How to Read a B-H Demagnetization Curve for Permanent Magnets

The hysteresis loop traces the magnetic state of a material as the external magnetic field is increased, decreased, and reversed:

First quadrant (initial magnetization): B increases rapidly from zero as the magnetizing field (H) increases. At saturation, B reaches Br (the remanence).

Second quadrant (demagnetization curve): H is reduced to zero (B falls to Br), then reversed (negative H). The path in this quadrant is the demagnetization curve-this is where the magnet operates when placed in a circuit.

Third quadrant: H continues negative until B reaches zero (Hcb, the coercivity), then continues to negative saturation.

Fourth quadrant: H sweeps back to positive, completing the loop.

For permanent magnet design, we focus exclusively on the second quadrant (the demagnetization curve). The curve shows B vs. -H (demagnetizing field).

There are two curves on the demagnetization graph:

Normal curve (B-H curve): B (total flux density) vs. H. This is the curve you use to calculate air gap flux and flux density in the magnetic circuit. It includes the contribution of the magnet's own field. The normal curve is used to find the operating point (Bop and Hop) with the load line.

Intrinsic curve (J-H or M-H curve): J (magnetization, or B - μ0H) vs. H. This curve represents the actual magnetic moment of the material, excluding the demagnetizing field. The intrinsic curve determines resistance to demagnetization: the knee point is on the intrinsic curve.

Why both matter: A magnet that has a high Br and a high normal curve may still be prone to demagnetization if the intrinsic curve has an early knee. For motor magnets (which experience reverse fields), the intrinsic curve is more important than the normal curve.

The knee point is where the demagnetization curve starts to "fall off" sharply. Below the knee, the magnet's flux drops rapidly with a small increase in demagnetizing field, and the demagnetization is irreversible-even if the reverse field is removed, the magnet does not fully recover.

On the intrinsic curve, the knee is where the curve begins to drop steeply. The H value at the knee is often called the "intrinsic coercivity" (Hcj) in practical terms (though Hcj is the field at which J = 0, not the knee itself). For a high-quality magnet, the knee is close to Hcj. For lower-grade magnets, the knee occurs well before Hcj.

For safe operation, the magnet's operating point must always stay above the knee of the intrinsic curve. If the demagnetizing field pushes the magnet below the knee, irreversible losses of 10-50% can occur.

Typical knee values:

N35: knee at H ≈ 10 kOe (intrinsic curve); normal curve remains linear.

N52: knee at H ≈ 6-7 kOe (intrinsic curve) - higher risk of demagnetization.

SmCo 2:17: intrinsic curve has no knee down to H = 0 - completely linear, safe in any reverse field.

The permeance coefficient (also called the load line slope) describes how a magnet's magnetic circuit (including air gaps, back iron, and surrounding materials) affects the operating point. It is defined as:

Permeance coefficient, Pc = B / H (in the second quadrant, with units of flux density divided by field strength).

High Pc (steep load line, e.g., Pc > 10): The magnet operates at high flux density (near Br) and low demagnetizing field. This occurs in closed circuits with good back iron and small air gaps. Safe, but uses the magnet's full potential.

Low Pc (flat load line, e.g., Pc < 1): The magnet operates at lower flux density and higher demagnetizing field. This occurs with large air gaps or no back iron. Risk of demagnetization.

To use the load line:

Calculate the permeance coefficient from your magnetic circuit geometry (using FEA or analytical formulas).

Draw a line from the origin on the B-H graph with slope Pc.

The intersection of the load line with the demagnetization curve is the operating point (Bop, Hop).

Check that this point is above the knee on the intrinsic curve. If not, the magnet will demagnetize. Increase magnet thickness, reduce air gap, or choose a higher-Hcj grade.

Example: An N42SH motor magnet (Hcj=20 kOe) with a load line Pc=2. The operating point is at H≈7 kOe, B≈14 kGs. The knee is at H≈10 kOe. The operating point is above the knee-safe. If Pc drops to 1 (large air gap), the operating point moves to H≈12 kOe-below the knee-unsafe. Use N42UH (Hcj=25 kOe) instead.

For motor and sensor manufacturers, we provide FEA simulation and load line analysis. We recommend the optimal grade and geometry to ensure the operating point stays above the knee at all operating temperatures (including worst-case reverse fields).

For more on demagnetization curves and load line analysis, please visit our Finite Element Analysis and TechBlog homepage on our website.

To request a demagnetization analysis for your magnet design-including grade selection and load line calculation-send us your magnetic circuit geometry and operating temperature. Our engineering team provides a full demagnetization risk report.

Q: What is the difference between Hcb and Hcj?
A: Hcb (coercivity) is the reverse field required to reduce B to zero (on the normal curve). Hcj (intrinsic coercivity) is the reverse field required to reduce J (magnetization) to zero (on the intrinsic curve). Hcj is always higher than Hcb. Hcj is the better indicator of demagnetization resistance.

Q: How do temperature and the demagnetization curve relate?
A: As temperature increases, both Br and Hcj decrease. The knee moves lower on the H-axis and the intrinsic curve drops. For high-temperature operation, select a grade with sufficient Hcj at the operating temperature. We provide temperature-corrected demagnetization curves for each grade.

Q: Can I demagnetize a magnet by operating below the knee by just a small amount?
A: Yes. Even a brief excursion below the knee causes irreversible loss. The loss is proportional to the area below the knee. For safety-critical applications (aerospace, automotive), we design with a 20% margin above the knee at the worst-case temperature and load.