# What is a hysteresis loop?

## What is a hysteresis loop?

The hysteresis loop represents the closed magnetization curve of the hysteresis phenomenon of ferromagnetic materials when the magnetic field intensity changes periodically. It shows the relationship between the magnetization M or the magnetic induction intensity B and the magnetic field intensity H during the repeated magnetization of a ferromagnetic substance. Since B=μ0(H+M), if the M-H curve of a material is known, the B-H curve can be obtained, and vice versa. In the formula, μ0 is the vacuum permeability.
The hysteresis loop is an important feature of ferromagnetic and ferrimagnetic materials. Paramagnetic and diamagnetic materials do not have this phenomenon.

## Basic concept

Hard magnetic materials, such as NdFeB strong magnets, have two distinctive features. One is that they can be strongly magnetized under the action of an external magnetic field, and the other is hysteresis, that is, the hard magnetic material still retains its magnetization state after the external magnetic field is removed.

### Physical process Figure.1 The hysteresis loop of a strong magnetic substance
Start the sample of ferromagnetic materials (including ferromagnetic and ferrimagnetic materials) from the residual magnetization M=0, and gradually increase the magnetic field intensity H of the magnetization field. The magnetization M will increase along the OAB curve in Figure 1 until it reaches Magnetic saturation state B. Now increase H, the magnetization state of the sample will remain basically unchanged, so the straight line BC is almost parallel to the H axis. When the magnetization reaches the saturation value Ms, the corresponding magnetic field intensity H is represented by Hs. The OAB curve is called the initial magnetization curve.
Afterwards, if the magnetization field is reduced, the magnetization curve starts from point B and does not return along the original initial magnetization curve. This indicates that the change in magnetization M lags behind the change in H. This phenomenon is called hysteresis. When H decreases to zero, M is not zero, but equal to the residual magnetization Mr. To reduce M to zero, a reverse magnetization field must be added, and when the reverse magnetization field is strengthened to -Hcm, M will be zero. Hcm is called the coercive force.
If the magnitude of the reverse magnetization field continues to increase to -Hs, the sample will be magnetized in the reverse direction to the saturation state E, and the corresponding magnetization saturation value is -Ms. Points E and B are symmetrical with respect to the origin.
After that, if the reverse magnetization field is reduced to zero, then it increases in the positive direction. The magnetization state of the sample will return to the positive saturation magnetization state B along the curve EGKB. The EGKB curve and the BNDE curve are also symmetrical with respect to the origin O. It can be seen that when the magnetization field changes from Hs to -Hs and then from -Hs to Hs repeatedly, the change of the magnetization state of the sample undergoes a cyclic process described by the closed loop of BNDEGKB. The curve BNDEGKB is called the hysteresis loop.
The two segments BC and EF correspond to the reversible magnetization process, and M is a single-valued function of H. Due to the hysteresis phenomenon, any given H on the hysteresis loop corresponds to two M values. Which magnetic state the sample is in depends on the magnetization history of the sample. It can be proved that the area enclosed by the B-H hysteresis loop is proportional to the energy loss in one cycle of magnetization.

### Normal magnetization curve Fig.2 Normal magnetization curve of a strong magnet
If the maximum |H| value of the magnetization field is repeatedly magnetized within a range smaller than |Hs|, a smaller hysteresis loop will be obtained (see Figure 2). Among all the hysteresis loops, the above-mentioned BNDEGKB is the largest one, which is often called the limit hysteresis loop. The line connecting the vertices at both ends of each hysteresis loop is called the normal magnetization curve, as shown by the dashed line in Figure 2, which basically coincides with the initial magnetization curve.
The direction and shape of the hysteresis loop of the ferromagnetic material denoted by B-H are roughly the same as the M-H hysteresis loop. In electrical engineering, the hysteresis loop represented by B-H is more used.
The above-mentioned hysteresis loop is obtained when the magnetic field changes slowly, and is also called quasi-static hysteresis loop. When the alternating magnetic field acts, there is still hysteresis, and the hysteresis loop is also a closed loop, which is called dynamic hysteresis loop. Due to the influence of eddy current effects, the shape and area of the dynamic hysteresis curve are different from those of the quasi-static hysteresis loop.
It can be proved that the area enclosed by the B-H hysteresis loop is proportional to the energy loss in one cycle of magnetization. Aim at the static hysteresis loop, this loss is only hysteresis loss, for dynamic hysteresis loop, this energy loss includes hysteresis loss and eddy current loss.

