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I am looking for an answer that is just a bit deeper than "because copper has a full 3d shell, thus no unpaired electrons".

Iron has a magnetic moment of 2.2 bohr magnetons per atom. You can explain this by starting with the number of valence electrons in an isolated iron atom (8) and then using Hall voltage measurements that show there is about 1 electron (I think the exact measurement is 0.95) per atom in the conduction band, leaving 7 electrons in the 3d band. Of those 7 electrons, 4.6 electrons per atom have a common spin (let's say up) and 2.4 have opposite (down) spin because of the exchange interaction, which gives 4.6 - 2.4 = 2.2.

I can do the same with Co and Ni, using 0.6 conduction electron per atom for both and allowing 5 electrons to be spin up, since exchange interaction energy gain cannot be compensated by promoting electrons to higher energy levels. That gives 1.6 b.m. per atom for Co and 0.6 b.m. per atom for Ni.

Now, I would like to apply a similar reasoning to explain why copper is not ferromagnetic. Copper has 11 valence electrons, but Hall voltage gives about 1.3 conduction electron per atom, leaving 9.7 electrons in the 3d band. Why doesn't copper end up with 5 electrons with spin up and 4.7 with spin down, thus giving it 0.3 bohr magneton per atom?

Qmechanic
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courno
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2 Answers2

1

Your starting point here seems to be something like the Stoner model of band ferromagnetism. The Stoner criterion involves the dispersion of the band, which is much greater for the Cu 4sp band than for the transition-metal 3d bands.

But that is not the way I think about magnetism in these materials. My background is taking local ionic moments as the starting point. The band model is very inadequate in describing the electron correlations in such narrow bands. That can be done by including the Hubbard U in model calcutions or also in band structure calculation (for example LDA+U).

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Ferromagnetism is not all about the magnetic moment of atoms constituting the solid/material. If that would be the case, then not only would copper be ferromagnetic but a lot of other atoms would, too.

There must be an exchange interaction which allows nearby atom spins to lign up somewhat in a same direction, forming what is known as magnetic domains. Only when one combines a non zero net magnetic moment of atoms with a favorable exchange interaction that one obtains ferromagnetism. The latter is what copper is missing.

untreated_paramediensis_karnik
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