Introduction to Magnetism and Magnetic Materials

David Jiles

• Éditeur: CRC Press
• Année: 2015
• ISBN:
  9781482238907
• Édition: 3
• Sujet: Sciences physiques
• Sous-sujet: Matière condensée

A long overdue update, this edition of Introduction to Magnetism and Magnetic Materials is a complete revision of its predecessor. While it provides relatively minor updates to the first two sections, the third section contains vast updates to reflect the enormous progress made in applications in the past 15 years, particularly in magnetic recordin

Section II

Magnetism in Materials

Magnetic Phenomena on the Microscopic Scale

5 Magnetic Properties

We will now look at the causes of hysteresis in ferromagnets and how the variation of magnetization with magnetic field can be quantified in restricted cases such as at low field and in the approach to saturation. High-resolution measurements of the variation of M with H indicate that there are discontinuities. This is known as the Barkhausen effect. We will also consider the change in length of a ferromagnet as it is magnetized, that is, the magnetostriction, and discuss anisotropy in relation to magnetostriction.

We have shown in the previous chapter that most of the important macroscopic magnetic properties of ferromagnets can be represented on a B-H plot or hysteresis loop. From this, the magnetization can be calculated at every point on the hysteresis curve using the general formula B = μ₀(H + M). As the magnetization curve is traversed, there are discontinuous, irreversible changes in the magnetization known as the Barkhausen effect after its discoverer. In recent years, the Barkhausen effect has become an important tool for investigating the microstructural properties of ferromagnetic materials.

One important bulk property of interest, which is not contained in the hysteresis plot, is the magnetostriction. This is the change in length of a material either as a result of a magnetic order (spontaneous magnetostriction) or under the action of a magnetic field (field-induced magnetostriction). This will also be discussed in this chapter.

5.1 HYSTERESIS AND RELATED PROPERTIES

5.1.1 INFORMATION FROM THE HYSTERESIS CURVE

Which are the most important macroscopic magnetic properties of ferromagnets?

From the hysteresis curve such as the one shown in Figure 5.1, we can define a number of magnetic properties of the material, which can be used to characterize the hysteresis loop. A question immediately arises: How many degrees of freedom are there in a hysteresis loop? Or to put the question another way: How many parameters are needed to characterize a hysteresis loop? Clearly, there is no general answer to this, but for the commonly encountered sigmoid-shaped hysteresis loop such as the one in Figure 5.1, we can start to enumerate the important properties and thereby make an estimate.

FIGURE 5.1 Typical sigmoid-shaped hysteresis curve of a specimen of iron containing 0.25 wt% carbon.

5.1.2 PARAMETRIC CHARACTERIZATION OF HYSTERESIS

Which are the parameters that can be used to define hysteresis?

First of all, the saturation magnetization M₀ will give us an upper limit to the magnetization that can be achieved. At temperatures well below the Curie point, the technical saturation M_s can be used instead. The width of the loop across the H axis, which is twice the coercivity H_c, is also an independent parameter since this can be altered by heat treatment and hence is not dependent on M_s. The height of the curve along the B-axis, that is, the remanence is also an independent parameter since it is not wholly dependent on M_s and H_c. The orientation of the hysteresis curve on the B-H plane, which can be represented by ${{\text{μ}}^{\prime }}_{\text{max}}$, the slope of the curve at the coercive point, is also independent of the other parameters.

The hysteresis loss W_H may also be an independent parameter as may the initial permeability ${{\text{μ}}^{\prime }}_{\text{in}}$. Finally, the curvature of the sides of the hysteresis loop, which although not immediately obvious as an independent parameter, is clearly not dependent on factors such ...