Every sintered NdFeB magnet loses performance as it heats up. For a motor designer, the question is never whether that happens—it’s how much, how fast, and whether the loss comes back when the machine cools down. Two coefficients answer those questions: α, the temperature coefficient of remanence (Br), and β, the temperature coefficient of intrinsic coercivity (Hcj).
Get these two numbers right and you can predict flux weakening, size your load line, and choose a grade that survives a locked-rotor event. Get them wrong and you ship motors that demagnetize in the field. This article explains what α and β physically represent, why β is the one that keeps engineers up at night, and how to move from a datasheet value to a defensible grade choice.
What Are the Temperature Coefficients α and β?
Both coefficients express a reversible fractional change in a magnetic property per degree Celsius, over a defined temperature span. “Reversible” is the operative word: as long as the magnet is not driven past the knee of its demagnetization curve, the property recovers fully when the magnet returns to its original temperature.
They are defined against a reference temperature (usually 20 °C or 23 °C) as follows:
- α (Br) = [Br(T₂) − Br(T₁)] / [Br(T₁) × (T₂ − T₁)] × 100%
- β (Hcj) = [Hcj(T₂) − Hcj(T₁)] / [Hcj(T₁) × (T₂ − T₁)] × 100%
Both are negative for NdFeB, and both are quoted in % per °C. A grade with α = −0.12 %/°C loses 0.12% of its remanence for every degree of temperature rise.
α — Reversible Temperature Coefficient of Remanence (Br)
α governs the usable flux the magnet delivers. It traces back to the Nd₂Fe₁₄B phase’s saturation magnetization, which declines gradually toward the Curie temperature (Tc ≈ 310–340 °C). Because Tc sits far above any motor’s operating range, α is comparatively mild and stays close to −0.11 to −0.12 %/°C across almost all commercial grades.
In practical terms, α tells you how much your air-gap flux density—and therefore your back-EMF constant and torque constant—will droop when the motor runs hot. It is a performance parameter.
β — Reversible Temperature Coefficient of Coercivity (Hcj)
β governs the magnet’s resistance to demagnetization. It traces back to the magnetocrystalline anisotropy field, which collapses far faster with temperature than saturation magnetization does. That makes β several times larger in magnitude than α—typically −0.45 to −0.65 %/°C depending on grade.
β is not a performance parameter; it is a survival parameter. As Hcj falls, the knee of the second-quadrant demagnetization curve marches upward toward—and eventually past—your operating point. β tells you how quickly that safety margin evaporates.
Why β Matters More Than α
β matters more than α because coercivity falls roughly four to six times faster than remanence as temperature rises, and it is coercivity—not remanence—that determines whether a magnet demagnetizes irreversibly.
A motor can tolerate a gradual drop in torque constant from a declining Br. What it cannot tolerate is the knee of the B–H curve rising above the load line during a transient event—an overload, a phase-to-phase short, or a locked rotor. When that happens, part of the magnet is pushed into irreversible demagnetization and the loss does not recover on cooling.
Because β is the larger coefficient, high temperature is far more dangerous to a magnet’s coercivity than to its flux. A grade can still have healthy remanence at 150 °C while its coercivity has collapsed to the point where ordinary armature reaction demagnetizes it. This is precisely why grade selection for hot motors is driven by Hcj, not Br.
Typical α and β Values by NdFeB Grade Family
The table below gives representative reversible coefficients and indicative maximum operating temperatures for common sintered NdFeB grade families. Note the pattern: α is nearly flat across the range, while β improves markedly as coercivity climbs.
| Grade suffix | Typical α (Br), %/°C | Typical β (Hcj), %/°C | Indicative max operating temp* |
|---|---|---|---|
| N (standard) | −0.12 | −0.60 | ≤ 80 °C |
| M | −0.12 | −0.58 | ≤ 100 °C |
| H | −0.12 | −0.55 | ≤ 120 °C |
| SH | −0.11 | −0.52 | ≤ 150 °C |
| UH | −0.11 | −0.50 | ≤ 180 °C |
| EH | −0.11 | −0.45 | ≤ 200 °C |
| AH | −0.10 | −0.45 | ≤ 230 °C |
*Maximum operating temperature is not a fixed material constant. It depends on the magnet’s permeance coefficient (Pc) in the actual magnetic circuit. A thick magnet on a high load line tolerates more heat than a thin one; the values above assume a typical, well-designed circuit and should be confirmed against your own operating-point analysis.
The key takeaway for grade selection: when you step up from N to SH to EH, you are buying coercivity headroom (a less-negative β and a higher room-temperature Hcj), usually at the cost of a modest reduction in achievable Br.
