  Spin crossover (SCO) materials are reversible molecular switches found in a
wide range of transition metal complexes and metal organic frameworks (MOFs).
They exhibit diverse spin state orderings and transitions between them. We
present an exact mapping from an elastic lattice mismatch model to a long-range
Ising model, with an inverse square decay of the interaction strengths at large
distances (on the square lattice). This provides a microscopic justification
for an Ising model description, which has previously only been justified on
phenomenological grounds. Elastic frustration is required for non-zero Ising
interactions, but whether or not the short-range interactions in the Ising
model are geometrically frustrated depends on the ratio of the bulk and shear
moduli or equivalently Poisson's ratio. We show that, for a simple square
lattice model with realistic parameters, sweeping the enthalpy difference
between the two spin-states at zero temperature leads to a large (probably
infinite) number of spin-state orderings and corresponding steps in the
fraction of high-spin ions, consistent with a Devil's staircase. The staircase
can also be climbed by varying the temperature, but then some of the steps are
hidden and only a finite number remain, consistent with experiments on relevant
framework materials, such as {(Fe[Hg(SCN)$_3$]$_2$(4,4'-bipy)$_2$)}$_n$. Our
results are also relevant to other binary systems with lattice mismatch, e.g.,
heterogeneous solids.
