Origins of\nPolar Crystal Structure and Multiferroicity\nin the Antiferromagnet TbFeWO<sub>6</sub>

Cation-ordered polar (<i>Pna</i>2<sub>1</sub>) materials\nRFeWO<sub>6</sub> (R = rare earth) have gained significant attention\ndue to their multiferroic properties. These materials are derived\nfrom the parent aeschynite-type material CaTa<sub>2</sub>O<sub>6</sub> possessing a centrosymmetric orthorhombic structure (<i>Pnma</i>). The ordering of M<sup>3+</sup> and W<sup>6+</sup> ions in the\noctahedral sites with distinct Wyckoff positions breaks the inversion\nsymmetry of the parent structure. Our investigation of TbFeWO<sub>6</sub> using symmetry-adapted mode analysis, neutron powder diffraction,\nand density functional theory calculations (DFT) has revealed that\nthe ordered polar (<i>Pna2</i><sub>1</sub>) structure can\nemerge from ordered centrosymmetric (<i>Pnam or Pnan</i>) structures through the relaxation of stress. Our low-temperature\nneutron diffraction experiments have provided evidence of a noncollinear\ncommensurate magnetic structure exhibiting polar magnetic symmetry <i>m</i> (magnetic space group: <i>C</i><sub>a</sub><i>c</i>), consistent with the observed additional polarization\nbelow <i>T</i><sub>N</sub>. Based on the spin structure,\nwe propose that the mechanisms of exchange striction and/or inverse\nDzyaloshinskii-Moriya may serve as origins of the multiferroic behavior\nexhibited by these materials.