Hysteresis Loop Characteristics: B-H and J-H Curves Analysis

Magnetic materials are ubiquitous in modern technology, from hard drives to motors, from transformers to sensors, and their performance directly affects equipment efficiency and reliability. Hysteresis, as a core property of magnetic materials, describes the hysteresis of the magnetization response of materials under the action of an external magnetic field. Through B-H curves and J-H curves, we can deeply understand the characteristics and application potential of magnetic materials. This article will discuss in detail the hysteresis phenomenon, curve characteristics, material classification, and its wide application in the field of science and technology.

What is hysteresis?

Hysteresis comes from the Greek word “lag”, which refers to the change of magnetization or magnetic induction intensity of ferromagnetic materials (such as iron, nickel, cobalt, and their alloys) under the action of an external magnetic field. When an external magnetic field is applied, the material gradually achieves magnetization through the movement of magnetic domain walls and the rotation of magnetic moments. Even if the magnetic field is removed, the pinning effect prevents the magnetic domains from fully recovering, causing the material to retain a certain degree of magnetization, called remanence (Br). This “magnetic memory” property makes magnetic materials important for applications in storage devices and permanent magnets.

Physical mechanism of hysteresis

The root of hysteresis lies in the dynamic behavior of magnetic domains inside the material. Magnetic domains are tiny areas in the material, each with a consistent magnetization direction. In the absence of an external magnetic field, the magnetic domains are randomly arranged, and the net magnetization intensity is zero. After applying an external magnetic field, the magnetization process is divided into: 1) reversible magnetic domain wall movement (low field region); 2) irreversible magnetic domain wall jump (mid-field region); 3) magnetic moment rotation (high field region). After removing the magnetic field, some magnetic domains cannot return to a random state due to the pinning effect, resulting in residual magnetism. To completely demagnetize, a reverse magnetic field must be applied or heated to above the Curie temperature to destroy the magnetic domain arrangement.

B-H curve (hysteresis loop)

The B-H curve is a curve graph that shows the relation between magnetic induction intensity and external magnetic field intensity, thus illustrating the magnetization properties of the material. Its formula is:

B = μ₀H + J

Here μ₀ is the vacuum magnetic permeability (4π×10⁷ H/m), and J = μ₀M is the magnetization density. The B-H hysteresis curve is typically the closed loop that represents the nonlinear magnetization properties of the material that can be derived.

Initial magnetization curve

First of all, in the neutral magnetic state, an external magnetic field H is applied, while the magnetic induction intensity B goes up with H, and so B shows the following stages:

Rayleigh region (low field): reversible magnetic domain wall movement, B increases linearly with H;

Irreversible magnetization region: domain wall jump dominates, B rises rapidly;

Approaching saturation region: magnetic moment rotation is dominant, B asymptotically approaches the saturation value Bs.

Remanence and coercive force

Remanence (Br): When H decreases from Hs to 0, B does not return along the initial magnetization curve, but decreases along a new path, retaining a certain magnetic induction intensity at H=0, which is called remanence Br. Remanence reflects the ability of a material to maintain magnetization.

Coercive force: There are two types:

Magnetic induction coercive force (Hcb): the reverse magnetic field required to reduce B to 0;

Intrinsic coercive force (Hcj): the magnetic field required to reduce J (or M) to 0 (Hcj ≥ Hcb, only for permanent magnetic materials).

Hysteresis loop

When H changes cyclically in the positive and negative directions (such as AC drive), the B-H curve forms a closed loop (a-b-c-d-e-f-a), which is called a hysteresis loop:

Forward magnetization: from 0 to positive saturation point (a to b);

Reduce magnetic field: H is reduced to 0, B is reduced to Br (b to c);

Reverse magnetization: Apply reverse H, B is reduced to 0 (c to d, Hcb), and continue to increase reverse H to negative saturation (d to e);

Cycle return: H is reduced to 0 again (e to f, negative Br), and then positively increased to saturation (f to a). The loop area represents the hysteresis loss energy density (W = ∮HdB), that is, the energy dissipated as heat during the magnetization cycle. A narrow loop means low loss, while a wide loop means greater loss.

J-H curve (intrinsic demagnetization curve)

The J-H curve describes the relationship between magnetic polarization intensity (J = μ₀M, unit: Tesla) and H, and is mainly used to evaluate the intrinsic magnetic properties of permanent magnetic materials.

Intrinsic coercivity (Hcj)

The H value corresponding to when J drops to 0 is called the intrinsic coercivity Hcj, which indicates the reverse magnetic field intensity required for complete demagnetization of the material. Hcj is a key indicator of the demagnetization resistance of permanent magnetic materials and is usually much larger than Hcb.

Inflection point (Hk)

During the increase of the reverse magnetic field, J decreases slowly until a certain point (J = 0.9Br), when it drops rapidly. This point is called the inflection point (Hk), marking the beginning of irreversible demagnetization. The closer Hk is to Hcj, the higher the stability of the material at high temperature or reverse field.

Squareness (Q)

Squareness is defined as Q = Hk/Hcj (0 ≤ Q ≤ 1). Q ≥ 0.9 indicates that the demagnetization curve is close to a rectangle, which is a characteristic of high-quality permanent magnets.

Characteristics of soft and hard magnetic materials

Magnetic materials are divided into soft and hard magnetic materials according to the shape of the loop:

Soft magnetic materials (such as silicon steel, ferrite):

Narrow hysteresis loop, low Br and Hc;

Low hysteresis loss, suitable for AC applications such as transformers and motors;

Silicon steel reduces eddy current and hysteresis losses by adding silicon.

Hard magnetic materials (such as NdFeB, SmCo, AlNiCo):

Wide hysteresis loop, high Br and Hcj;

High anti-demagnetization ability, used for permanent magnet motors and magnetic storage.

Effect of temperature on magnetic properties

Remanence (Br) and coercivity (Hc, Hcj): decrease with increasing temperature;

Curie temperature (Tc): when T≥Tc, the material becomes paramagnetic and hysteresis disappears;

Irreversible demagnetization may occur at high temperatures, especially when the operating temperature is close to the field strength corresponding to the Hcj inflection point.

Barkhausen effect

During the magnetization process, the discrete magnetization jump caused by the depinning of the domain wall is called the Barkhausen effect, which appears as a noise signal on the magnetization curve. This effect can be used for non-destructive testing of stress distribution and defects inside the material.

Material selection

Soft magnetic materials (such as amorphous alloys) have extremely low Hc.

Process improvement: reducing domain wall resistance through grain orientation control (such as silicon steel rolling);

Frequency management: using thin-film stacking to reduce eddy current losses in high-frequency applications.

Conclusion

Hysteresis, B-H, and J-H graphs depict the main relationships that allow us to understand and improve the magnetism of materials. Reversible magnetization in the Rayleigh region and the intrinsic coercive force of permanent magnets are properties that not only allow understanding the microstructure of materials, but also facilitate their use in modern science and technology. Through the continuous progress of materials science, the creation of novel magnetic substances will further facilitate the implementation of high-efficiency, low-loss technologies and enable greater innovations in energy, storage, and healthcare sectors.

Ethan Huang

I'm dedicated to popular science writing about magnets. My articles mainly focus on their principles, applications, and industry anecdotes. Our goal is to provide readers with valuable information, helping everyone better understand the charm and significance of magnets. At the same time, we're eager to hear your opinions on magnet-related needs. Feel free to follow and engage with us as we explore the endless possibilities of magnets together!

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