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The physical properties of crystals are governed by their symmetry accordingto Neumann's principle. However, we present a case that contradicts thisprinciple wherein the polarization is not invariant under its symmetry. We termthis phenomenon as unconventional ferroelectricity in violation of Neumann'sprinciple (UFVNP). Our group theory analysis reveals that 33 symmorphic spacegroups have the potential for UFVNP, with 26 of these symmorphic space groupsbelonging to non-polar groups. Notably, the polarization component in UFVNPmaterials is quantized. Our theory can explain the experimentally provenin-plane polarization of the monolayer {\alpha}-In2Se3, which has C3v symmetry.Additionally, we employ first-principles calculations to demonstrate theexistence of UFVNP in Td phase AgBr, which was not initially anticipated toexhibit polarization. Thus, UFVNP plays an integral role in characterizing andexploring the possible applications of ferroelectrics, significantly expandingthe range of available materials for study.

Unconventional Ferroelectricity in Violation with Neumann's Principle