Basic Permanent Magnetism:

the demagnetization curve.

by Dr. Peter Campbell

In Section 1B, we showed that a fully magnetized permanent magnet maintains a magnetization of +*M_sat* until it experiences a reverse applied field of magnitude -*H_ci, at which point the magnetization* flips over to -*M_sat. This mechanism described the second quadrant of the intrinsic magnetization characteristic* of the material.
To remind yourself of this ideal intrinsic magnetization characteristic, click on this button.

Furthermore, in Section 1A we showed that a permanent magnet's magnetization M will provide a magnetizing force H which establishes a flux density B, these three being directly related via B=µ_o(H+M). This relationship may therefore be used to convert the intrinsic M vs. H magnetization characteristic into the "normal" B vs. H magnetization characteristic shown here, and since M exists only within the magnet while B flows through the magnet and out into the surrounding media, the B vs. H characteristic is far more useful for practical magnet design.

Notice that the slope of the B vs. H curve, dB/dH=µ_o, at least for -H_ci<H<+H_ci. Now µ_o is the permeability of free space, and dB/dH has this same value in air gap regions where there is no magnetic material (M=0), so even though this ideal permanent magnet does have magnetization M, it appears to the surrounding media like an air gap! This will be important, for example, in determining the inductance of a coil in a magnetic circuit which also contains a magnet.

When this "normal" B vs. H curve is used for magnet design, the values of three points on the curve are most commonly quoted in the magnet manufacturers' literature:

Remanence is the intercept of the B vs. H curve on the positive B axis. For the ideal material, its value B_r=µ_oM_sat, but B_r is always the value of flux density for the condition when a magnet develops no magnetizing force (H=0).
Coercivity is the intercept of the B vs. H curve on the negative H axis. Its value -H_c is the magnetizing force required to reduce the magnet's flux density B to zero, which on this ideal curve is -H_c=M_sat. Notice that by comparing the "normal" and intrinsic characteristics, the values of -H_c and -H_ci are not the same, i.e. the magnetizing force required to make B=0 may be less than that required to reverse the direction of the material's magnetization.
Maximum energy product (BH)_max is the point on the second quadrant of the B vs. H curve at which the product of B and H for the magnet are maximized. On this ideal curve, it is located exactly halfway down the second quadrant line, with a value of -(BH)_max=µ_o(½M_sat)². We will discuss the significance of this permanent magnet parameter in subsequent sections.

While a magnet maintains its +M_sat magnetization until it experiences a reverse applied field of magnitude -H_ci, the typical range of operation for a magnet to provide forward magnetic flux will be a reverse applied field of |-H|<|-H_c|, i.e. the second quadrant. Consider, for example, a position at a magnet/air boundary at which the B and M vectors are normal to this boundary. For the regions immediately adjacent to the boundary, the field vectors are then generally as depicted by this diagram. The principal of conservation of magnetic flux dictates that B must be continuous across the boundary, so H must be discontinuous as shown.

We can now describe the behavior of a real permanent magnet with reference to the second quadrant of its actual B vs. H curve, known as the demagnetization curve. For reference, the ideal curves from the previous diagrams are shown here in blue. An actual permanent magnet material neither achieves its theoretical intrinsic coercivity -H_ci, nor does the entire magnetization flip over exactly when a reverse field of -H_ci is reached. The actual intrinsic demagnetization curve (shown dashed in this diagram) does not have an abrupt transition at -H_ci, but rather a "knee" in the curve represents a more gradual reversal of the material's magnetization. The actual "normal" demagnetization curve (shown solid in this diagram) obviously mirrors this "knee". The coercivities -H_ci and -H_c are now defined as the intercepts of the actual intrinsic and normal curves with the H-axis.

We showed that the B within the magnet is indicative of the flux density it will deliver into the adjacent air gap, and the point at which a magnet operates on its demagnetization curve relates B to the demagnetizing force -H it experiences. The demagnetization curve shows us that, as the magnitude of -H increases, the flux density delivered by the magnet will fall, ultimately at H=-H_c to B=0. And, bad things begin to happen in the magnet well before -H_ci is reached, because the "knee" in the demagnetization curve represents the onset of a reversal of the material's M. It is clearly most desirable that the operating point of a permanent magnet always remain above any portion of the "knee" in the demagnetization curve.