### Coercivity

When H=-Hc, B=0 (B≈μ0(H+M), so M≈0 at this time), which means that to completely eliminate the remanence of ferromagnetic material, a reverse magnetic field Hc must be added. Hc is called coercive force. Because H=B/μ0-M, strictly speaking, the coercive force required to make B=0 and M=0 is different, and the coercive force to make M=0 and B=0 should be distinguished.
When the coercivity is not large (that is, when H≪M, B=μ0(H+M)≃μ0M), the two coercive forces are considered the same (that is, when B=0, M=0). The magnitude of coercivity reflects the ability of ferromagnetic materials to preserve the remanence state. It is the size of the coercive force that divides ferromagnetic materials into hard magnetic materials and soft magnetic materials.

## Classification of hysteresis loops

Hysteresis loops can be divided into the following types:

• (1) Normal hysteresis loop. This is the loop shape of the vast majority of magnetic materials, which is symmetrical with the origin, or S-shaped loop.
• (2) Rectangular hysteresis loop refers to the hysteresis loop with br / BM > 0.8, which can be obtained by heat treatment or stress treatment.
• (3) Degenerate hysteresis loop. If a material is subjected to magnetic field heat treatment or stress treatment, a rectangular hysteresis loop is obtained in a certain direction. If the material is magnetized in the vertical direction, the hysteresis loop close to the straight line will be obtained, br / BS < 0.2.
• (4) The hysteresis loop of wasp waist. In a few magnetic materials, such as some cobalt containing ferrites and perminvar alloys, the hysteresis loops at medium magnetic field strength show a special shape, that is, the b value near br decreases significantly, such as a bee waist.
• (5) Asymmetric hysteresis loop. The first four are called symmetrical loops (HC = HC). However, for materials containing both ferromagnetic and antiferromagnetic components (such as cobalt oxide layer on the surface of powdered cobalt), or ferrite after heat treatment in a constant magnetic field, the hysteresis loops often appear asymmetric, that is, HC ≠ HC.
• (6) Saturation hysteresis loop. When the magnetization field is large enough to make the magnetization reach saturation state, the normal hysteresis loop obtained is the saturation hysteresis loop. The size of HC and BR is usually defined in this state.

## Application of hysteresis loop

The hysteresis loop is sensitive to structure and is easily affected by various factors. The hysteresis loop is caused by the irreversible process in technical magnetization, which may occur in the process of domain wall movement and domain rotation. The area enclosed by the hysteresis loop represents the energy consumed for one cycle of magnetization of ferromagnetic materials, which is often converted into heat energy and consumed.
The hysteresis loop reflects the magnetization of ferromagnetic materials. It shows that the magnetization of ferromagnetic materials is rather complicated, and the relationship among m, B and h of ferromagnetic materials is not only non-linear, but also not single valued. That is to say, for a certain value of H, m and B, it cannot be uniquely determined, and it is also related to the magnetization history.
Different ferromagnetic materials have different shapes of hysteresis loops, and different shapes of hysteresis loops have different applications. For example, permanent magnetic materials require high coercivity and high remanence; soft magnetic materials require low coercivity; and memory elements require low coercivity. In order to meet the needs of new technology in production and scientific research, it is necessary to develop new ferromagnetic materials to make their hysteresis loops meet the requirements of application. The hysteresis loop provides a basis for material selection. Because the area enclosed by B-H hysteresis loop is directly proportional to the hysteresis loss, the hysteresis loss is harmful in AC electrical appliances. Its existence not only wastes electric energy but also makes the core heat up, which is unfavorable to the equipment. Therefore, the area enclosed by the hysteresis loop of soft magnetic materials should be reduced as far as possible to reduce the loss.
Source: China Permanent Magnet Manufacturer – www.ymagnet.com              