A Worked Example: What Happens to N42 at 150 °C
Coefficients are abstract until you run the numbers. Take a standard N42 magnet with Br ≈ 1.29 T and Hcj ≈ 955 kA/m (≈ 12 kOe) at 20 °C, and apply α = −0.12 %/°C and β = −0.60 %/°C:
| Temperature | ΔT from 20 °C | Br (T) | Hcj (kA/m) |
|---|---|---|---|
| 20 °C | 0 | 1.29 | 955 |
| 60 °C | 40 | 1.23 | 726 |
| 100 °C | 80 | 1.17 | 497 |
| 150 °C | 130 | 1.09 | 210 |
At 150 °C the remanence has dropped about 16%—noticeable, but manageable. The intrinsic coercivity, however, has fallen roughly 78%, to around a fifth of its room-temperature value. At that point even routine armature reaction can drive the magnet past its knee. This single comparison explains why standard N grades are confined to cool applications and why traction, pump, and industrial-drive motors reach for SH, UH, or EH material.
Two caveats on the arithmetic. First, this first-order linear model slightly overstates the loss at large ΔT; real curves are mildly nonlinear, so always cross-check against grade-specific demagnetization curves at temperature. Second, the numbers above are reversible losses—they assume the operating point stays above the knee. Cross the knee and you add irreversible loss on top.
Reversible vs. Irreversible Losses
α and β describe only the first of three loss categories a motor designer needs to keep straight:
- Reversible loss — governed by α and β. The magnet weakens with heat and fully recovers on cooling. This is the loss you design around with your load line.
- Irreversible but recoverable loss — occurs when the operating point crosses the knee of the demag curve (from heat, an external field, or both). The magnet does not recover on cooling, but it can be restored by re-magnetizing to saturation. In an assembled rotor, re-magnetizing is rarely practical, so treat this as a failure.
- Irreversible and unrecoverable loss — structural or metallurgical damage, such as oxidation or thermal degradation above the material’s limit. Not recoverable by any means.
Good design keeps the magnet firmly in the first category across the entire duty cycle, including worst-case transient events, with margin to spare.
From Coefficients to Grade Selection
Turning α and β into a grade decision comes down to a few disciplined steps:
- Define the hot-spot temperature, not the ambient. Use the magnet’s peak temperature under worst-case duty—including self-heating and thermal soak—rather than nameplate ambient.
- Establish the load line (Pc). The permeance coefficient sets where the operating point sits on the demag curve. A higher Pc pushes the point away from the knee and buys temperature headroom.
- Check Hcj at temperature against the knee. Use β and grade-specific curves to confirm the knee stays below the operating point, with margin for transient demagnetizing fields (short circuit, overload, locked rotor).
- Choose the lowest-cost grade that clears the margin. Over-specifying coercivity wastes remanence and money; under-specifying risks field failures. The right grade is the one that clears your worst case with a sensible safety factor.
For high-temperature designs, achieving the necessary Hcj without leaning heavily on scarce, price-volatile heavy rare earths (Dy, Tb) is where modern grade engineering pays off. Grain boundary diffusion (GBD) and optimized microstructures let manufacturers deliver SH- and UH-class coercivity with far less heavy rare earth than legacy alloys required. XHMAG’s Dy/Tb-free NdFeB grades are built around exactly this priority—giving motor designers the coercivity headroom they need while keeping supply and cost predictable, and shipping under standard export procedure in 25–30 days without dual-use permits.
Design Checklist for Motor Engineers
- Work from the magnet hot-spot temperature, not ambient.
- Use β and demagnetization curves at temperature—never a single room-temperature Hcj—to check the knee.
- Reserve margin for transient demagnetizing events, not just steady-state operation.
- Remember that max operating temperature depends on your load line (Pc), not on the grade alone.
- Select for Hcj headroom first, then confirm Br meets your flux target.
- Prefer grades that reach your coercivity target with minimal heavy rare earth for cost and supply stability.
Frequently Asked Questions
What is the difference between α and β for NdFeB magnets? α is the reversible temperature coefficient of remanence (Br) and governs how much usable flux the magnet loses with heat. β is the reversible temperature coefficient of intrinsic coercivity (Hcj) and governs how much demagnetization resistance the magnet loses. β is several times larger in magnitude and is the primary driver of demagnetization risk.
Why is β larger than α? β tracks the magnetocrystalline anisotropy field, which falls with temperature much faster than the saturation magnetization that governs α. As a result, coercivity typically declines four to six times faster than remanence.
Are temperature coefficient losses permanent? The losses described by α and β are reversible—they recover when the magnet cools, provided the operating point never crossed the knee of the demagnetization curve. Losses from crossing the knee are irreversible and require re-magnetization to restore, if they can be restored at all.
How do I choose an NdFeB grade for a high-temperature motor? Start from the magnet’s peak (hot-spot) temperature and load line, then use β and grade-specific demag curves to confirm the knee stays below your operating point with margin for transients. Higher coercivity suffixes (SH, UH, EH) offer more headroom; pick the lowest-cost grade that clears your worst case.
Does maximum operating temperature depend only on the grade? No. It depends on the magnet’s permeance coefficient (Pc) in the actual circuit. The same grade tolerates a higher temperature on a fatter load line than on a thin one, so quoted maximum temperatures are guidelines that must be verified against your operating point.
Designing a motor that runs hot? XHMAG’s engineering team can help you match a Dy/Tb-free NdFeB grade to your load line and temperature profile—and back it with demagnetization data at your operating temperature. Reach out to tony@xh-magnet.com to discuss your grade selection and request samples.
