Anisotropic Phonons Reveal Hidden One-Dimensional Order in Ice Ih

Water ice exhibits a remarkable interplay between covalent and hydrogen bonds, producing a long-range oxygen lattice that hosts a disordered yet correlated hydrogen network. Using large four-dimensional single-crystal neutron scattering datasets, we identify one-dimensional strings of partial order within this disordered hydrogen network. Anisotropic librational phonons separate into soft and hard branches with a crossover near 68 meV, revealing coherent hydrogen motion along zigzag and armchair chains. A data-driven six-parameter harmonic model quantitatively reproduces the phonon spectrum and diffuse scattering, while Monte Carlo simulations show that nearest-neighbor intermolecular interactions, rather than dipole forces, drive the observed ordering. This mechanism connects the disordered ice Ih phase to the ferroelectric ice XI ground state. Our results reveal that hidden one-dimensional order governs the lattice dynamics of ice and establish a quantitative, data-driven framework for understanding proton ordering in hydrogen-bonded materials, with broader implications for non-periodic systems exhibiting local symmetry.