Material Science : Magnetic Materials
INTRODUCTION TO MAGNETIC MATERIALS
Magnetic materials are used in electric motors, transformers, loudspeakers, cranes, data processing, and in households. Hard magnets must retain their magnetization even in stray magnetic fields, and soft magnets must change their magnetization with the lowest possible resistance. In this chapter we explore the different magnetic materials and the processing that endows them with the desired properties. In order to do that, we first review the concepts of magnetism and examine how a material becomes magnetic.
We are all familiar with magnets: they are used in the home to attach notes to the refrigerator door, as magnetic catches holding the refrigerator door closed, or to pick up small metallic objects. With these magnets, we require that the magnetization be strong enough and that it be permanent; we do not wish the magnetization to be weakened or modified by contact with other magnets or by stray magnetic fields. Such devices use hard ferromagnetic materials. Advances in the magnetic strength of these materials allow for greater efficiency and miniaturization in motors,
1.1 Magnetic fields, induction and Magnetization:
The ability to attract steel and redistribute iron filings in a characteristic pattern is familiar evidence that a magnetic field (H) is established in space by a bar magnet (figure 1(A)). A magnetic field is distributed geometrically the same way by a solenoid as shown in figure 1(A) and 1(B)
Figure 1. (A) Magnetic field surrounding a bar magnet. (B) Magnetic field surrounding an air-filled solenoid. (C) Magnetic field surrounding a solenoid with an iron core.
1.2 Magnetic Susceptibility:
- Magnetic field produces lines of force that penetrate the medium to which the field is applied.
- The density of the lines of force is known as the magnetic flux density.
- In a vacuum, the magnetic field and the magnetic flux density are related by the permeability of free space, μ0. B = μ 0 H
- If a magnetic material is placed in the field, it can increase or decrease the flux density.
1.3 Magnetic Descriptions of Atoms & Ions
1.3.1 Diamagnetic - Atoms or ions with a closed shell of electrons, all of the electrons are paired.
1.3.2 Paramagnetic - Atoms or ions with unpaired electrons, where the moment of an atom with unpaired electrons is given by the spin, S, and orbital angular, L and total momentum, J, quantum numbers
The field of the sample in the applied field is known as its magnetization, M, where H is the applied field.
The magnetic flux density, B, is given by:
B = μ0(H+M)
μ0 is the permeability of free space, 4Π*10-7H/m
where H is the symbol for henry
μ0 H is the induction generated by the field alone
μ0M is the additional induction contributed by the sample
Typically, the magnetization is discussed in terms of the magnetic susceptibility, χ :
1.3.3 Ferromagnetism – Magnetic moments of atoms align to produce a strong magnetic effect. For ferromagnetism, the Curie Law becomes χ=C/(T-TC), where TC is the Curie Temperature.
1.3.4 Antiferromagnetism – magnetic moments of atoms align anti-parallel to produce a strong magnetic effect. For antiferromagnetism, the Curie Law becomes χ=C/(T+TN), where TN is the Neel temperature.
1.4 Magnetic Susceptibility vs. Temperature
Interplay of applied field and thermal randomization leads to temperature dependence described by the Curie Law, χ= C/T (where C is a constant known as the Curie constant, and T is in Kelvin)
Paramagnetic substances with localized, weakly interacting electrons obey the 1.4.1 Curie-Weiss law.
where χm is the molar magnetic susceptibility, C = Curie constant, and θ = Weiss constant.
A plot of 1/χm vs. temperature is known as a Curie-Weiss plot. Ideally, it should be linear if the C-W law is obeyed. From such a plot we can then extract the Curie constant from the inverse of the slope and the Weiss constant from the y-intercept.
1.5 Hysteresis Curves
Magnetic behavior of different ferromagnetic substances is demonstrated by hysteresis curves, a plot of magnetic flux density (B) against applied magnetic field (H).
- Starting with a nonmagnetic sample (domains randomly aligned) B and H are zero, but as the field is increased the flux density also increases.
- Upon reaching the maximum value of magnetization all the spins are aligned in the sample, but when the applied field is reduced the flux density does not follow the initial curve, because of the difficulty of reversing processes where domains have grown through crystal imperfections.
- A sufficiently large magnetic field in the reverse direction must be applied before the magnetization process can be reversed.
- The magnetization where H is zero, but B is not zero is known as the remnant magnetization.
- The field that needs to be applied in the reverse direction to reduce magnetization to zero is the coercive force. Materials that are magnetically soft are those of low coercivity, Hc.
