Coercivity is another core magnetic performance parameter of strong magnets, which measures the ability of a magnet to resist demagnetization. Unlike remanence, which reflects the "strength" of the residual magnetism, coercivity reflects the "stability" of the magnetism—how much external demagnetizing field the magnet can withstand without significant loss of magnetic properties. There are two main types of coercivity commonly used in the field of strong magnets: intrinsic coercivity (Hci) and coercivity of magnetic induction (Hcb). Understanding the differences and characteristics of these two parameters is crucial for the correct selection and application of strong magnets.

First, let us clarify the definition of coercivity of magnetic induction (Hcb), also known as the B-H coercivity. It refers to the strength of the external reverse magnetic field required to reduce the magnetic induction intensity (B) of a fully magnetized magnet to zero. In the B-H hysteresis loop of a magnet, Hcb is the abscissa value corresponding to the point where the B curve intersects the zero line (B=0). Its unit is Oersted (Oe) or Ampere per meter (A/m), with 1 Oe ≈ 79.577 A/m. Hcb reflects the ability of the magnet to resist demagnetization from the perspective of magnetic induction intensity; when the external reverse magnetic field exceeds Hcb, the magnetic induction intensity of the magnet becomes zero, but this does not mean that the magnet is completely demagnetized—its internal magnetic domains still have a certain degree of alignment, and the magnetization intensity (M) is not zero.

Intrinsic coercivity (Hci), also known as the M-H coercivity, is the strength of the external reverse magnetic field required to reduce the magnetization intensity (M) of a fully magnetized magnet to zero. The magnetization intensity M is an intrinsic property of the magnetic material, representing the magnetic moment per unit volume. In the M-H hysteresis loop, Hci is the abscissa value corresponding to the point where M=0. Compared with Hcb, Hci is a more fundamental parameter reflecting the anti-demagnetization ability of the magnet, because it directly relates to the reversal of magnetic domains inside the material. When the external reverse magnetic field reaches Hci, the magnetic moments of the internal magnetic domains of the magnet are completely reversed or randomly oriented, and the magnet is truly fully demagnetized. For strong magnets, Hci is usually much larger than Hcb; for example, the Hcb of sintered NdFeB magnets is generally between 800-2000 Oe, while Hci can reach 10,000 Oe or higher.

The measurement of coercivity also relies on professional equipment such as hysteresisgraphs and vibrating sample magnetometers (VSM). The measurement process for Hcb is as follows: after saturating the magnet, apply a reverse magnetic field and gradually increase its strength; continuously measure the magnetic induction intensity B of the magnet during this process; the reverse magnetic field strength when B decreases to zero is Hcb. The measurement of Hci is similar, but it measures the magnetization intensity M instead of B. Since M cannot be measured directly, it is usually calculated by the formula B = μ0(M + H) (where μ0 is the permeability of vacuum). By measuring B and H, M can be derived, and then the reverse magnetic field strength when M=0 is determined as Hci. It should be noted that the measurement of coercivity is also affected by the sample's shape, size, and temperature. For example, thin or long strip magnets have a larger demagnetizing factor, which may lead to lower measured coercivity values; therefore, standard samples with small demagnetizing factors (such as short cylinders) are often used in tests.

The coercivity of strong magnets is mainly determined by the material's microstructure and composition, especially the pinning effect of magnetic domain walls. The magnetic domain wall is the transition region between adjacent magnetic domains with different orientations. When an external reverse magnetic field is applied, the magnetic domain walls move—domains with orientations opposite to the reverse field expand, while domains with orientations consistent with the original magnetization direction shrink. The resistance to this movement of magnetic domain walls is the key to generating coercivity. In strong magnets, defects such as grain boundaries, impurity phases, and dislocations in the material act as "pinning centers" to hinder the movement of magnetic domain walls. The stronger the pinning effect, the higher the coercivity.

