1. Remanence (Br): The Core Parameter of Magnetic Flux Retention

Remanence, denoted by the symbol Br, is one of the most fundamental and critical magnetic performance parameters of strong magnets. It refers to the magnetic induction intensity remaining in a magnet after the magnet has been fully magnetized to saturation and then the external magnetic field is removed to zero. In essence, remanence quantifies the maximum magnetic flux density that a magnet can retain in a closed magnetic circuit, directly reflecting the "residual magnetic strength" of the magnet. For strong magnets such as neodymium iron boron (NdFeB) and samarium cobalt (SmCo), remanence is a primary indicator of their magnetic output capability, and its unit is typically Tesla (T) or Gauss (G), with 1 T = 10,000 G.

To understand remanence comprehensively, it is necessary to connect it with the magnetization process of magnetic materials. Strong magnets are ferromagnetic materials, and their internal structure consists of numerous magnetic domains—small regions where the magnetic moments of atoms are aligned in the same direction. In the unmagnetized state, these magnetic domains are randomly oriented, and their magnetic moments cancel each other out, resulting in no net magnetic field externally. When an external magnetic field is applied, the magnetic domains gradually rotate and align with the direction of the external field. As the external field strength increases, more magnetic domains align until all magnetic domains are oriented in the same direction; at this point, the magnet reaches saturation magnetization (Ms). When the external field is removed, due to the pinning effect of defects (such as grain boundaries, impurities, and dislocations) in the magnetic material, the magnetic domains cannot return to their original random state, and a certain degree of magnetic induction intensity is retained—this is remanence.

The measurement of remanence is typically carried out using a hysteresisgraph or a vibrating sample magnetometer (VSM), which are standard instruments in the field of magnetic material testing. The measurement process generally involves the following steps: first, the sample magnet is placed in a closed magnetic circuit (to minimize magnetic flux leakage, ensuring accurate measurement); then, a sufficiently strong external magnetic field is applied to saturate the magnet; next, the external magnetic field is slowly reduced to zero; finally, the magnetic induction intensity at this point is measured, which is the remanence value. It should be noted that the measurement results are affected by factors such as the shape, size, and surface state of the sample. For example, irregularly shaped magnets may have uneven magnetization, leading to deviations in remanence measurements; therefore, standard sample sizes (such as cylindrical or cuboid) are usually used in formal tests.

The remanence value of strong magnets is determined by a variety of factors, with material composition and microstructure being the most critical. For neodymium iron boron magnets, the main phase is Nd2Fe14B, which has a high saturation magnetization. The purity of the Nd2Fe14B phase, the grain size, and the degree of orientation all directly affect remanence. A higher purity of the main phase (fewer impurity phases such as Nd-rich phases) means more magnetic moments contributing to the remanent magnetic field; fine and uniform grain sizes can reduce the pinning effect of grain boundaries to a certain extent, facilitating the alignment of magnetic domains; and a higher degree of orientation (i.e., the crystal axes of most grains are parallel to the magnetization direction) ensures that the magnetic moments of the magnetic domains are aligned in the optimal direction, thereby maximizing remanence. For example, sintered NdFeB magnets with a high degree of orientation can have a remanence of up to 1.45 T or higher, while bonded NdFeB magnets, due to the low degree of orientation of the magnetic powder and the presence of non-magnetic binders, have a lower remanence, generally between 0.6-1.1 T.

Temperature is another important factor affecting remanence. Most strong magnets exhibit a negative temperature coefficient of remanence, meaning that as the temperature increases, the remanence decreases. This is because the thermal motion of atoms intensifies at higher temperatures, which disrupts the alignment of magnetic domains, leading to a decrease in the residual magnetic induction intensity. For example, the temperature coefficient of remanence for sintered NdFeB magnets is typically -0.11%/°C to -0.13%/°C; if a magnet with a Br of 1.4 T at 25°C is used at 100°C, its remanence will decrease to approximately 1.4 1.4 × 0.12% × 75 = 1.278 T. This temperature dependence is crucial for applications in high-temperature environments, such as automotive engines and aerospace equipment, where magnets with low temperature coefficients (such as samarium cobalt magnets, whose Br temperature coefficient is about -0.03%/°C) are often selected to ensure stable magnetic performance.

The practical significance of remanence in engineering applications is enormous. It directly determines the magnetic flux density that a magnet can provide in a given magnetic circuit, thereby affecting the performance of devices such as motors, sensors, and magnetic separators. For example, in permanent magnet motors, a higher remanence of the magnet means that the motor can generate a higher back electromotive force under the same rotor size, improving the motor's power density and efficiency. A 10% increase in remanence can reduce the volume of the magnet by about 10-15% while maintaining the same motor performance, which is crucial for miniaturization and lightweight design of equipment such as electric vehicles. In magnetic separation equipment, a higher remanence ensures a stronger magnetic field in the separation area, improving the separation efficiency of magnetic minerals or impurities. In contrast, if the remanence of the magnet is too low, it may not be able to meet the magnetic field requirements of the device, leading to reduced performance or even failure.

It should be distinguished from saturation magnetization (Ms). Although both are related to the magnetic moment alignment of magnetic domains, Ms is the maximum magnetic moment per unit volume when all magnetic domains are perfectly aligned, which is an intrinsic property of the material; while Br is the residual magnetic induction intensity after the external field is removed, which is an extrinsic property affected by the material's microstructure, shape, and measurement conditions. For ideal soft magnetic materials, Br is close to zero because their magnetic domains can easily return to a random state after the external field is removed; for hard magnetic materials (strong magnets), Br is much higher, which is the fundamental reason why they can retain magnetism for a long time.

In summary, remanence is a core parameter that reflects the magnetic retention capability of strong magnets. Its magnitude is determined by material composition, microstructure, and orientation, and is affected by temperature and measurement conditions. In engineering applications, selecting a magnet with an appropriate remanence value based on the specific requirements of the device (such as magnetic field strength, volume constraints, and temperature environment) is crucial to ensuring the performance and reliability of the equipment. With the continuous development of magnetic material technology, improving the remanence of strong magnets (such as through the development of rare-earth permanent magnet materials with higher Ms, optimizing the sintering process to improve the degree of orientation) has always been a key research direction in the field, which will further promote the miniaturization, high-efficiency, and energy-saving of magnetic devices.