For permanent magnets like NdFeB, we primarily utilize their ability to generate and retain magnetism. This is the most fundamental functional requirement for magnetic materials. So how do we measure this ability? We typically use four indicators: remanence Br, coercivity Hcb, intrinsic coercivity Hcj, and maximum magnetic energy product BH(max).
To truly understand these indicators, we must first understand the demagnetization curve. Because permanent magnets must first be magnetized, these magnets must withstand various adverse effects during use. The demagnetization curve effectively reflects the overall performance of the magnet.
The figure above shows a typical hysteresis loop for a permanent magnet. The first quadrant represents the magnetization curve, the second quadrant represents the demagnetization curve, the third quadrant represents the reverse magnetization curve, and the fourth quadrant represents the reverse demagnetization curve. The horizontal axis represents the applied magnetic field H, and the vertical axis represents the magnetic induction B and the magnetic polarization J. [Simply put, the magnetic induction B is the sum of the external magnetic field and the internal magnetic field of the magnet, and the magnetic polarization J is the internal magnetic field of the magnet.] The four magnetic properties—remanence, coercivity, intrinsic coercivity, and maximum magnetic energy product—are all derived from the demagnetization curve. The red line in the figure above is the J-H demagnetization curve (the curve plotting the magnetic polarization J versus the applied magnetic field H), also called the intrinsic demagnetization curve. The blue line is the B-H demagnetization curve (the curve plotting the magnetic induction B versus the applied magnetic field H). Small squares represent magnetic domains. Magnetic domains can be thought of as tiny magnets. A magnet is composed of many domains. The arrows indicate the spontaneous magnetization direction (C-axis) of the domains. For a permanent magnet in a magnetically neutral state (simply understood as an uncharged magnet), the magnetic domains are mostly located in the same coordinate system but their directions cancel each other out, resulting in no apparent magnetism, as shown in Figure 1.
Figure 1
When a magnetic field is applied along the magnetization direction, the magnetic domains gradually shift and rotate through domain walls, aligning their C-axes, as shown in Figures 2 and 3. This is the magnetization curve. The magnetic polarization intensity corresponding to the saturation magnetization is called the saturation magnetic polarization intensity, Js.
Figure 2
Figure 3
When a magnet reaches saturation magnetization and the external magnetic field is removed, the majority of the magnetic domains maintain their orientation. A few rotate slightly, but the orientation remains unchanged, as shown in Figure 4. This results in both the magnetic flux density and magnetic polarization remaining high. This value is called the remanent magnetic flux density Br or remanent magnetic polarization Jr. Intuitively, this represents the magnetic flux density B or magnetic polarization J remaining after the external magnetic field is removed from the saturated magnet. When the external magnetic field H is zero, Br = Jr. Br is often used to describe what we commonly call remanence, expressed in Gs or T.
The higher Br, the greater the retained magnetic flux density, and the greater the potential for a strong magnetic material.
Figure 4
When the applied external magnetic field increases in the reverse direction, the magnetic domains of the magnet gradually shift and rotate, as shown in Figure 5. When the magnetic field strength reaches a certain value, the magnetic induction intensity (B) of the magnet drops to zero. Simply put, the magnetic field strength retained within the magnet and the external reverse magnetic field cancel each other out. The corresponding magnetic field strength at this point is called the magnetic coercivity (Hcb) (also written as bHc), with units of Oe or kA/m. The magnetic coercivity (Hcb) is closely related to the slope of the J-H demagnetization curve. If the magnetic domains of the magnet are unlikely to shift or rotate in the short term, the J-H curve will be very straight, and Hcb will approach Br. The upper limit of Hcb is Br, where Hcb = Br. This is the ideal situation, meaning that no magnetic domain reversal occurs before the reverse magnetic field strength reaches Br. This means that the magnet is very stable, meaning that the magnet is very resistant to demagnetization when the reverse magnetic field strength is initially below Br.
Figure 5
When the reverse magnetic field continues to increase, it reaches a critical value, causing reverse magnetic domains to rapidly emerge, causing the magnetic polarization intensity of the magnet to rapidly drop to zero. Simply put, the magnetic field strength retained within the magnet drops to zero, as shown in Figure 6. The corresponding magnetic field strength at this point is called the intrinsic coercivity, Hcj (also written as jHc), with units of Oe or kA/m. The intrinsic coercivity is a physical quantity that reflects the magnet’s resistance to demagnetization. The greater the intrinsic coercivity, the greater the resistance to demagnetization, or more precisely, the greater the resistance to complete demagnetization. It’s important to note the difference between Hcj and Hcb. When Hcj is greater than Br, the limit value of Hcb is Br. When Hcj is less than Br, the limit value of Hcb is Hcj.
Figure 6
The product of B and H corresponding to any point on the B-H demagnetization curve is called the magnetic energy product. The maximum value is the maximum magnetic energy product (BH)max. Theoretically, the maximum magnetic energy product (BH)max = (½ Br)². The maximum magnetic energy product takes into account both remanence and coercivity. Its value represents the amount of magnetic energy contained in the magnet and also reflects the initial slope of the J-H curve. The unit is GOe or j/m³.
If the above four parameters are still difficult to understand, you can simply think of a magnet as a glass of water. Magnetization is heating, remanence is the heat of the water after heating stops, and demagnetization is like cooling the water. Hcb is the value at which the ambient temperature reaches a certain level at which the heat of the water is offset, resulting in no external heat. Hcj is the ambient temperature required to completely reduce the heat of the water to zero. Below is a simplified diagram of the second quadrant of the hysteresis loop to help you deepen your understanding of the relevant concepts.
Regarding the above magnetic parameters, we should pay attention to the following points in practical applications:
1. For magnets requiring a strong magnetic field, we generally need to maximize their remanence to release more magnetism. However, it is important to note that this assumes no demagnetization. If demagnetization is present, simply increasing the remanence may be ineffective. It is also necessary to increase Hcj to reduce demagnetization. For the simplest example, for a D10*1 disc magnet, the surface magnetism of a 52H magnet is higher than that of an N52 magnet. This is because the higher Hcj of a 52H magnet allows its Br to be fully utilized, while the lower Hcj of an N52 magnet prevents it from demagnetizing. Therefore, even a higher Br value will not fully utilize its magnetism.
2. For magnets requiring strong resistance to demagnetization and stability, we generally need to increase Hcj and keep the Hcb value as close to the Br value as possible.
3. For magnets that require good temperature resistance, we usually choose to increase Hcj. Because the temperature coefficient of coercivity of NdFeB permanent magnets with the same Hcj is not much different, the most direct effect of increasing Hcj is to make the inflection point of the B-H line appear as late as possible or not appear at all. If strict requirements are placed on temperature stability, the requirements for Hcb must also be considered. Try to reduce the slope of the B-H line as much as possible to reduce the irreversible attenuation of the magnet.