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Magnetic materials

Magnetite Fe₃O₄ has the inverse spinel structure: the A sites (tetrahedral) hold one Fe³⁺, the B sites (octahedral) hold one Fe³⁺ and one Fe²⁺, and the moments on the A and B sites are antiparallel. Taking Fe³⁺ as 5 µB and Fe²⁺ as 4 µB, with only spin contributing, what is the magnetic moment per Fe₃O₄ formula unit?

  1. A0 µB
  2. B4 µB
  3. C14 µB
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Answer: B. 4 µB

The B-site moment is 5 + 4 = 9 µB and the A-site moment is 5 µB, and since they are antiparallel, 9 − 5 = 4 µB remains. You can also think of the Fe³⁺ ions on the A and B sites as exactly canceling each other, leaving only the contribution of Fe²⁺. The value obtained from the measured saturation magnetization is about 4.1 µB, in good agreement with this estimate. 14 µB assumes all the moments are parallel (the mistake of treating it as ferromagnetic), and 0 µB assumes everything cancels (the mistake of treating it as antiferromagnetic). Replacing Fe²⁺ with another divalent ion (such as Ni²⁺ or Mn²⁺) changes the saturation magnetization according to that ion's moment.

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