We present an improved model for studying the interactions between dipole moments of water molecules confined in beryl crystals inspired by recent NMR experiments. Our model is based on a local crystal potential with dihexagonal symmetry for the rotations of water dipole moments, leading to deflection from the $ab$ hexagonal crystallographic plane. This potential shape has significant implications for dipole ordering, which is linked to the nonzero projection of the dipole moment on the hexagonal $c$ axis. To reveal the tendency toward equilibrium-ordered states, we used a variational mean-field approximation, Monte Carlo simulations, and quantum tunneling. Our analysis reveals three types of equilibrium-ordered states: a purely planar dipole order with an antiparallel arrangement in the adjacent $ab$ planes, a configuration with deflected dipole moments ordered in antiparallel directions, and a helical structure of the dipoles twisting along the $c$ axis.

• Received 25 April 2023
• Accepted 14 July 2023

DOI:https://doi.org/10.1103/PhysRevB.108.064101