When does irreversible demagnetization occur?

When the field inside the magnet is driven in reverse beyond the knee of the demagnetization curve. The classic case is an NdFeB magnet whose coercivity has dropped at high temperature, hit by the opposing MMF of a short-circuit or field-weakening current.

How much does NdFeB coercivity fall with temperature?

Its temperature coefficient is roughly −0.5 to −0.6 %/K. In the worked example, a magnet with 1600 kA/m at 20 °C drops, in a linear approximation, to about 896 kA/m at 100 °C and about 456 kA/m at 150 °C. Ferrite magnets are the opposite: their coercivity falls as temperature drops, so cold is the dangerous side.

How is demagnetization assessed with FEM?

Solve the field at the worst temperature and current (short circuit or maximum field weakening), compare each magnet element's field with the demagnetization curve for that temperature, re-solve with reduced remanence in elements that passed the knee, and judge by the percentage drop in back-EMF or torque.

Irreversible Demagnetization Analysis for Permanent Magnet Motors

Category: Electromagnetic Field Analysis | Revised 2026-09-28

Permanent magnet demagnetization analysis showing B-H curve knee point and temperature-dependent coercivity

Demagnetization Analysis for Permanent Magnet Motors — B-H Curve Knee Point Determination and Temperature Dependency Evaluation

Theory: where a magnet “breaks”

Overview

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In a motor test, a short circuit at high temperature dropped the back-EMF by 3% and it never came back. Don't magnets recover when they cool down?

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There are two kinds of loss. A reversible drop disappears when the temperature returns; an irreversible one does not. The irreversible kind happens when the field inside the magnet is driven hard enough in reverse to pass the knee of the demagnetization curve. Past that point the magnetization in that region is no longer aligned, and cooling does not restore the original remanence. Unless the magnet is re-magnetized, the motor stays weaker.

The demagnetization curve (second quadrant)

$$ B = \mu_0 H + J, \qquad B \approx B_r + \mu_0 \mu_{rec} H \quad (\text{above the knee}) $$

Symbol	Meaning	Typical sintered NdFeB
$B_r$	Remanence	1.2–1.4 T
$H_{cB}$	Coercivity where B = 0	About 900–1000 kA/m
$H_{cJ}$	Intrinsic coercivity (J = 0)	About 1000–2500 kA/m depending on grade
$\mu_{rec}$	Recoil relative permeability (slope of the linear part)	About 1.05

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The curve that matters is the intrinsic one, $J$. The knee is where $J$ starts to drop sharply; in practice the field $H_k$ at which $J$ falls to 90% of $B_r$ is often used as its marker. Looking only at the $B$ curve can be misleading, because its knee may lie in the third quadrant and look safe.

Temperature coefficients

$$ B_r(T) = B_{r,20}\left[1 + \alpha\,(T-20)\right], \qquad H_{cJ}(T) = H_{cJ,20}\left[1 + \beta\,(T-20)\right] $$

Magnet	Remanence coefficient α	Coercivity coefficient β	Critical condition
Sintered NdFeB	About −0.12 %/K	About −0.5 to −0.6 %/K	High temperature
Ferrite	About −0.2 %/K	About +0.2 to +0.4 %/K	Low temperature

For NdFeB with $B_r = 1.25$ T and $H_{cJ} = 1600$ kA/m at 20 °C, a linear estimate gives $B_r \approx 1.13$ T and $H_{cJ} \approx 896$ kA/m at 100 °C, and $B_r \approx 1.06$ T and $H_{cJ} \approx 456$ kA/m at 150 °C. Coercivity falls much faster than remanence. Ferrite is the reverse: a grade with 300 kA/m at 20 °C drops to about 246 kA/m at −40 °C.

Coffee Break Trivia

How a rare-earth price spike changed magnets

NdFeB magnets for high-temperature use have long relied on heavy rare earths such as dysprosium (Dy) to raise coercivity. When rare-earth prices spiked in 2010–2011, cutting heavy rare earths became a major challenge for the motor industry. The answer that spread was grain-boundary diffusion, which diffuses heavy rare earths from the magnet surface along the grain boundaries. Raising coercivity only near the surface, where demagnetization starts, greatly reduces the amount needed. For analysts it made demagnetization modelling harder, because coercivity is no longer uniform inside the magnet.

