Structure–property relationships are identified and applied to explain multi-step transitions and the different antiferroelastic patterns found in spin crossover frameworks.

Spin crossover materials contain metal ions that can access two spin-states: one low-spin (LS), the other high-spin (HS). We propose that frustrated elastic interactions can give rise to spin-state ices -phases of matter without long-range order, characterized by a local constraint or 'ice rule'. The low-energy physics of spin-state ices is described by an emergent divergence-less gauge field with a gap to topological excitations that are deconfined quasi-particles with spin fractionalized midway between the spins of the LS and HS states. FIG. S2. Snapshot of the full lattice from which Fig. 4b is taken.

Spin-crossover (SCO) materials display many fascinating behaviors including collective phase transitions and spin-state switching controlled by external stimuli, e.g., light and electrical currents. As single-molecule switches, they have been fêted for numerous practical applications, but these remain largely unrealized–partly because of the difficulty of switching these materials at high temperatures. We introduce a semiempirical microscopic model of SCO materials combining crystal field theory with elastic intermolecular interactions. For realistic parameters, this model reproduces the key experimental results including thermally induced phase transitions, light-induced spin-state trapping (LIESST), and reverse-LIESST. Notably, we reproduce and explain the experimentally observed relationship between the critical temperature of the thermal transition, T 1/2, and the highest temperature for which the trapped state is stable, T LIESST, and explain why increasing the stiffness of the coordination sphere increases T LIESST. We propose strategies to design SCO materials with higher T LIESST: optimizing the spin–orbit coupling via heavier atoms (particularly in the inner coordination sphere) and minimizing the enthalpy difference between the high-spin (HS) and low-spin (LS) states. However, the most dramatic increases arise from increasing the cooperativity of the spin-state transition by increasing the rigidity of the crystal. Increased crystal rigidity can also stabilize the HS state to low temperatures on thermal cycling yet leave the LS state stable at high temperatures following, for example, reverse-LIESST. We show that such highly cooperative systems offer a realistic route to robust room-temperature switching, demonstrate this in silico, and discuss material design rationale to realize this.

S1. Synthesis and characterisation S2. Thermogravimetric analysis (TGA) S3. Differential scanning calorimetry (DSC) S4. Powder X-ray diffraction S5. Single crystal X-ray diffraction S6. Magnetic susceptibility S7. Elastic model S8. References S2 S1. Synthesis and characterisation General ProceduresAll materials were available commercially and used as received (iron(II) perchlorate was handled carefully and in small amounts to avoid any potential explosions). Metal cyanides are toxic and should be used with care and in small amounts.

Spin crossover molecules have two accessible states: high spin (HS) and low spin (LS). We show that, on the pyrochlore lattice, elastic interactions between SCO molecules can give rise to three spinstate ice phases. Each is a "Coulomb phase" where a local ice-rule can be mapped to a divergence free gauge field and the low energy excitations carry a spin fractionalized midway between the LS and HS states. The unique nature of spin crossover materials allows temperature to change the ice rules allowing straightforward access to Coulomb phases not yet observed in water or spin ices.