Magnetic Dipoles Are Far Too Weak to Explain a Magnet
Treat two iron atoms as classical bar magnets and you predict an ordering temperature of about one kelvin. Iron stays magnetised to 1,043 K. Classical magnetism is wrong by three orders of magnitude.
Magnets and Motors · Part 1 — The Physics of Magnetism · Chapter 2 · 19 min read
Calculate the magnetic force between two neighbouring iron atoms treated as classical bar magnets. It corresponds to an ordering temperature of about one kelvin.
Iron stays magnetised to 1,043 K. Classical magnetism is wrong by three orders of magnitude, and the thing that fixes it is not magnetic at all.
~1 K
Ordering temperature dipoles predict
1,043 K
Where iron actually loses it
3
Elements in the ferromagnetic window
312 °C
Nd₂Fe₁₄B Curie temperature
2.1 — Classical magnetism is wrong by a thousand
The magnetic dipole interaction between neighbouring atoms is real, and it is far too weak to explain a magnet. If it were the only thing holding moments parallel, iron would lose its magnetisation just above absolute zero.
What actually holds them parallel is electrostatic, filtered through quantum mechanics.
2.2 — What actually holds the moments parallel
In plain English
The exchange interaction. Electrons are indistinguishable fermions, so their total wavefunction must be antisymmetric under exchange. If two electrons have parallel spins, the spatial part must be antisymmetric — which forces them apart, lowering their Coulomb repulsion energy.
Parallel spins are therefore cheaper. The energy saved has nothing to do with magnetic forces; it is ordinary electrostatics obeying the Pauli principle.
The size and sign of that saving depend on how far apart the atoms sit relative to how far their d orbitals extend. Too close and antiparallel alignment wins; too far and there is no coupling at all.
2.3 — The Bethe–Slater curve — a very narrow window
Important
Three elements out of ninety-odd land in the window where parallel alignment is favoured at room temperature. The distance between manganese and iron on that axis is about ten per cent — and it is the difference between a magnet and not.
2.4 — Five kinds of magnetic behaviour
- •Ferromagnetic — moments align parallel and net magnetisation survives with no applied field. Fe, Co, Ni, Gd, and that is the complete list of elements at or near room temperature.
- •Ferrimagnetic — two sublattices point opposite ways but with unequal moments, so a net magnetisation remains. All ferrites work this way: magnetite, barium ferrite, the magnet in a loudspeaker.
- •Antiferromagnetic — equal and opposite sublattices, so zero net moment. Cr, Mn, MnO, NiO. Useless as magnets, indispensable in spintronics for pinning a reference layer.
- •Paramagnetic — unpaired moments exist but do not couple; they align only while a field is applied. Aluminium, platinum, oxygen.
- •Diamagnetic — no unpaired electrons at all. An applied field induces opposing currents per Lenz’s law, so the material is faintly repelled. Copper, water, graphite, and every organic molecule you are made of.
2.5 — The Curie temperature
Exchange holds the moments parallel; thermal energy tries to randomise them. The Curie temperature is where thermal energy wins and ferromagnetism vanishes entirely.
It is a property of the exchange strength, so a compound’s T_C is set by what is doing the exchange — not by what carries the moment.
2.5.1 — Gadolinium, briefly
Gadolinium is ferromagnetic — below 19 °C. It would be a room-temperature magnet in Delhi in January and a paramagnet by March. That is the 4f problem in one element: the biggest moments and the weakest exchange, because buried 4f orbitals barely overlap between neighbouring atoms.
2.6 — Nd₂Fe₁₄B as a division of labour
Technical framing
This is the single most important idea in permanent magnets. Iron supplies the exchange — the sublattice that stays ordered to 312 °C. Neodymium supplies the anisotropy — the mechanism that stops the magnetisation from turning, and the subject of chapter 4. Boron supplies neither; it stabilises the tetragonal crystal structure that lets the other two coexist.
No element does two of those jobs well, which is why the magnet is a compound rather than a metal.
Quick check: test yourself
1.Why can’t magnetic forces explain ferromagnetism?
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2.Manganese and iron are neighbours in the periodic table. Why is one a magnet and the other not?
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3.A material has two sublattices pointing opposite ways. Is it useless as a magnet?
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Chapter summary
- ✓Ferromagnetism is not a magnetic effect. It is the Pauli principle applied to Coulomb repulsion — parallel spins are electrostatically cheaper.
- ✓The Bethe–Slater window is narrow enough that only iron, cobalt and nickel land in it at room temperature.
- ✓Five behaviours: ferro, ferri, antiferro, para and dia. Only the first two make useful magnets, and all ferrites are the second.
- ✓Curie temperature measures exchange strength, so it is set by what does the exchange rather than by what carries the moment.
- ✓Nd₂Fe₁₄B is a division of labour: iron holds the order, neodymium holds the direction, boron holds the structure.
Frequently asked questions
Why is ferromagnetism not a magnetic effect?+
Because the magnetic dipole interaction between neighbouring atoms is far too weak — it corresponds to an ordering temperature around one kelvin, while iron stays magnetised to 1,043 K. What actually holds the moments parallel is the exchange interaction, which is electrostatic. Electrons are indistinguishable fermions, so parallel spins force the spatial wavefunction to be antisymmetric, which keeps the electrons apart and lowers their Coulomb repulsion energy. Parallel alignment is cheaper for reasons that have nothing to do with magnetic forces.
What does the Bethe–Slater curve show?+
The exchange integral plotted against the ratio of interatomic spacing to 3d orbital radius. Too close and antiparallel alignment wins; too far and there is no coupling at all. There is a narrow window where parallel alignment is favoured, and iron, cobalt and nickel are the only elements that land in it at room temperature. The distance between manganese and iron on that axis is about ten per cent — the difference between a magnet and not.
What are the five kinds of magnetic behaviour?+
Ferromagnetic — moments align parallel and survive with no applied field (Fe, Co, Ni, Gd, and that is the complete elemental list near room temperature). Ferrimagnetic — two sublattices point opposite ways with unequal moments, so a net magnetisation remains; all ferrites work this way. Antiferromagnetic — equal and opposite sublattices giving zero net moment (Cr, Mn, MnO, NiO). Paramagnetic — unpaired moments that do not couple and align only while a field is applied. Diamagnetic — no unpaired electrons, so an applied field induces opposing currents and the material is faintly repelled.
Why is Nd₂Fe₁₄B a compound rather than a metal?+
Because no element does two of the required jobs well. Iron supplies the exchange — the sublattice that stays ordered to 312 °C. Neodymium supplies the anisotropy — the mechanism that stops the magnetisation turning. Boron supplies neither; it stabilises the tetragonal crystal structure that lets the other two coexist. That division of labour is the single most important idea in permanent magnets.
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Magnets and Motors is an original educational series on permanent magnets and electric machines. Datasheet ranges, temperature coefficients and efficiency figures are representative standard-condition literature values, not measurements of a specific product, and sources differ on several. Always verify against the specific magnet and lamination datasheets in use before making design, procurement or certification decisions.