The Hysteresis Loop Is the Magnet’s Entire Specification
Remanence, coercivity, intrinsic coercivity and energy product — four numbers from one measurement. And a permanent magnet in service never leaves the second quadrant.
Magnets and Motors · Part 2 — The Permanent Magnet · Chapter 3 · 21 min read
Part 2 — The Permanent Magnet
One measurement, four numbers
The shape of the hysteresis loop tells you how strong the magnet is, how hard it is to destroy, and how much energy it can store per unit volume.
Drive a magnetic material around a full cycle of applied field and plot what comes back. Everything a datasheet tells you about a magnet is a feature of that curve.
B_r
How strong
H_cJ
How hard to destroy
(BH)max
Energy per unit volume
~80 %
Of NdFeB’s theoretical ceiling, already reached
3.1 — The full loop, and the one quadrant that matters
A permanent magnet in service never leaves the second quadrant — positive B, negative H — because its own demagnetising field opposes its magnetisation. The other three quadrants exist for magnetising, and for understanding what happens when something goes wrong.
3.2 — The four numbers on every datasheet
- •Remanence, B_r (tesla). The flux density left when the applied field returns to zero. How strong the magnet is. Sets the back-EMF and the torque per amp.
- •Coercivity, H_cB (kA/m). The reverse field that drives B to zero. Often quoted, rarely the number you want.
- •Intrinsic coercivity, H_cJ (kA/m). The reverse field that drives the magnetisation to zero — the field that genuinely destroys the magnet rather than merely cancelling its flux. This is the number that matters for demagnetisation safety, and it is always the larger of the two.
- •Maximum energy product, (BH)max (kJ/m³). The largest value of B × H anywhere on the second-quadrant curve — physically, twice the magnetic energy the magnet can supply to its external circuit per unit volume.
Important
(BH)max is the single best figure of merit because it captures strength and resistance to demagnetisation together. A datasheet quoting only H_cB is not telling you what you need to know.
3.3 — How much headroom is left in NdFeB
(BH)ₕₐₓ = B_r² / 4μ₀
Worked example 3.1 — The theoretical ceiling for Nd₂Fe₁₄B
Saturation B_r = 1.61 T
(1.61)² / (4 × 1.2566×10⁻⁶) = 516 kJ/m³
Commercial N52 reaches 398 to 422 kJ/m³ — about 80 per cent of the theoretical ceiling for this compound.
Why this matters
There is very little headroom left in NdFeB. Any large gain has to come from a different compound, not better processing — which is why the research money goes to MnBi, tetrataenite and cerium substitution rather than to refining what already exists.
3.4 — The load line — why an identical magnet performs differently in two motors
A magnet does not choose its own operating point. Its shape and the magnetic circuit around it do, through the demagnetising field it generates in itself.
A long thin magnet magnetised along its length has weak self-demagnetisation and sits high on the curve, near B_r. A short flat one sits low. The ratio is the permeance coefficient, or load line slope, and it is the reason a magnet quoted at 1.4 T delivers considerably less in an actual airgap.
In plain English
Drag the temperature slider and watch two things happen at different speeds. The whole curve drops as remanence falls at about −0.12 %/°C. But the knee climbs up and to the right much faster, because intrinsic coercivity falls at about −0.6 %/°C.
The knee is what kills magnets, and it moves five times faster than the strength does.
3.5 — Reversible and irreversible loss
Reversible loss is the ordinary weakening of a hot magnet. Cool it down and the strength returns exactly. Nothing has happened.
Irreversible loss occurs when the operating point is driven past the knee. Whole domains flip and do not flip back. Cool the magnet down and it is permanently weaker; the only recovery is to remove it and re-magnetise it in a saturating field, which in a bonded rotor means scrap.
Important
Both conditions are needed at once. A hot magnet at a benign operating point is fine. A cold magnet hit with a large reverse field is fine. A hot magnet hit with a large reverse field — a short-circuit fault at the end of a hill climb — is how rotors are destroyed.
