The maximum energy product, denoted by (BH)max, is a comprehensive magnetic performance parameter of strong magnets that integrates remanence (Br) and coercivity (Hc). It represents the maximum energy density that a magnet can store and release in a magnetic circuit, directly reflecting the "energy storage capacity" of the magnet. Unlike Br and Hc, which reflect single aspects of magnetic performance, (BH)max is a synthetic indicator that comprehensively evaluates the magnetic performance of a magnet. Its unit is Mega-Gauss-Oersted (MGOe) or Kilo-Joule per cubic meter (kJ/m³), with 1 MGOe ≈ 7.9577 kJ/m³. For strong magnets, (BH)max is often the most important parameter considered in engineering applications, as it directly determines the volume and weight of the magnet required for a given application.

To understand the maximum energy product, it is necessary to start with the B-H hysteresis loop of the magnet. The B-H hysteresis loop is a closed curve describing the relationship between magnetic induction intensity (B) and magnetic field strength (H) during the magnetization and demagnetization of a magnet. In the second quadrant of the B-H loop (the demagnetization curve), each point (H, B) on the curve corresponds to a certain working state of the magnet. The product of B and H at each point (i.e., BH) represents the energy density of the magnet in that working state. As H changes from 0 to -Hcb (the coercivity of magnetic induction), the BH value first increases to a maximum and then decreases. This maximum value is the maximum energy product (BH)max. Therefore, (BH)max is the peak value of the BH product on the demagnetization curve of the magnet, which is determined by the shape and position of the demagnetization curve.

The physical meaning of (BH)max can be understood as the maximum work that a unit volume of magnet can do in a magnetic circuit. In a permanent magnet device, the magnet provides magnetic energy to the circuit, and the (BH)max value determines how much magnetic energy the magnet can supply per unit volume. A higher (BH)max means that the magnet can provide more magnetic energy with a smaller volume, which is crucial for the miniaturization and lightweight design of devices. For example, if two magnets have (BH)max values of 35 MGOe and 50 MGOe respectively, to generate the same magnetic energy, the volume of the 35 MGOe magnet needs to be about 1.43 times that of the 50 MGOe magnet (since the volume is inversely proportional to (BH)max under the same energy requirement). This is particularly important in applications with strict volume and weight constraints, such as electric vehicles, aerospace equipment, and portable electronic devices.

The measurement of (BH)max is based on the measurement of the demagnetization curve. First, use a hysteresisgraph or VSM to measure the demagnetization curve (the second quadrant of the B-H loop) of the fully magnetized magnet; then, calculate the BH product for each point on the curve; finally, find the maximum value of these products, which is (BH)max. The accuracy of the measurement depends on the accuracy of the B and H measurements. During the measurement, it is necessary to ensure that the sample is in a closed magnetic circuit as much as possible to reduce magnetic flux leakage, which otherwise will cause deviations in the measured B value and thus affect the (BH)max result. In addition, the temperature during measurement also affects (BH)max, so the measurement is usually carried out at a standard temperature (25°C) unless otherwise specified.

The maximum energy product (BH)max of strong magnets is closely related to remanence (Br) and coercivity (Hc). In general, (BH)max increases with the increase of Br and Hc, but there is a mutual constraint between Br and Hc. For a given magnetic material, improving Hc (e.g., by adding Dy to NdFeB magnets) often leads to a decrease in Br, and vice versa. Therefore, (BH)max is the result of the balance between Br and Hc. The theoretical maximum value of (BH)max for a magnetic material is (Br/2)²/(μ0), which is derived under the ideal condition that the demagnetization curve is a straight line from (0, Br) to (-Hc, 0) and Hc = Br/μ0. This theoretical value is called the "ideal maximum energy product". In practice, due to the non-ideal shape of the demagnetization curve (the curve is usually concave), the actual (BH)max is lower than the theoretical value. For example, the theoretical maximum (BH)max of Nd2Fe14B is about 64 MGOe, while the actual (BH)max of high-performance sintered NdFeB magnets can reach 55-60 MGOe, approaching the theoretical limit.

