Dear Indra and Melisa

Fitting with Origin will not give you any physics parameters. What you need is to Integrate a weighted volume distribution Langevin function (see attached). You need to assume the distribution function and when the fit achieved you can estimate the average particle size and the standard deviation.  See full article.  Just a simple routine program to calculate equation 3 using a certain function for the particle size. The type of distribution can be hinted from electron microscopy information about the particles physics sizes. 

Please check 

Ieee transaction on magnetics, vol mag-14 no. 5, 1978.

I have discussed discussed methods and results of evaluating particle size and magnetic anisotropy in Fe3O4 fine particles in details in a previous publication, and compared results of different methods (Magnetic data, Mossbauer results, and electron microscopy) and theoretical models there in. Please refer to the attached article for clarifications

Thanks for the reply.

@Mahmood. Thanks for the articles. I want to clarify few things. Langevin function you define in the article has Ms(saturation magnetization of the bulk material) and M0(saturation magnetization of the sample). M0 also can be calculated by extrapolation M vs 1/H curve to higher fields. Which calculation in more accurate? In the paper you calculate Vl and Vs using two different equations (both have Ms). How do we calculate Ms value from the data? Can we assume Ms=M0?

Could someone please recommend me a good book or books that explain well about M(H), M(T), field cooled and other magnetic measurements and how those measurement depend with particle size, shape, material, composition etc. Also what properties we can calculate from the measurements.

Thanks

Dear Melisa,

independent of S. Mahmood's articles, you can convince yourself that a simple analysis in terms of a single Langevin function is normally bound to give erroneous results in real samples.

Consider first an ensemble of identical particles without anisotropy, i.e. behaving as an ensemble described by the Langevin function (limit of large total angular momentum, total Moment M per Particle). The thermodynamic expectation value of the orinted moment per particle is then

= M * L(MB/kT)

As B/T goes towards infinity, L goes towards 1 and hence converges to M.

When B/T is small, L is linear in the argument, and therefore is proportional to M2.

 In a real sample, you will have a distribution of moments, e.g. due to a size distribution. The saturation magnetic moment of the ensemble is simply the addition (proportional to the average) of all moments, while the susceptibility will be given by the addition (the average) of the square of all moments. A single Langevin function cannot reproduce both facts and a fit therefore will find some compromise according e.g. to the prescription of minimizing the deviation between experimental data and model curve.

On top of that, anisotropy terms can (and in general do) modify the shape of magnetization curves, so that they're not identical to the shape of the Langevin curve. On top of that, there will typically be a distribution of magnetizations and anisotropy properties (material inhomogeneities), as well as interactions between particles (potentially by form of exchange upon contact and dipolar coupling). I am sure that Sami's papers will provide a good read on (some of) these issues. So you're confronted with a serious, complicated challenge.

Ways to disentangle at least some of these aspects will always include to do a large set of measurements, including M(H) loops at various temperatures, as well as the FC/ZFC cycles you have mentioned.

I would recomment going through the (joint) publications of F. Tournus and A. Tamion, who both have profiles on RG. They especially have developed a protocol they call "triple fit". the aim is to determine a unique set of parameters which would be able to simultaneously explain all these measurements. There is also some work they did together with M. Hillenkamp for experimentally proving their concept. There you will see how much effort was put in obtaining well-defined specimens for this purpose.

I additionally link two papers devoted to the study of not-too-badly defined nanoparticle ensembles from work I was involved in. You will see that despite some success there remain open issues.

Finally, let me say that in conventional magnetometry what you measure (provided everything is done well) is the total moment of your sample. Assuming all parts of the sample to be exactly the same material with same properties, this is given by magnetization times specimen volume. Ideally, the ("average") moment appearing in the Langevin function would be exactly that magnetization times "average" particle volume. Also, how well your (whatever) model will produce "correct" results will sensitively depend on how accurately you have corrected for extrinsic (oftentimes diamagnetic) contributions to the total moment measured. These contributions may e.g. arise from a substrate on which the NPs are collected or deposited. [Diamagnetic contributions are "nice" since they are, in general, temperature independent. Paramagnetic impurities in a substrate may be very nasty, since they are temperature dependent and may ruin low temperature data. The third paper linked gives an example where this was exploited to obtain a magnetometry measurement (almost) free from extrinsic contributions at the one single temperature where para- and diamagnetic contributions compensate].

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Dear Prof. Fauth,

Thank you very much for your explanation and publications. I will learn more about triple fit and experiment concept. Could you please also recommend me any favorite books to read or must read book in magnetism and magnetic material.

Thank you. 

Suggested Books for magnetic properties and magnetic materials [1-3]

[1] B.D. Cullity, C.D. Graham, Introduction to magnetic materials, John Wiley & Sons2011.

