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There are at least three different mechanisms which can give rise to ferromagnetic order in iron.

  1. First is due to the band electrons called band magnetism or itinerant magnetism which is an exchange interaction between conduction electrons.

The page 91 of Fundamentals of Many-body physics by W. Nolting, page 251 (sidenote 1) of Oxford Solid State Basics by Steven H. Simons tells that Fe is itinerant.

  1. Second is indirect exchange i.e. exchange between unpaired d electrons and conduction electrons.

  2. The third is the direct exchange between localized magnetic moments of two neighbouring Fe ions as described by the Heisenberg model.

Which one of them is responsible for ferromagnetism in iron (and also cobalt and nickel) and why? I expect that the third effect would be least because d orbitals are inner orbitals and do not have much overlap.

I read this, this, this and the question titled "What is the difference between a localized and itinerant magnetism?". None seem to address my concern.

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For ferromagnetic materials like iron the cause of alignment of the individual atomic magnetic moments is the direct exchange interaction, that is number 3.

Fe is definitely not an itinerant magnet. The electrons responsible for the magnetism are localised. The magnetic transition is an order-disorder transition. In itinerant magnets delivalised electrons are responsible and the transition is a phase transition. No magnetism persists above the transition temperature.

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  • $\begingroup$ I agree. One can also Google for titles like "Stoner I or Hubbard U". The reason for abandoning the itinerant explanation for iron etc is that the local moments persist above the Curie temperature. $\endgroup$ – Pieter May 13 at 11:45
  • $\begingroup$ @my2cats All the interactions I have written are different types of exchange interactions. Look at the book Oxford Solid State Basics by Steven H. Simon which clearly says "Most of the ferromagnets that we are familiar with, such as iron, are itinerant." Page 251. $\endgroup$ – mithusengupta123 May 14 at 6:06
  • $\begingroup$ @Pieter See my comment above. I cite a counter reference. This creates confusion because it does not explain why. $\endgroup$ – mithusengupta123 May 14 at 6:07
  • $\begingroup$ Please see the references I have newly added. You say, " The electrons responsible for the magnetism are localised. ". In this context, see section 17.7 "Itinerant magnetism" in the book Solid State Physics by Grosso and Parravicini where they say "the localized spin picture may become inadequate for transition metals with unfilled d bands, where the electrons participating in the magnetic state are itinerant." $\endgroup$ – mithusengupta123 May 14 at 14:04
  • $\begingroup$ Hey, I have been quite intrigued by the question and after reading many papers, it seems that the conclusion is that Fe's ferromagnetism is definitely due to itinerant electrons. See for example annualreviews.org/doi/pdf/10.1146/annurev.ms.14.080184.000245. $\endgroup$ – thermomagnetic condensed boson Jun 19 at 20:01
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Normally, it is 1. This is when the unpaired outer valence electrons of neighboring atoms overlap and the distribution of their electric charge in space are farther apart when they have parallel spins. This reduces the electrostatic energy so when they have parallel spin, it is more stable.

Normally this is very short ranged, called intra-atomic (electrons in the same atom) exchange or direct exchange between neighboring atoms.

But iron has a characteristic, it is able to create something called magnetic domains. Though the spins are aligned inside the domains, the domains themselves cancel out each other and the whole peace of iron will not be magnetic.

Now this is when longer ranged interactions can occur via intermediary atoms, called superexchange, or indirect exchange, that is 2 and 3.

Please see here:

https://arxiv.org/ftp/cond-mat/papers/0701/0701423.pdf

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    $\begingroup$ This answer contains some inaccuracies. It states that Fe has itinerant ferromagnetism but then describes direct exchange. The paper it referred to us about Anderson superexchange which is relevant mainly to oxides. This mechanism is different from the three listed by the OP. $\endgroup$ – my2cts May 13 at 5:51

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