Collaborators and I just posted a preprint.

Hidden Devil's staircase in a two-dimensional elastic model of spin crossover materials Gian Ruzzi, Jace Cruddas, Ross H. McKenzie, Ben J. Powell

Condensed matter physicists study diverse states of matter (crystals, antiferromagnets, liquid crystals, superfluids, …), the types of ordering and symmetry associated with each state, and the transitions that can occur between different states when external parameters such as temperature and magnetic field are varied. A challenge for theorists is to create simple models that can describe the orderings in broad classes of materials, taking into account properties at the microscopic (atomic) level. Spin-crossover materials are a broad class of materials that are chemically and structurally complex: composed of transition metal ions surrounded by large molecules. The quantum spin (magnetic) state of the metal ion can change as the temperature is varied, leading to changes in magnetism, colour, and structure. A diversity of spatially periodic orderings of the spin states has been observed and transitions between these ordered states can be smooth, or discontinuous with hysteresis. Chemists love these materials because of their chemical and structural complexity and their potential technological applications, including as switchable magnetic memories.

We present a general procedure to derive a simple lattice Hamiltonian that can describe the diversity of spin-state orderings and transitions, based on physically realistic microscopic interactions. We show that two classes of models that have been considered previously, Ising models and ball-and-spring elastic models are equivalent. Furthermore, our work shows that the Ising interactions arise from elastic interactions, whereas previously the Ising interactions were just treated as empirical parameters with no clear physical origin. These interactions compete with one another (they are frustrated). At zero temperature there appears to be an infinite number of possible spin-state orderings and transitions between them are described by a Devil’s staircase. At finite temperature, some of this structure is washed out, but there are first-order transitions between some of these ordered states. This complexity is similar to that found in spin-crossover materials, and here is produced by a theoretical model with just a single elastic parameter, the ratio of the bulk and shear moduli.

The physical insight and methodology advances in our work provide a foundation for more detailed microscopic descriptions (such as using electronic structure methods) and the establishment of structure-property relations that may guide the development of new materials tailored for specific technological applications.

This supersedes an earlier preprint. (Aside: given the new paper is so different we thought this should be a new submission to the arxiv, but they did not agree).

We got so much helpful feedback on that work that we did more calculations and discovered the hidden Devil's staircase.

We welcome any comments.