Material composition and microstructure are the fundamental factors determining (BH)max. For sintered NdFeB magnets, the key factors affecting (BH)max include the purity of the Nd2Fe14B main phase, the degree of orientation, grain size, and the distribution of the Nd-rich phase. A high-purity main phase ensures a high Br; a high degree of orientation makes the demagnetization curve steeper, increasing the BH product; fine and uniform grain sizes reduce magnetic flux leakage at grain boundaries, improving the utilization of magnetic energy; and a uniform distribution of the Nd-rich phase (which acts as a pinning center for magnetic domain walls) improves Hc, thereby balancing Br and Hc to increase (BH)max. For example, by optimizing the sintering temperature and time, the grain size of NdFeB magnets can be controlled between 3-5 μm, and the degree of orientation can be increased to over 95%, which significantly improves (BH)max.

Temperature has a significant impact on (BH)max. Since both Br and Hc decrease with increasing temperature, (BH)max also decreases with increasing temperature. The temperature coefficient of (BH)max is usually the sum of the temperature coefficients of Br and Hc (with appropriate weight coefficients), so it has a larger negative temperature coefficient than either Br or Hc. For example, the temperature coefficient of (BH)max for sintered NdFeB magnets is about -0.8%/°C to -1.0%/°C. A magnet with (BH)max=50 MGOe at 25°C will have a (BH)max of only about 50 50 × 0.9% × 75 = 16.25 MGOe at 100°C, which is a significant decrease. This means that in high-temperature applications, the energy storage capacity of the magnet is greatly reduced, and a larger volume of magnet is required to compensate for this loss. Samarium cobalt magnets have better high-temperature stability of (BH)max, with a temperature coefficient of about -0.3%/°C to -0.5%/°C, so they are more suitable for high-temperature energy storage applications.

The practical application of (BH)max is mainly reflected in the selection and design of magnets. In engineering design, the required magnetic energy of the device is first determined according to the performance requirements; then, the minimum volume of the magnet is calculated based on the (BH)max value of the selected magnet. For example, in the design of a permanent magnet synchronous motor for an electric vehicle, the required magnetic flux of the motor is determined based on the power and torque requirements; then, the volume of the rotor magnet is calculated according to the (BH)max of the selected NdFeB magnet. Using a magnet with a higher (BH)max can significantly reduce the volume and weight of the rotor, thereby improving the power density of the motor and reducing the overall weight of the vehicle, which is conducive to improving the driving range. In addition, (BH)max is also an important indicator for classifying strong magnets. For example, sintered NdFeB magnets are divided into different grades according to (BH)max, such as N35 (33-36 MGOe), N45 (43-46 MGOe), N52 (50-53 MGOe), etc. The higher the grade, the higher the (BH)max and the better the magnetic performance.

It should be noted that (BH)max is not the only parameter to consider in all applications. In some cases, such as high-temperature or high-demagnetizing-field environments, coercivity (especially Hci) may be more critical than (BH)max. For example, a magnet with a high (BH)max but low Hci may be demagnetized quickly in a high-temperature environment, losing its magnetic performance, while a magnet with a slightly lower (BH)max but high Hci can maintain stable performance for a long time. Therefore, in practical applications, it is necessary to comprehensively consider (BH)max, Br, Hci, temperature stability, and cost to select the most suitable magnet.

In recent years, with the continuous demand for high-performance magnetic devices, the research on improving the (BH)max of strong magnets has never stopped. For NdFeB magnets, the main research directions include optimizing the alloy composition (such as developing rare-earth lean or Dy-free alloys), improving the preparation process (such as hot-pressed and hot-deformed NdFeB magnets with higher degree of orientation), and modifying the microstructure (such as introducing nanocomposite structures to balance Br and Hc). For example, nanocomposite NdFeB magnets, which consist of fine grains of Nd2Fe14B and α-Fe, have the potential to achieve higher (BH)max because α-Fe has a high saturation magnetization, which can improve Br, while the Nd2Fe14B phase provides high Hci. Although the current (BH)max of nanocomposite magnets is still lower than that of sintered NdFeB magnets, it has broad development prospects due to its low rare earth content and low cost.

In summary, the maximum energy product ((BH)max) is a comprehensive indicator of the magnetic performance of strong magnets, integrating the effects of remanence and coercivity. It directly reflects the energy storage capacity of the magnet and is the key parameter for determining the volume and weight of the magnet in engineering applications. The (BH)max value is determined by the material's composition, microstructure, and the shape of the demagnetization curve, and is significantly affected by temperature. In the selection and design of magnets, it is necessary to comprehensively consider (BH)max and other parameters according to the specific application requirements to ensure the optimal performance and cost-effectiveness of the device. With the continuous progress of magnetic material technology, the (BH)max of strong magnets will continue to approach the theoretical limit, providing stronger support for the development of high-efficiency, miniaturized magnetic devices.