Motor demagnetisation analysis is always run at maximum temperature and maximum fault current simultaneously, never at either alone. Chapter 9 works through that case.
3.6 — Reading a grade code
Two parts. The number is (BH)max in MGOe — multiply by 7.96 for kJ/m³. The letters are the maximum operating temperature, and they are bought by adding heavy rare earths.
3.6.1 — The letters are not free
Each step up the temperature ladder means more dysprosium or terbium substituted for neodymium, which raises coercivity and lowers remanence — heavy rare earths couple antiparallel to iron. You pay in magnet strength, and in the scarcest elements in the crust, for the right to run hot.
Quick check: test yourself
1.A supplier quotes H_cB = 900 kA/m and does not mention H_cJ. Why is that a problem?
Show answer
2.N52 reaches about 80 per cent of NdFeB’s theoretical (BH)max. What follows from that?
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3.Why does a hot magnet sometimes recover fully and sometimes not?
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Chapter summary
- ✓A permanent magnet in service lives entirely in the second quadrant, because its own demagnetising field opposes its magnetisation.
- ✓Four numbers from one measurement: B_r for strength, H_cB, H_cJ for demagnetisation safety, and (BH)max as the best single figure of merit.
- ✓NdFeB is already at roughly 80 per cent of its theoretical ceiling, so further large gains need a different compound.
- ✓Shape and circuit set the operating point through the permeance coefficient — which is why datasheet remanence is not what you get in an airgap.
- ✓Coercivity falls about five times faster with temperature than remanence does, so magnets fail suddenly at a knee rather than fading gradually.
Frequently asked questions
What is the difference between H_cB and H_cJ?+
H_cB, ordinary coercivity, is the reverse field that drives B to zero. H_cJ, intrinsic coercivity, is the reverse field that drives the magnetisation to zero — the field that genuinely destroys the magnet rather than merely cancelling its flux. H_cJ is always the larger of the two and it is the number that matters for demagnetisation safety. A datasheet quoting only H_cB is not telling you what you need.
What is the maximum energy product and why is it the best single figure?+
(BH)max is the largest value of B × H anywhere on the second-quadrant curve, in kJ/m³ — physically, twice the magnetic energy the magnet can supply to its external circuit per unit volume. It is the best single figure of merit because it captures strength and resistance to demagnetisation together. The theoretical ceiling is B_r²/4μ₀, which for NdFeB at saturation gives about 516 kJ/m³; commercial N52 reaches 398 to 422, roughly 80 per cent of the limit. Any large gain must come from a different compound, not better processing.
Why does an identical magnet perform differently in two motors?+
Because a magnet does not choose its own operating point — its shape and the magnetic circuit around it do, through the demagnetising field it generates in itself. A long thin magnet magnetised along its length has weak self-demagnetisation and sits high on the curve near B_r; a short flat one sits low. That ratio is the permeance coefficient, or load line slope, and it is why a magnet quoted at 1.4 T delivers considerably less in a real airgap.
What is the difference between reversible and irreversible loss?+
Reversible loss is the ordinary weakening of a hot magnet — cool it and the strength returns exactly, because nothing has happened. Irreversible loss occurs when the operating point is driven past the knee: whole domains flip and do not flip back, so cooling leaves the magnet permanently weaker. The only recovery is removal and re-magnetisation in a saturating field, which in a bonded rotor means scrap.
What do the letters in a grade code like N42SH mean?+
N is neodymium, 42 is (BH)max in MGOe — multiply by 7.96 for kJ/m³, so 42 becomes 334 — and SH is the maximum operating temperature, 150 °C. The letters are not free: each rung up the temperature ladder means more dysprosium or terbium substituted for neodymium, which raises coercivity and lowers remanence because heavy rare earths couple antiparallel to iron. You pay in magnet strength, and in the scarcest elements in the crust, for the right to run hot.
Reviewed by
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.