Worked example: operating point and reverse field in a short circuit

Operating point from a magnetic circuit

Take a simple circuit with a magnet of thickness $l_m$ in series with an air gap $g$ (iron reluctance and leakage ignored, equal areas). With an opposing armature MMF $F_a$, the field inside the magnet is:

$$ H_m\,l_m + \frac{B_m}{\mu_0}\,g = -F_a \;\;\Rightarrow\;\; H_m = -\frac{F_a + B_r g/\mu_0}{l_m + \mu_{rec}\, g} $$

With $l_m = 4$ mm, $g = 1$ mm (permeance coefficient $P_c = l_m/g = 4$), $\mu_{rec} = 1.05$ and a short-circuit opposing MMF of $F_a = 2000$ A:

Temperature	No-load $H_m$	Short-circuit $H_m$	$H_{cJ}$ (linear)	Verdict
20 ℃	−197 kA/m	−593 kA/m	1600 kA/m	Ample margin
100 ℃	−178 kA/m	−574 kA/m	896 kA/m	Margin of about 1.4×
150 ℃	−166 kA/m	−562 kA/m	456 kA/m	Irreversible demagnetization

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The reverse field barely changes with temperature, but the limit it has to stay under drops to less than a third.

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Exactly. And $H_k$ is smaller than $H_{cJ}$, so the real margin is even less. Also note how the permeance coefficient works: a thicker magnet or smaller gap moves the no-load point to the safe side, but the short-circuit $H_m$ is governed mainly by $F_a/l_m$. Against current-driven demagnetization, magnet thickness is what counts.

Choosing the worst case

Temperature: maximum magnet temperature for NdFeB, minimum for ferrite. Magnets usually run cooler than the windings, but eddy-current loss can create local hot spots, so use thermal-analysis results.
Current: the transient peak of a three-phase short circuit (near the first cycle), inverter-fault currents and the largest negative d-axis current used in field weakening. Steady-state maximum current alone is not enough.
Rotor position: the position with the strongest reverse field depends on the case, so evaluate over a full electrical period.

Demagnetization assessment with FEM

Procedure

Enter the demagnetization curves at each temperature (manufacturer data) as the magnet material — the full curves including the knee, not a straight-line approximation.
Compute back-EMF and torque in the undemagnetized state as the reference.
Run a transient analysis at the worst current and temperature and check, element by element, whether the field along the magnetization direction passed the knee.
Replace the elements that passed the knee with a model whose remanence is reduced so that they follow the recoil line from that point.
Recalculate under normal operating conditions and judge by the percentage drop in back-EMF or torque. The acceptable value comes from the product requirements.

The main electromagnetic packages provide magnet models with temperature-dependent demagnetization curves and recoil behaviour. Feature names and settings differ by tool and version, so check the manual.

Mesh and magnet segmentation

Demagnetization starts at the magnet corners, especially the leading and trailing edges on the stator side. Refine the mesh near the corners.
Judging by the average field over a whole magnet misses local demagnetization at the corners. Judge element by element.
If the magnets are segmented axially or circumferentially (to cut eddy losses), each segment may run at a different temperature. Ideally, map the temperature field from the thermal analysis.

Coffee Break Trivia

IPM bridges and demagnetization

In IPM motors, thin iron “bridges” surround the magnet pockets. They are meant to saturate and limit leakage flux, but the degree of saturation changes how the reverse field is distributed in the magnet. There are cases where a design change that thinned the bridges to gain output concentrated the reverse field at the magnet corners and made demagnetization easier. A dimension chosen for mechanical strength turns out to matter electromagnetically too.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Modelling the magnet with a straight-line B-H only	No knee, so demagnetization never appears	Use curves including the knee at each temperature
Locating the knee on the B curve	Danger is missed	Use the intrinsic (J) curve and $H_k$
Checking only steady-state maximum current	The short-circuit transient peak is missed	Run a three-phase short-circuit transient
Checking ferrite at high temperature	The cold-side risk is missed	Check at the minimum operating temperature
Judging on the average magnet field	Local corner demagnetization is missed	Judge per element and refine the corners

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I'd like to try the magnetic-circuit calculation myself.

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With the magnetic circuit and reluctance simulator you can vary the gap and magnet thickness and watch the operating point move. Compare demagnetization curves by material with the magnetic materials B-H curve simulator and explore magnet–gap relations with the neodymium magnet air-gap simulator. For the overall motor design flow see the PMSM motor design calculator and the article on PMSM design.

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