Orientational ordering of water molecules confined in beryl: A theoretical study

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 non-zero 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 planes, a configuration with deflected dipole moments ordered in antiparallel directions, and a helical structure of the dipoles twisting along the $c$ axis.