Magnet Stability:

We have derived the demagnetization curves of permanent magnets in previous Sections, and have showed actual curves for some of the most popular materials in Section 2A. It was apparent that, while the characteristic shape of each curve is retained as the magnet's temperature varies, the curve's position relative to each axis changes. In terms of a magnet's intrinsic demagnetization curve, its magnetization +M_sat and its intrinsic coercivity -H_ci are both changing with temperature. Because B_r=µ_oM_sat, the magnet's "normal" B vs. H curve will move by virtue of both its remanence B_r and its coercivity -H_c changing with temperature.

Whatever flux density we expected the magnet to provide at room temperature, this will be different at any other temperature, directly affecting the performance of the device in which the magnet is installed. Furthermore, in Section 1C we warned that the "knee" in the demagnetization curves represents the onset of a reversal of the material's magnetization, but now we see that the position of the "knee", and hence the threshold for magnetization reversal, is dependent upon temperature.

Change in Remanence

If a magnet delivers flux density B corresponding to a point on its B vs. H curve which is below the "knee", the reversal of some of the material's magnetization will require a remagnetization of the magnet to restore its full saturation magnetization M_sat. In this case, it is said that the magnet has suffered an irreversible loss, because although the condition is in fact reversible with full remagnetization, this is not usually something a user can perform on an assembled device. However, if the magnetic properties vary with temperature without causing the magnet to operate at a point on the B vs. H curve which is below the "knee", then the magnet is only suffering a reversible loss, since the original operating condition is fully restored when the temperature returns to its normal level. The latter reversible condition is explained in this Section.

Magnetization M is the bulk material property, defined in Section 1A as the sum of the magnetic dipole moments µ_m per unit volume.

M will assume its saturation value of M_sat when all the µ_m are aligned. Increasing temperature thermally agitates the dipole moments, disrupting their alignment and reducing M below its M_sat level. At a sufficiently high temperature, there is enough thermal agitation to yield no net alignment of the µ_m, so that M completely disappears. This critical value is known as the Curie Temperature T_c, which is a fundamental parameter of every magnetic material. This general relationship between M and temperature T is illustrated in the diagram to the right. Permanent magnet materials are likely to have better thermal stability if they contain constituent elements with higher values of T_c, the most commonly used being:

Since B_r=µ_oM_sat at room temperature, the remanence at elevated temperature is the new value of flux density for the condition when a magnet now develops no magnetizing force (H=0). Therefore, the relationship between B_r and temperature follows the same form as the diagram above. Furthermore, as a practical matter one doesn't want a permanent magnet material to operate anywhere close to its T_c, so B_r will gradually change over the normal range of operating temperature as illustrated. This was seen in each set of demagnetization curves in Section 2A , by looking at the characteristics' intercepts with the B-axes. It is seen again in the demagnetization curves shown below, which are for another grade of fully dense anisotropic neodymium-iron-boron.

By plotting the intercepts of these curves with the B-axis, we can see the change in B_r with temperature. The decline is approximately linear up to some transition temperature (almost 200^oC for this neodymium-iron-boron grade), above which there is a rapid degradation in B_r. This linear region is a reversible loss, whose slope is known as the reversible temperature coefficient of B_r (α) for the material. Above the transition temperature, the magnet is suffering an irreversible loss, such that B_r does not recover its original value upon return to room temperature. This irreversible loss is easily visualized from the set of demagnetization curves above, which clearly show the "knee" approaching the B-axis as the temperature rises towards 200^oC.

The reversible temperature coefficient of B_r (α) is defined as the percentage deviation in B_r from its value at room temperature (%/^oC). Typical values for the permanent magnets described in Section 2A are:

From the Curie Temperatures of the constituent elements, it is clear that cobalt-based alloys should have better temperature stability than iron-based alloys, and indeed the Table above confirms this. The problem is, of course, that cobalt is a much more costly element than iron.

Change in Coercivity

The change in a magnet's coercivity H_c with temperature will depend upon the changes occurring both in B_r and in H_ci. In Section 1B, we derived the intrinsic coercivity for a magnet with magnetocrystalline anisotropy as:

We would therefore expect that, as temperature rises and M falls below its M_sat level, H_ci will increase. This is indeed what happens with ceramic ferrites, whose actual characteristics strongly adhere to magnetocrystalline anisotropy.

However, with the samarium-cobalt and neodymium-iron-boron materials described in Section 2A, H_ci is seen to decrease with temperature. This is not specifically due to nucleation or pinning complicating the magnetocrystalline anisotropy mechanism. The cause is at the atomic level, where magnetic moments µ_m of the rare earth elements are themselves strongly temperature dependent, and (since K₁ = 8µ_oµ_mM) K₁ is no longer constant but will control the change in H_ci via the equation above.

While it was possible to assign an approximately constant value to the reversible temperature coefficient of B_r (α), the changes in H_ci and hence H_c are not as easy to predict, so the actual demagnetization curves should be used to study these parameters.

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