Triangular lattice structure orientational ordering

Figure 3. Mean-field phase diagram for the orientational ordering quantum 7=1 point quadrupoles in three dimensions on a triangular lattice with an axially symmetric out-of-plane crystal field (2.1) -I- (2.3) V = Vc/Fo denotes the reduced crystal field and T — TITq the reduced temperature, where Fq is the nearest-neighbor quadtupolar coupling constant (2.2). Dashed (solid) lines represent first (second)-order transitions, the dot (Tri) in the inset marks a tricritical point, para denotes the pararotational (orientationally disordered) phase, and the structures of the ordered phases are shown schematically in Fig. 4. (Adapted from Fig. 2 of Ref. 141.)...

For large negative crystal field at low temperatures the stable stmcture is the ideal two-sublattice in-plane herringbone phase—that is, the 2-in phase in Fig. 4a. The two sublattices which can be oriented in three different ways relative to the triangular lattice lead to six equivalent ground states. The excitation spectrum of this phase in general has a gap. In this phase the molecular wave functions are localized in the substrate plane, and classically the molecular axes are parallel to the surface see Appendix A of Ref. 141 for an interpretation of the order parameters. Thus, the orientational degeneracy of the pararotational phase is broken by the quadrupolar interactions. A closely related structure was already proposed based on atomistic Lennard-... 

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