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Briefly: recall the tiny 'magnetostriction' effect I mentioned earlier.
Well, this is how the energy of the crystal changes when you apply a
C44 elastic distortion (pull opposite corners of the cube) to both
NiO and MnO. If you distort the ferromagnetic crystal, the cubic cell is
stable. If you distort the AF2 antiferromagnetic solution, the cube is not
stable and the minimum lies at some non-cubic angle [PICTURE]. This is because
same-spin electrons tend to stay out of each others way; they tend to repel
each other (Pauli repulsion). In NiO the same-spin nickel ions in the [111]
planes kind of push each other apart and we get this distortion, which converts
to an angle of 90.12 degrees (experiment 90.15 degrees). In MnO there are five
majority spin electrons and no minority spin electrons, so the Pauli repulsion
is greater. You get a bigger rhombohedral distortion. Expt. 90.6 degrees,
calculated 90.5. So it looks like we have found something which is a reasonable
approximation to the ground state of these Mott insulator crystals, even with
something as simple as Hartree-Fock.
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