Magnetization Curves and Magnetic Properties 

Author: Mike Gedeon, Market Manager for Telecomm & Server 

When a magnetic material is placed into a magnetic field , it’s magnetic dipoles will align to create a response magnetization , which will combine with the applied field to generate a magnetic induction .  If the response were linear, it would be an easy calculation. However, the response is nonlinear, resulting in hysteresis curves when the applied magnetic field is cycled. 

The magnetization curve of a magnetic material is as descriptive of a material’s magnetic properties as its stress-strain curve is descriptive of its mechanical properties. Just as key tensile properties can be found on a stress-strain curve, key magnetic properties can also be found on the magnetization curve.

The first thing to note is that there are two types of magnetization curves generated in response to an applied field. M-H curves focus on the internal response of the magnetic material, while B-H curves focus on the magnetic induction. Therefore, it is important to know what type of curve you are looking at when trying to determine magnetic properties.

Figure 1 shows schematically what happens when a magnetic field  is applied to a magnetic material. As the field increases in strength, the magnetic moment of the material ( increases as well, as the magnetic dipoles begin to align with the applied magnetic field. That is, the material is becoming magnetically polarized. Since M is increasing, the corresponding magnetic induction  increases as well. Eventually, when the magnetic dipoles are fully aligned with the field,  can increase no more. This is known as the saturation magnetization.

The slope of the magnetization curve is the magnetic permeability (μ) of the material. Note, however, that the initial magnetization is usually not a straight line! This means that the magnetic permeability will vary depending on the magnetic field strength. Often, test labs will therefore report 3 values of permeability. These will be the initial (low slope), intermediate (maximum slope), and the final (lower slope again). Since the longest, linear part of the curve is the maximum slope, this would often be considered to be the default permeability.

Figure 1 – Initial Magnetization Curve.  When a magnetic material is placed in a magnetic field, the magnetization (M) and the associated induction (B) will increase. The rate of increase is determined by the magnetic permeability of the material.

Figure 2 shows a full hysteresis curve for a ferromagnetic material. I chose a ferromagnetic material since it is easy to see the features of the hysteresis curve, but even soft magnetic materials will show the same features, although the curve will be a different shape.

After the material is originally magnetized to saturation, the magnetic file is reduced to zero and reversed. When the applied field drops to a strength of zero, there is still residual magnetization  in the material, resulting in an induction  that is greater than zero. This residual manetization or inductance is known as Remanance. On a B-H curve, this would be designated as .  On an M-H curve, it will be designated as . Since the applied field  is zero,  in SI units, and  in Gaussian (cgs) units.

As the magnetic field continues to strengthen in the direction opposite the initial saturation, the induction will continue to fall and will eventually reverse. On the way down, there will be a point where the net induction  is zero. (This is where the B-H curve crosses the X axis). The applied magnetic field strength where this happens is called the coercivity (H_C). At this point, the applied field  is negative, and it is exactly balanced out by the remaining positive magnetic moment of the material.

As the magnetic field becomes stronger in the negative direction, eventually the magnetic moment will also become equal to zero. (In other words, this is where the M-H curve crosses the X axis.)  The applied magnetic field strength where this happens is called the intrinsic coercivity (H_Ci). Since the hysteresis curve crosses the X axis on an M-H curve outside of where it crosses on a B-H curve, H_Ci>H_C.  

Eventually, saturation will be reached in the other direction. If the field is reversed again, the material will return to saturation along a curve equal and opposite the demagnetization curve.  In other words, the re-magnetization curve will be equal to the demagnetization curve flipped symmetrically across both axes.

Figure 2 – Magnetic Hysteresis Curve of a Ferromagnetic Material.  The magnetic remanence (Br) is the residual induction when the applied magnetic field drops to zero after reaching saturation.  (where the hysteresis loop crosses the Y axis (induction). The coercivity H_c) is the reversed magnetic field strength required to demagnetize the saturated material. This is where the hysteresis loop crosses the X axis (applied field strength). 

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