The Knee Point: The “Cliff Edge” of Irreversible Demagnetization

In the design of high-performance magnetic systems, relying solely on standard datasheet data is risky. While materials like Neodymium (NdFeB) behave predictably in ideal conditions, they undergo a drastic change under stress.

The demagnetization curve doesn’t just shrink—it changes shape. At high temperatures, the usually straight normal curve (B-H curve) begins to bend.

This deviation from linearity introduces the most critical constraint in magnetic design: the knee point.

The Hidden Cause (On the J-H Curve: Hk)

Why does the B-H curve bend? Because the intrinsic curve (J-H curve) behind it has collapsed. Many engineers recognize this critical boundary by its industry parameter: Hk.

• The Root Cause: The magnet’s internal resistance to demagnetization is defined by the intrinsic curve (J).

• Hk: This is the specific coordinate on the intrinsic curve where the magnet’s internal alignment begins to crumble (typically defined where J drops to 90% of Br).

• The Link: Once the external opposing field (H) exceeds Hk, the intrinsic curve (J) drops off the cliff. Since B = J + H, the collapse of J drags the B-H curve down with it, creating the visual “knee” you see on the normal curve.

The Danger: Suddenly, without the external load changing, your magnet is at risk simply because the “safe limit” (the knee) has moved closer to your operating point.

The position of the knee relative to your operating point determines the fate of the magnet.

Scenario A: Linear Response (Reversible)

Condition: At this specific temperature, the operating point sits above the knee point(on the straight line).

• Heating Phase: As the magnet heats up, the flux density (B) drops. This is a natural physical property.

• The Check: Because the operating point remains in the linear region, the magnet’s internal stability remains intact. The drop in flux is temporary and strictly due to temperature.

• Cooling Phase: When the magnet returns to room temperature, the flux rises back to its exact original value.

• Outcome: The loss was temporary. This is reversible demagnetization.

Scenario B: Non-Linear Response (Irreversible)

Condition: At this specific temperature, the operating point falls below the knee point (onto the curved, non-linear slope).

• Heating Phase: As the magnet heats up, the knee point rises and crosses the operating point.

• The Check: The magnet has entered the non-linear region. The external stress has overwhelmed the magnet’s internal stability, causing a permanent drop in magnetization.

• Cooling Phase: When the magnet returns to room temperature, it cannot follow the original path back. It follows a lower “recoil line,” resulting in a permanent reduction in strength.

• Outcome: The magnet has suffered irreversible demagnetization.

To ensure your design survives, you must calculate the operating point, determined by the permeance coefficient (Pc).

While the calculation depends on geometry, the concept is simple: Pc represents the “stiffness” of your magnetic circuit.

• High Pc (Thick Magnets): The operating line is steep. It intersects the curve high up, keeping a safe distance from the knee.

• Low Pc (Thin Magnets): The operating line is flat. It intersects the curve low down, dangerously close to the knee.

Three Ways to Fix a Dangerous Design

If your simulation shows your operating point falling below the knee (into the non-linear zone), you have three options:

• Change the Geometry (Increase Pc): Make the magnet thicker in the direction of magnetization. This raises the Pc line, moving your operating point up to safety.
• Change the Material (Increase Hcj): Switch to a higher grade (e.g., from “SH” to “UH”). High-coercivity grades keep the knee point lower, providing a larger safety margin.
• Cooling: Improve thermal management to prevent the knee point from rising into the operating zone.

Source Acknowledgment Some graphical data and technical illustrations regarding intrinsic curves in this article are referenced from Arnold Magnetics. We acknowledge and appreciate their contribution to the technical community.