{"id":23717,"date":"2026-07-20T14:07:05","date_gmt":"2026-07-20T06:07:05","guid":{"rendered":"https:\/\/www.cndailymag.com\/?p=23717"},"modified":"2026-07-20T15:51:38","modified_gmt":"2026-07-20T07:51:38","slug":"a-detailed-explanation-of-remanence-coercivity-intrinsic-coercivity-and-maximum-energy-product-using-hysteresis-loops","status":"publish","type":"post","link":"https:\/\/www.cndailymag.com\/ja\/explanation-of-remanence-coercivity-intrinsic-coercivity-and-maximum-energy-product-using-hysteresis-loops\/","title":{"rendered":"A detailed explanation of remanence, coercivity, intrinsic coercivity, and maximum energy product using hysteresis loops."},"content":{"rendered":"

For permanent magnet materials such as neodymium iron boron (NdFeB), we primarily utilize their ability to generate and retain magnetism. This is the most basic functional requirement for magnetic materials. So how do we measure a magnet’s ability to generate and retain magnetism? We typically use four indicators: remanence (Br), coercivity (Hcb), intrinsic coercivity (Hcj), and maximum energy product (BH(max)).<\/p>\n

To truly understand these indicators, we must first understand demagnetization curves. Because permanent magnet materials need to be magnetized before use, and the magnetized permanent magnet must withstand various factors detrimental to its magnetic properties during use, the demagnetization curve effectively reflects the overall performance of the magnet.<\/p>\n

Hysteresis loop of permanent magnet materials:<\/em>\"\"

The image above is a typical hysteresis loop of a permanent magnet. The first quadrant is the magnetization curve, the second quadrant is the demagnetization curve, the third quadrant is the demagnetization curve, and the fourth quadrant is the anti-demagnetization curve. The horizontal axis represents the applied magnetic field strength H, and the vertical axis represents the magnetic flux density (B) and magnetic polarization intensity (J). In simple terms, magnetic flux density B is the sum of the applied magnetic field and the magnet’s internal magnetic field, while magnetic polarization J is the magnet’s internal magnetic field. Remanence, coercivity, intrinsic coercivity, and maximum energy product\u2014these four magnetic property parameters all originate from demagnetization curves. In the above figure, the red line is called the J-H demagnetization curve (the curve showing the change in magnetic polarization J versus the applied magnetic field H), also known as the intrinsic demagnetization curve. The blue line is called the B-H demagnetization curve (the curve showing the change in magnetic flux density B versus the applied magnetic field H). We use small squares to represent individual magnetic domains. A magnetic domain can be understood as a tiny magnet; a magnet is composed of many magnetic domains. The arrows indicate the spontaneous magnetization direction of the domains along the C-axis. For a magnetically neutral permanent magnet (simply put, a magnet that has never been magnetized), most of the magnetic domains are at the same coordinate but their directions cancel each other out, thus not exhibiting magnetism externally, as shown in Figure 1.<\/p>\n

When a magnetic field is applied along the magnetization direction, the magnetic domains gradually shift and rotate through their domain walls, aligning their C-axis directions, as shown in Figures 2 and 3. This is the magnetization curve. The magnetic polarization intensity value corresponding to saturation magnetization is called the saturation magnetic polarization intensity Js.<\/p>\n

Figures 2 and 3 show the magnetic field. After the magnet is saturated and the applied magnetic field is removed, it can be seen from the figures that most of the magnetic domains maintain their direction, while a small number rotate slightly but their main direction remains unchanged, as shown in Figure 4. In this way, both the magnetic flux density and magnetic polarization intensity of the magnet retain high values. This value is called the remanent magnetic flux density Br or remanent magnetic polarization intensity Jr. Intuitively, it is the remaining magnetic flux density B or magnetic polarization intensity J of a saturated magnet after the external magnetic field is removed. When the applied magnetic field H is 0, Br = Jr. We often use Br to describe this, which is the most common term for remanence, measured in Gs or T.<\/p>\n

The higher the Br, the stronger the retained magnetic flux density, and the greater the potential to become a strong magnetic material.<\/p>\n

Refer Figure 4<\/p>\n

When the applied external magnetic field increases in the opposite 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 flux density B of the magnet drops to 0. Simply put, the magnetic field strength retained inside the magnet and the applied reverse magnetic field strength cancel each other out. The corresponding magnetic field strength value 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. In this case, Hcb will be infinitely close to Br, and the upper limit of Hcb is Br. Hcb = Br is the ideal situation, meaning that no magnetic domain reversal tendency occurs before the reverse magnetic field strength reaches Br. In this case, the magnet is very stable, meaning that the magnet has a very strong resistance to demagnetization in an initial state with a reverse magnetic field strength below Br.<\/p>\n

Refer Figure 5<\/p>\n

As the reverse magnetic field continues to increase, it reaches a critical value, causing reverse magnetic domains to rapidly appear. This results in the magnet’s magnetic polarization rapidly decreasing to 0. Simply put, the magnetic field strength retained inside the magnet drops to zero, as shown in Figure 6. The corresponding magnetic field strength value at this point is called the intrinsic coercivity Hcj (also written as jHc), with units of Oe or kA\/m. Intrinsic coercivity is a physical quantity reflecting the magnet’s resistance to demagnetization. The greater the intrinsic coercivity, the stronger the resistance to demagnetization, or more precisely, the stronger the resistance to complete demagnetization. It is important to note the difference between Hcj and Hcb. When Hcj is numerically greater than Br, the limit of Hcb is Br; when Hcj is numerically less than Br, the limit of Hcb is Hcj.<\/p>\n

