Dear Youssef Esshouba

The magnetic susceptibility (χ ) of a material is related to the magnetization (M) resulting from an applied magnetic field (H) -> (χ=dM/dH).

In a hysteresis loop (obtained in a VSM, for example), χ varies from point to point on the curve as H grows from 0 to the maximum value (Hmax).

Thus, a good alternative to determine X of the studied material would be to perform several hysteresis cycles as a function of Hmax. Determine the saturation magnetization (Msat) in these cycle and then plot Msat as a function of Hmax and from this graph determine the susceptibility of the material.

1. The magnetic permeability m is roughly the ratio of the magnetic induction B (magnetic flux density) to the magnetic field strength H: B = mH (in the SI system B = mm0H). In the Gaussian system of electromagnetic units, permeability is expressed in terms of magnetic susceptibility as m = 1+4pi*x, in the International System of Units as m = 1+x, therefore, the value of susceptibility in these systems differs by a factor of 4pi, and when switching to permeability, this difference must be taken into account, depending on the units in which you register the primary data from the hysteresis loop.

2. It is necessary to distinguish the initial magnetization curve (realized at the first magnetization from the demagnetized state) from hysteresis cycles.

3. Depending on the needs introduce several types of permeability:

a) differential md = dB/dH,

b) initial ma = md (at H = 0),

c) maximal mmax = max md,

d) full mc as the ratio achieved in this field, the values of magnetic induction to the value of this field strength (this is the achieved value of B for each H, apparently, what Carlos meant in his answer),

f) average (in saturation field Hs): ms = Bs/Hs, i.e. ms = mc (at H = Hs)

and others.

Dear Youssef,

I will describe in more detail the procedure for your data and the notation system.

In the Gaussian system we have: Magnetization = M*d, where d is the density of your material, M is your value of specific magnetization, M = magnetic moment of sample/mass. Otherwise: Magnetization = magnetic moment of sample/V, where V is the volume of your sample. The dimensions of these units are: [magnetic moment] = 1 emu = 1 Gs*cm^3, [M] = 1 emu/g , [Magnetization] = 1 Gs.

You need to first plot the dependence of B(H) using an expression linking magnetic induction (magnetic flux density) with magnetization and an external field:

B [Gs] =4 pi *M +H [Oe].

The following steps were described in my previous post.

In addition, sometimes it is necessary to take into account the influence of the sample shape on the magnetization curve.

One more remark concerns Carlos' message. Be careful, most likely, in his answer, the letter M indicates exactly the magnetization (in Gs units, as it is usually meant), and not your specific magnetization (expressed in emu/g), which is a more convenient value when taking measurements. If you use the expression x = dM/dH, meaning by M the specific magnetization, you will need to specify this specifically in order to avoid confusion or misunderstanding.

I hope this helps you.

Magnetic permeability is the value dM/dH+1 where M is magnetization, H is the intensity of the external magnetic field. In ferromagnets, the magnetic permeability is not a constant value but depends on the magnetic field. Therefore, you should proceed as follows: On the initial magnetization curve M(H), select a certain point of it. Draw a tangent line to the curve at this point and find the tangent of the angle of inclination of this tangent line to the H axis (it means the tangent of a physical angle, not a geometric one, i.e. the M/H ratio). This will be the value of dM/dH at this point of the curve. Add 1 to it and this is the magnetic permeability for that field value. Do this for many points of the curve and you will get the dependence of the magnetic permeability on the intensity of the external magnetic field. In this formula, the unit can be neglected only for field values in the middle of the scale, but at the beginning of the field and, especially, in the saturation field, this unit plays the main role. Keep in mind that H and M must be in the same units, for example A/m.

Dear Youssef,

Please note that Yuriy in his post described a situation where the data is presented in the SI system, and in your case the measurements are carried out and the data is expressed in the Gaussian system. Therefore, either you must first convert them to the SI system, or add a 4pi coefficient to Yuriy's formulas.

check our website

https://www.txemm.com/services/material-characterization/magnetic-hysteresis

The magnetic permeability can be calculated from the hysteresis loop by finding the area enclosed by the loop. This area is equal to the product of the maximum magnetization (Mmax) and the maximum applied field (Hmax).

The magnetic permeability is then calculated as:

μ = Mmax/Hmax

This relation is known as the B-H loop equation. It is important to note that the magnetic permeability is a material property and is independent of the size of the sample.