The Demagnetisation Curve and its Parameters
In hard magnetic materials the second quadrant of hysteresis is most important and is called demagnetization curve. Demagnetization curves as well as the other quadrants of hysteresis can be drawn both in the J(H) picture as well as in the B(H) description which follows from eq. (A.8). This is also the case in Fig. B1, which supplies those basic parameters of the demagnetization curve, which are mainly used in technical literature about permanent magnets.
Demagnetization curve ( second quadrant) as well as the first and parts of the third quadrant of magnetic hysteresis. The first quadrant is located at the top rightside of the coordinate cross, the second quadrant is the top left side. The third quadrant is placed at the bottom left side. The demagnetization curve, i.e. the second quadrant, defines the parameters Br, bHc, jHc, μr and (BH)max.
The most important parameters of a demagnetization curve are named as:
Br = Remanence induction [T]
jHc = Coercitivity of J [A/m], bHc = Coercitivity of B [A/m]
μr = Recoil permeability [no units]
(BH)max = Maximum energy product [kJ/m3]
Now lets describe the behavior of demagnetization curves in more detail. As we examine here only one spatial direction, a scalar description is used. In modern magnetic materials we have a nearly linear behavior of J(H) and B(H) on the demagnetization curve up to a point where the curve bents down more or less sharply. If the magnets working points are located in this linear area, these points can be moved up and down by external H changes without leaving the demagnetization curve.
The behavior of the magnet is then called to be reversible.
In the M(H) picture the linearity of the demagnetization curve is described by introducing a constant recoil susceptiblity cr by:
M(H) = Mr +χ r ×H (B.1)
Here Mr is the remanent magnetization. Using eq. (A.2) we get for J(H)
J(H) = Br +μ 0 ×χ r ×H (B.2)
From this we get that the remanence induction in fig. B1 is related to the remanence
magnetization simply by the factor m0:
Br = μ 0 ×Mr (B.3)
In the B(H) description it follows from eq. (A.7) that:
B(H) = Br +μ 0 ×μ r ×H (B.4)
Here we have introduced the recoil permeability (or often called permanent permeability) by
μ r = 1+χ r (B.5)
The recoil permeability describes the steepness of the demagnetization curve in the B(H) description. The above formulas are not only true for linear demagnetization curves but can also be used, when there is a deviation from linearity. In this case μr and cr are H dependent. From the above equations it can be seen, that the remanence induction is equivalent to the magnetization nearly over the whole linear or quasilinear range of the demagnetization curve.
This can be taken especially from eQ. as cr is close to zero (μr close to one)for most modern magnetic materials. As the spatial distribution of magnetization determines the field of permanent magnets, see in chapter E, the importance of remanence induction can easily be understood.
The coercivity of B i.e. bHc describes that magnetic field which makes the B distribution in the magnet to change its direction. It is smaller than iHc which is the field being necessary to demagnetize the polarization or magnetization to zero. Generally it can be stated that as higher the iHc value as more energy has to be used to magnetize a magnet to its saturation.
This means that a higher hsat is needed which can be found in the first quadrant of hysteresis.