Most of the questions are inter-related. Most have been discussed in earlier posts.
How do we tune physical properties (e.g. hysteresis width) by varying chemical composition?
How do we understand two-step transitions? Are they associated with spatially inhomogeneous arrangements of the spin?
Are spin ice phases possible?
What is the physical origin of the intermolecular interactions that lead to a first-order transition?
Is it electronic (magnetic) and/or elastic?
Are there long-range interactions? Are they crucial?
Is there a simple way to understand the change in vibrational spectra (and thus entropy) associated with the transition?
What is the role of spatial anisotropy?
What is the simplest possible effective model Hamiltonian that captures the physical properties above?
Can the elastic degrees of freedom be "integrated out" to give a "simple" Ising model?
How do the model parameters depend on structural and chemical composition?
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