- Soft materials have low permeability and a hysteresis loop that is 'narrow at the waist' and of small area. Materials that are magnetically hard are those of high coercivity, Hc, and a high Mr (Br).
- Hard materials are not easily demagnetized, find use a permanent magnets.
Typical hysteresis loops for (I to r) high coercivity permanent magnets, lower coercivity permanent magnets, and soft magnetic materials
The magnetization M varies according to the hysteresis curve shown in Figure 6. It is customary to plot the induction B (in Vs/m2), rather than the magnetization M (in A/m). B is the quantity we need to analyze properly. Let us start with a material that is not magnetized. As the field H is increased from zero, the induction increases along the segment shown as a dotted line. The induction increases rapidly at first, then reaches saturation Bs. When the magnetic field is then reduced to zero, the induction does not disappear but decreases only slightly to the value Br, known as the remanent induction. When we reverse the magnetic field B decreases, reaching the value B=0 when H = Hc. Hc A is known as the coercive field. Increasing the intensity of the reversed field H increases the induction in the opposite direction until saturation is reached. When we decrease H, in the direction of the arrow, B decreases to the remanent induction Br when H is zero. Increasing the magnetic field in the positive direction causes B=0 again at the coercive field Hc. Further increase of H increases B until saturation Bs. In an alternating magnetic field H, the induction B follows the hysteresis curve.
1.6 Energy Losses in an Alternating Magnetic Field
When the ferromagnet is subjected to an alternating magnetic field, such as in a transformer, energy is lost at each cycle by two mechanisms: hysteresis losses and eddy currents.
1.6.1 Hysteresis Losses
At each cycle of the alternating field, an energy corresponding to the area inside the hysteresis curve is lost and transformed into heat. If, for instance, the coercive field is Hc=500 A/m and the saturation induction is Bs=2 T, the energy loss is 4,000 J/m3 at each cycle. With a frequency of 60 Hz, this represents 240 kW/m3.
1.6.2 Eddy Currents
The magnetic core can be considered to be made of many loops in which the time variation dB/dt induces a voltage. If the magnet is electrically conductive, this causes an electric current to flow. This current is proportional to the frequency. This current heats the material and constitutes an important loss of energy, especially at high frequencies. (Such energy absorption is used in heating by inductive coils and in microwave ovens.)
1.7 Soft Magnets
When the magnetization is produced by an ac current, as for instance in electric transformers, one uses magnetic materials with a small coercive field to reduce hysteresis losses. These are the soft magnets. Table 1 presents the properties of a number of commercial soft magnets.
Materials and composition
Saturation induction BS Tesla (gauss)
Coercive field A/m (oersted)
Hysteresis loss per cycle J/m3
Commercial iron ingot
45 Permalloy (45 Ni, 55Fe)
Supermalloy (79 Ni, 15Fe)
Ferrocube A (MnSn ferrite)
Table 1. Properties of Soft Magnets
1.8 Hard Magnets
When it is desired that a magnet conserves its magnetization in the presence of external magnetic fields, one selects a material with a high coercive field Hc. These are the hard magnets, which are represented in Table 2. Note that the coercive field in the hard magnets is indicated in kA/m and in A/m for soft
Note the change in scale from Table 1. Coercivity is here measured in k-A/m. Data from various sources.
Material and composition (wt %)
Remanent magnetization Tesla (gauss)
Coercivity HC kA/m (oersted)
BHmax kJ/m3 (MGOe)
Curie temperature (°C)
Carbon steel (0.9C, 1 Mn)
Cunife (20Fe, 20Ni, 60Cu)
Alnico V (50 Fe, 14 Ni, 25 Co, 8Al, 3Cu)
Samariu, cobalt (SmCo3) Nd2Fe14B
Barium ferrite (Ba-6Fe2O3)
1.9 The BH Product of Hard Magnets
Good hard magnetic materials possess a high saturation induction and a high coercivity. These properties are combined in a single quantity, the maximum BH product or (BH)max, which is used as a convenient figure of merit for permanent magnet materials. (BH)max is derived from the demagnetization portion, or second quadrant of the B-H curve shown in Figure 7. It is the largest rectangle (B × H) that can be inscribed in the hysteresis curve. (The right side of Figure 3 B is a plot of BH versus B from which (BH)max is readily obtained.) This is the way the values reported in Table 2. and noted in Figure 1. were obtained. Since it is derived from the hysteresis curve, the BH product is also known as the energy (density) product with units of J/m3 cycle. In the cgs system, the strength of magnets is measured in mega-gauss-oersted (MGOE). It is often also indicated as N followed by the number of MGOE’s. (A magnet N32 has a strength of 32 MGOE.)