  When the spins on the frustrated pyrochlore lattice obey the celebrated
2-$in$-2-$out$ ice rule, they stay in a correlated disordered phase and break
the third law of thermodynamics. Similarly, if the atomic ions on the
pyrochlore lattice move in and outward of the tetrahedra, they may obey a
constraint resembling the ice rule. We discover that a model for pyrochlore
molybdates $A_2$Mo$_2$O$_7$ ($A=$Y, Dy, Tb) exhibits a "supercooled ice" state
of the displacement degrees of freedom of Mo$^{4+}$ ions, when we take account
of the Jahn-Teller (JT) effect. The JT effect occurs when the lattice
distortions reduce the symmetry of the local crystal field, resulting in the
orbital-energy-splitting that causes the local energy gain. Unlike the standard
JT effect that leads to periodic long range ordering, the displacements of
Mo$^{4+}$ ions are disordered following the ice-like rule. We microscopically
derive a model that describes this situation by having the 2nd and 3rd neighbor
interactions between in-out lattice displacements comparably as strong as the
nearest neighbor interactions of standard ice. There, the well-known nearly
flat energy landscape of the ice state is altered to a metastable highly
quasi-degenerate ice-like liquid state coexisting with a crystalline-like
ground state. Our Monte Carlo simulations show that this liquid remains
remarkably stable down to low temperatures by avoiding the putative first order
transition. The relaxation in the supercooled JT ice state exhibits glassy
dynamics with a plateau structure. They fit the feature of a "good glassformer"
very often found in molecular liquids, but that has never been observed in
material solids. The high glass-forming ability of the interacting lattice
degrees of freedom will play a key role in the spin-glass transition of the
material.
