Overview
This research utilized large-scale density matrix renormalization group calculations to investigate the quantum phases of dipolar molecules confined within bent (zigzag) endofullerene chains. The study examined the behavior as a function of the chain angle, specifically exploring the range $\gamma 60^\circ$ through $180^\circ$. The findings indicated distinct quantum phases for different molecular species, namely LiF, o-D$_2$O, and p-H$_2$O, and highlighted the role of geometric frustration and next-nearest-neighbor interactions.
Approach
The study employed large-scale density matrix renormalization group (DMRG) calculations. These calculations were applied to model dipolar molecules confined within bent, or zigzag, endofullerene chains. The primary variable investigated was the chain angle, denoted as $\gamma$, across a range from $60^\circ$ to $180^\circ$. This methodical approach allowed for the examination of how the structural configuration of the chain influenced the quantum phases of the confined molecules, specifically LiF, o-D$_2$O, and p-H$_2$O.
Findings
LiF in Zigzag Chains
- For LiF molecules, ferroelectric order was observed to persist across the full range of chain angles investigated, from $60^\circ$ to $180^\circ$.
- The critical effective dipole moment for LiF was found to increase as the chain bent, indicating that parallel alignment becomes less favorable under these conditions.
- Near the equilateral configuration ($\gamma = 60^\circ$), geometric frustration was identified as the driving mechanism for a transition to an antiferroelectric Néel-ordered phase. In this phase, neighboring dipoles exhibit anti-alignment along the chain axis.
- Capturing this reorientation of dipoles specifically required the inclusion of dipolar couplings beyond the nearest-neighbor approximation. Next-nearest-neighbor interactions were found to become equally strong at the $\gamma = 60^\circ$ configuration, emphasizing their significance in understanding this phase transition.
Confined Water Molecules
- When orthodox-D$_2$O (o-D$_2$O) was confined, the system reproduced both the ferroelectric and the antiferroelectric Néel-ordered phases observed with LiF.
- For para-H$_2$O (p-H$_2$O), due to its large rotational constants, no ordered phase developed at any of the investigated chain angles. This absence of order occurred despite the enhanced coordination provided by the bent geometry of the chain.
Why This Matters
The results of this study suggested that engineered endofullerene layers could potentially host a diverse array of dipole-ordered quantum phases. This is because a zigzag chain is considered the narrowest stripe of a two-dimensional lattice. The findings indicate the possibility of observing quantum phases beyond the ferroelectric ordering that has been observed in previous related work, implying a richer landscape of quantum phenomena in such confined systems.