Refer Figure 6<\/p>\n

The product of B and H at 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 = (\u00bd Br)\u00b2. The maximum magnetic energy product takes into account both remanence and coercivity, and its value represents the amount of magnetic energy contained in the magnet. It can also reflect the initial inclination of the J-H line, and the unit is GOe or j\/m\u00b3.<\/p>\n

If the above four parameters are still difficult to understand, you can simply think of the magnet as a cup of water. Magnetization is like heating, remanence is like the heat in the water after heating stops, demagnetization is like cooling the water, Hcb is the temperature at which the ambient temperature reaches a certain value, canceling out the heat in the water, and Hcj is the ambient temperature required to completely reduce the heat in the water to 0. Below is a simplified version of the hysteresis loop in the second quadrant, which can help deepen your understanding of the related concepts.<\/p>\n

Remanence Br: The intersection of the hysteresis loop and the vertical axis; it represents the magnetic flux density in the magnet after the external magnetic field weakens to zero.<\/em><\/p>\n

Coercivity Hcb: The intersection of the B-H demagnetization curve and the horizontal axis; it represents the strength of the demagnetizing field when the magnet’s flux density weakens to zero.<\/em><\/p>\n

Intrinsic Coercivity Hcj: The intersection of the intrinsic demagnetization curve and the horizontal axis; it represents the strength of the demagnetizing field when the magnet’s intrinsic magnetic polarization weakens to zero.<\/em><\/p>\n

\"\"

Regarding the above magnetic parameters, in practical applications, we should pay attention to the following points:<\/p>\n

1. For magnets requiring a strong magnetic field, we usually need to maximize their remanence to release more magnetism. However, it’s important to note that this is under the premise of no demagnetization. If demagnetization occurs, simply increasing the remanence may be ineffective; it’s also necessary to increase Hcj to reduce demagnetization. The simplest example is a D10*1 disc magnet; the surface magnetism of 54H is higher than that of N54 because 54H has a higher Hcj, allowing its Br to fully exert its magnetism. N54, on the other hand, has a very low Hcj and cannot maintain its non-demagnetized state; even with a high Br, it cannot fully exert its magnetism.<\/p>\n

2. For magnets requiring strong resistance to demagnetization and high stability, we usually need to increase Hcj, and the Hcb value should be as close as possible to Br.<\/p>\n

3. For magnets requiring good temperature resistance, we usually choose to increase Hcj because the coercivity temperature coefficient of NdFeB permanent magnets with the same Hcj is not significantly 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 at all. If strict temperature stability requirements are required, the requirements of Hcb also need to be considered to reduce the slope of the B-H line as much as possible, so as to reduce the irreversible decay of the magnet.<\/p>","protected":false},"excerpt":{"rendered":"

For permanent magnet materials such as neodymium iron boron (NdFeB), we primarily utilize their ability to generate and retain magnetism. This is the most basic functional requirement for magnetic materials. So how do we measure a magnet’s ability to generate and retain magnetism? We typically use four indicators: remanence (Br), coercivity (Hcb), intrinsic coercivity (Hcj), and maximum energy product (BH(max)). To truly understand these indicators, we must first understand demagnetization curves. Because permanent magnet materials need to be magnetized before use, and the magnetized permanent magnet must withstand various factors detrimental to its magnetic properties during use, the demagnetization curve effectively reflects the overall performance of the magnet. Hysteresis loop…<\/p>","protected":false},"author":15,"featured_media":23718,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-23717","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-technical"],"acf":[],"yoast_head":"\nA detailed explanation of remanence, coercivity, intrinsic coercivity, and maximum energy product using hysteresis loops. - Dailymag Technology | Magnet, NdFeB Magnet, Magnetic Assembly, Permanent Magnet, Linear Actuator, Sharps Container<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.cndailymag.com\/ja\/explanation-of-remanence-coercivity-intrinsic-coercivity-and-maximum-energy-product-using-hysteresis-loops\/\" \/>\n<meta property=\"og:locale\" content=\"ja_JP\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A detailed explanation of remanence, coercivity, intrinsic coercivity, and maximum energy product using hysteresis loops. - Dailymag Technology | Magnet, NdFeB Magnet, Magnetic Assembly, Permanent Magnet, Linear Actuator, Sharps Container\" \/>\n<meta property=\"og:description\" content=\"For permanent magnet materials such as neodymium iron boron (NdFeB), we primarily utilize their ability to generate and retain magnetism. This is the most basic functional requirement for magnetic materials. So how do we measure a magnet’s ability to generate and retain magnetism? We typically use four indicators: remanence (Br), coercivity (Hcb), intrinsic coercivity (Hcj), and maximum energy product (BH(max)). To truly understand these indicators, we must first understand demagnetization curves. Because permanent magnet materials need to be magnetized before use, and the magnetized permanent magnet must withstand various factors detrimental to its magnetic properties during use, the demagnetization curve effectively reflects the overall performance of the magnet. 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This is the most basic functional requirement for magnetic materials. So how do we measure a magnet’s ability to generate and retain magnetism? We typically use four indicators: remanence (Br), coercivity (Hcb), intrinsic coercivity (Hcj), and maximum energy product (BH(max)). To truly understand these indicators, we must first understand demagnetization curves. Because permanent magnet materials need to be magnetized before use, and the magnetized permanent magnet must withstand various factors detrimental to its magnetic properties during use, the demagnetization curve effectively reflects the overall performance of the magnet. 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