Taking sintered NdFeB magnets as an example, the addition of alloying elements and the optimization of the heat treatment process are important ways to improve coercivity. Elements such as Dysprosium (Dy), Terbium (Tb), and Cobalt (Co) are often added to NdFeB alloys. Dy and Tb can replace part of the Neodymium (Nd) in the main phase Nd2Fe14B, increasing the anisotropy field of the material (the magnetic field required to reverse the magnetic moments of the magnetic domains), thereby enhancing the pinning effect on magnetic domain walls and significantly improving Hci. For example, adding 2-3% Dy to NdFeB magnets can increase Hci from 10,000 Oe to 15,000 Oe or higher. However, the addition of Dy and Tb also has drawbacks: these elements are rare and expensive, which increases the cost of the magnet; at the same time, they will reduce the remanence and saturation magnetization of the magnet. Therefore, there is a trade-off between coercivity and remanence in the design of NdFeB magnets. Co can improve the temperature stability of coercivity, making the magnet's Hci less sensitive to temperature changes, which is suitable for high-temperature applications.

Temperature has a significant impact on coercivity, and like remanence, the coercivity of most strong magnets also has a negative temperature coefficient—coercivity decreases as temperature increases. This is because the thermal motion of atoms at high temperatures weakens the pinning effect of magnetic domain walls, making it easier for magnetic domain walls to move under the action of reverse magnetic fields. The temperature coefficient of Hci is usually larger than that of Br; for example, the Hci temperature coefficient of sintered NdFeB magnets is about -0.5%/°C to -0.7%/°C. A magnet with Hci=15,000 Oe at 25°C will have an Hci of only about 15,000 15,000 × 0.6% × 75 = 10,500 Oe at 100°C. This characteristic is particularly important for high-temperature applications: if the coercivity of the magnet is too low at high temperatures, it may be demagnetized by the external demagnetizing field (such as the armature reaction magnetic field in motors), leading to permanent failure of the device. Samarium cobalt magnets have better high-temperature coercivity stability, with an Hci temperature coefficient of about -0.1%/°C to -0.2%/°C, so they are widely used in high-temperature environments such as aerospace and oil drilling.

The practical application value of coercivity is reflected in ensuring the long-term stability and reliability of magnetic devices. In most engineering applications, magnets work in a certain demagnetizing field environment. For example, in permanent magnet motors, the armature reaction generates a reverse magnetic field during operation; in magnetic sensors, the magnet may be affected by external interference magnetic fields; in magnetic separators, the magnet is in contact with magnetic materials for a long time, which may also generate a certain demagnetizing effect. If the coercivity of the magnet is insufficient, it will be gradually demagnetized under the action of these demagnetizing fields, resulting in a decrease in the magnetic field strength, which in turn affects the performance of the device. For example, if the Hci of the magnet in an electric vehicle motor is too low, after long-term operation at high temperatures, the magnet will be demagnetized, leading to a decrease in the motor's power and efficiency, and even affecting the vehicle's driving range. Therefore, when selecting magnets, it is necessary to ensure that the coercivity of the magnet is sufficiently high to resist the maximum demagnetizing field encountered during operation, and a certain safety margin should be considered.

It should be emphasized that the selection of coercivity is not as high as possible. Higher coercivity usually means higher material costs (such as the addition of rare earth elements like Dy) and lower remanence. Therefore, a balance should be struck between coercivity, remanence, and cost according to the specific application scenario. For example, in low-temperature, low-demagnetizing-field environments (such as small household appliances), magnets with moderate coercivity and high remanence can be selected to reduce costs; in high-temperature, high-demagnetizing-field environments (such as automotive engines and aerospace equipment), magnets with high coercivity (even if the remanence is slightly lower) should be selected to ensure stability.

In summary, coercivity (including Hcb and Hci) is a critical parameter reflecting the anti-demagnetization ability and magnetic stability of strong magnets. Its magnitude is determined by the material's microstructure, composition, and pinning effect of magnetic domain walls, and is significantly affected by temperature. In engineering applications, the correct selection of magnets with appropriate coercivity values is essential to ensure the long-term reliable operation of magnetic devices. With the development of magnetic material technology, research directions such as reducing the dependence on rare earth elements (such as developing Dy-free high-coercivity NdFeB magnets) and improving the high-temperature coercivity stability are constantly advancing, which will further expand the application range of strong magnets and improve the performance of related equipment.