Origin requires fairly good parameter guess to fit the function. Your problem here appears to be the function variable is field dependent as the effective field depends on H_external and H_molecular, where the latter changes with the temperature. you probably will have to write explicit dependence of the H_effective on temperature and then redo the whole x variable to reflect this.

Relative curve plot can be seen in the web page: https://darrengoossens.wordpress.com/category/magnetism/   taken from

M I Darby 1967 Br. J. Appl. Phys. 18 1415 doi:10.1088/0508-3443/18/10/307.

My advice is that start by X=M/( ρ  x H) where ρ is density of your material. This gives you magnetic susceptibility. First start with this basic plot. Then try to fit it to your actual curve. Origin 8 does not fit realtime where origin 9 does. So I advice to work in Origin 9. 

Regards.

There may be a fundamental issue with trying to model your experiment by a "simple" Brillouin or Langevin function. This is related to the fact that [depending what your magnetic objects are] some quantities (such as the actual, "thermodynamically active" magnetic moment, i.e. the magnetization in what Murat recommends) may actually be temperature dependent. The jump in your data just below 300K might even indicate that you have some magnetic transition in this temperature range.

So you have to first make sure that using a Brillouin function makes sense physics wise. If you wish to get recommendations in this respect, then you should provide some relevant information on your specimens. In practical magnetometry there might be quite a few things to ponder before proceding to modelling/fitting!

I don't think the fit is possible with Origin.  This software "knows" how to fit expressions like y=f(x) but not the implicit relations like the one you want to attack:  M(H,T)=B(M,H,T).  The same applies to many other "data fitting" popular software products (if not to all of them).

Here is what you get if you try to...

Your measurement is NOT described by (just) a Brillouin function whatsoever.

In the fit I have fixed J (angular momentum) to 1/2, larger values give even worse agreement. So the function assumes that angular momentum is constant, saturation (limiting value for T->0) amounts to 1, I have set the g-factor to 2 (would mean pure spin, but unimportant here), fixed the Field to 1 (in T) and let the fit search for the number of such moments which yeld best agreement (only gNB as a product matters, and we don't need to think about the physics of the approach, because...)

...you see that the data are not described by this ansatz. The physics behind the measurement must be different from a moment associated with a temperature independent angular momentum.

First of all, thanks for all the answers.

I'm not sure if my measurement could be fitted using Brillouin function, but I have found these articles and there are several curves whose the shapes are like that in my measurement. Please have a look at the attached files

Why don't you tell us what you actually have? It would make things much easier if we knew what we're talking about. The similarity of measurements does not imply the applicability of the same physical ideas (but maybe on a formal level).

If you write above: "I'm not sure if my measurement could be fitted using Brillouin function" I can assure you that it cannot.

(P.S. if you want your readers to look into the papers you indicated, please dont have us find on our own what to look for, but do at least indicate the figures you have in mind for each of them.)

(P.P.S. In case you happen to know Olivier Margeat, please say 'hello' to him from my part)

Thanks for your comment. I really appreaciate it.

Those figures are figures 4 to 7 in the first paper (1%2E4861869.pdf). Figures 4 and 5 in the second (JAP115(123908).pdf). And figure 5 in the last (smith_2016_mossbauer spectroscopy,...w temp heat capacity of Na2NpO4.pdf).

At the time I posted the question I hadn't found the papers yet. So...

But it seems to me that if we carry out the same measurement, and then we have kind of the same shape, there would probably be a same function to fit. Otherwise, I don't know. Do you have any advices for me to deal with this kind of curve?

It's pity that I don't know Olivier Margeat. I had a look on the Internet and found out he also works in my lab. If I have a chance to meet him I would send your "hello" to him

Dear Tung Pham,

I don't have enough time at the moment to go into the details of these Refs. But taking a quick glance at the first one, it says in the 1st sentence of the abstract: "A positive-feedback mean-field modification of the classical Brillouin magnetization theory...", so what is done there goes well beyond a simple use of a Brillouin function. You probably cannot escape studying and understanding in detail what is the physical picture behind that treatment (starting out from the usual mean field picture of local moment ferromagnets) in order to think about whether it makes sense to apply the ideas to your material (and what you learn from doing so - having a function you can use to fit does not yet provide insight, this only happens if you can make connection with the physics of the underlying model). Btw., I am not immediately sure whether I agree that the tail beyond TC (so yes, here we are talking about a magnetic phase transition, as I also suspected to be the case in your data) Harrison alludes to is really so little understood. But going into this would cost me more time than I have at this moment, sorry. I might be coming back later.

Dear Kai Fauth

Thank you so much for your time. I really appreciate it. I hope you'll come back soon. I will keep searching for the solution. Have a nice day!

In sigmaplot (similar to origin), we can fit the curve by using the "fit curve" in right. There are a lot of functions you can choose

In Maple plot function, you can fit the experimental data.

Come on guys, the discussion has moved beyond a technical one to a physics related one.

First of all

Brillouin zone function for M-H data , that function you can fit in origin. In case M-T function you try to fit curie wiess law@ Tung Pham