[2] S. Chikazumi, Physics of Ferromagnetism 2e, Oxford University Press 2009.

[3] J. Smit, H.P.J. Wijn, Ferrites, Wiley, New York, 1959.

Dear Prof. Sami Mahmood

Peace be upon you

Please, If you have soft copies of these valuable books attach them here or Please send them via e-mail, [email protected]

My great thanks in advance

Yours,

Ahmed Saeed Hassanien 

Apply the well known R.W Chantrell method which published, ref. is 

R.W. Chantrell, J. Popplewell and SW. Charles, IEEE

Trans. Magn. MAG-14 (1978) 975.

The method is used for magnetic liquids, Since the anisotrpy energy will not play any role because the Langevin behavior can only be applied when KV is small compared to kT.  

For recent study see my article which is posted on RG 

Nano-particle magnetism with a dispersion of particle sizes

JOURNAL OF APPLIED PHYSICS 112, 103915 (2012)

This article contains all the information that you need regarding particle size in nano-magnetic systems. 

Dear Prof. Mahmood and Prof. El-Hilo,

Thanks for the information.

Dear Ahmed Hassanien

Please find personal copies at your e-mail address

Be careful with what kind of distribution you put in, is it a volume or a number distribution??

Dear Dr. Sami Mahmood 

السلام عليكم ورحمة الله وبركاته

Thank you very much for your attention and sharing this valuable book of "Physics of Ferromagnetism". The other book of "Ferrites has been already received.

My great thanks, May Allah bless you

Most welcome A.S, Hassanien. Thanks Mohamed. I was aware of that, but I failed in sending a private copy. So I intended to delete comment after receipt of copy

Dear Melisa Ruiz,

If may I know, what kind of software do you use to fit your curve. Thanks

Regards,

Indra

Dear Indra, I used Origin to fit the curve.

Dear Indra and Melisa

Fitting with Origin will not give you any physics parameters. What you need is to Integrate a weighted volume distribution Langevin function (see attached). You need to assume the distribution function and when the fit achieved you can estimate the average particle size and the standard deviation.  See full article.  Just a simple routine program to calculate equation 3 using a certain function for the particle size. The type of distribution can be hinted from electron microscopy information about the particles physics sizes. 

Dear M. El-Hilo,

in my opinion, the most "honest" kind of distribution would actually be a moment distribution. With (however weighted) size distributions I do assume size independent and totally homogeneous magnetization, which could be invalid for a given sample.

And of course it gets worse when anisotropy terms cannot be neglected but this was mentioned (by you) already.

And a slight remark: of course one can create fitting routines in Origin which do such tasks as fitting magnetization curves under the assumption of distributions of magnetic moments (whatever their factual description in the model) as in the equation uploaded by M. El-Hilo. But it's not built-in to Origin and takes some effort.

Correct, the first line in Eqn. 3 represent a distribution of particles  moments and yes this is better since you do not have to assume the value of the saturation magnetization for the particle material which could be different from the bulk value. 

... and size dependent (consider e.g. surface oxidation or chemical coordination/functionalization of metallic nanoparticles), and even for a single size still be subject to statistics (e.g. through statistical distributions of elements in bimetallic particles). I usually stress that a lot must be known (and hence somehow be characterized) in order to work with size distributions in a quantitative way. I may of course still do so, but depending on the available information I should be aware that I am using assumptions about my materials. Realistically, I think that this is many times the case without even the scientists being aware of that fact.

What adds to the problem is that in magnetometry, actually the total moment of the sample is being measured, and that information on magnetization os then to be inferred from knowledge of the relative mass and/or volume, where again assumptions (or information) about the material are required.

Hi, Thanks for your contributions, I have a new question, I would appreciate if you help me,

What is the physical concept of super-exchange coefficient (molecular field coefficient) (w). Which parameters does super-exchange coefficient depend on? 

(Hin=wMs)

It would be better to open a new thread for a new question.

Nevertheless: the concept of a molecular field ignores the nature of the interaction ("Weiss-field").

Superexchange is a specific form of quantum mechanical exchange coupling between magnetic sites via an intermediate atom (See good magnetism text books such as Stöhr & Siegmann (Springer, 2006) or the like).

A superexchange coefficient as a molecular field parametr, that sounds a bit like an oxymoron to me.

Maybe the paper Langevin granulometry of the particle size distribution (2004) will deliver the answer?  It is available at RG at: https://www.researchgate.net/publication/216481584_Langevin_granulometry_of_the_particle_size_distribution?_iepl%5BviewId%5D=1v0r0Va3GMaLpjzpoxFuBv1P&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BinteractionType%5D=publicationTitle

Article Langevin granulometry of the particle size distribution

Thanks for your time and your answer Prof. Kai