ferroelectricity in a 2D network, one can further challenge an uncharted mechanism of ferroelectricity in a 1D channel of MO x and estimate its feasibility. Here, ferroelectricity and coupled ferromagnetism in a 1D FeO 4 tetrahedral chain network of a brownmillerite SrFeO 2.5 epitaxial thin film are presented. The result provides a new paradigm for designing low-dimensional MO x networks, which is expected to benefit the realization of macroscopic ferro-ordering materials including ferroelectric ferromagnets.
Multiferroic MaterialsComplex transition-metal oxides can be analytically viewed as a network of transition-metal-oxygen polyhedra (MO x ) ( Table 1). A collective distortion of such networks in a (quasi) 2D space can lead to inversion symmetry breaking and geometric ferroelectricity through trilinear coupling among distortions and electric polarization. [1][2][3][4][5][6] In comparison with the