Most likely, it is the surface magnetism or vacancy-induced magnetism. Frankly speaking, it s not quite unusual situation.

 @Bannikov

Thank you for your response. I know what you have answered. Any other mechanism to understand the origin other that this? 

Well, my first question would be how you actually make really sure that the ferromagnetism observed is actually intrinsic to your material. That can be a nontrivial task.

[Just as an example: Co doped ZnO has been reported by many to be ferromagnetic. After a while, some people found out that the Co in their ferromagnetic samples actually gave a paramagnetic response (finding this out of course required a method capable of evaluating the Co response separately. They used XMCD.). So, ferromagnetism was not intrinsic or specific to Co doping in this case.]

@Kai Fauth

Thank you very much for your response. We first tried pure TeO2 nanostructure and did the magnetization study. No trace of magnetic impurity was there and it is confirmed by a simple EDS. We found that it shows hysteresis. Our immediate understanding on this may be because of any defect, However, to understand the nature we put a small quantity of Mn and observe its magnetic response. The FM infact enhances. We added more Mn and only see all higher concentration of Mn gives linear response. Is there any other factor responsible for magnetic behavior or pure TeO2 other than defect? 

Hm, this does not sound dissimilar to the Co doped ZnO case in some respects!

In order to produce some understanding of your results, you have to answer (at least) two questions:

A) what is the nature of the ordered moments (which atoms/sites/vacancies contribute, what is the local moment magnitude and the density of the contributing sites, does this make sense...)

B) How do they couple to produce magnetic order?

Later, one might be interested in finding out about (C) the mechanism of magnetization reversal and how it relates to the magnitude of hysteresis you observe.

Probably, none of these questions can be answered quickly out of the blue (imho), it would always amount to speculation. Like in the Co doped ZnO case, (A) is probably the easiest to be tackled by experiment, using element specific methods, i.e. XMCD. That amounts to making a good enough proposal to synchrotron radiation sources such that you will be granted beam time. Alternatively you may try to interest people working there to do a preliminary test.

Caveats: using soft x-rays, you will get access to (i) O-K, (ii) Mn-L and (iii) Te M edges. (i) and (iii) are tough to measure (small sensitivity). (ii) is measured with relative ease normally, but very small doping concentrations may still represent a challenge. Alternatively, Hard x-rays may be used for Mn-K edges (but then probably also a challenge at low concentration) and some deeper-lying Te edges (have no clue how well that works). Soft x-ray XMCD is (1) surface sensitive in the electron yield mode and (2) not quantitative but more volume sensitive in the fluorescence mode. Hard x-rays probe the volume (microns of probing depth).

If I were you I would strive for access to the XMCD technique. At the same time, I would also try to get other techniques involved. FMR, for example, can be very useful. You obtain the magnetization (from the resonance frequency/field), which would be a valuable cross-check of your magnetometry results. And, from doing FMR at various frequencies, you get information on the Landé g-factor, which might be telling about the nature of the moments. Concerning Mn, electron spectroscopy might be useful to determine whether it exists in a well defined electronic state independent of concentration and to find out what that state actually is.

As for (B), it usually takes theory to answer it, and that can be a very tough problem. "Just doing some DFT" will not solve the problem. If you know or review the (vast!) literature on Mn doped GaAs, you might get an idea of what's involved and how difficult a question that is. Personally I would not invest much into going after (C) unless there is some clarification about (A).

@Kai Fauth

Thank you for your valuable suggestions. I will access XMCD/FMR soon and get back to you.

I'd be curious to see the M-H behavior. A common explanation is iron contamination, which could be from tweezers etc. When I started studying epitaxial oxides I used to gently scratch the back of my STO substrates with a steel scriber to mark the sample number. Needless to say that the magnetic signal was through the roof in these first couple of samples.

Just as an example of how sensitive to impurities this could be, I recommend anyone who's interested in this discussion to go through the abstract of one of Coey's latest paper: https://arxiv.org/abs/1606.09422

Several oxides shown magnetic features; so the behavior is not unexpected. Combined spectroscopic/magnetic measurements can provide an answer. Eventually I would suggest magnetic resonance and Raman/FTIR. If interested, we may do for you the Raman measurements at room temperature. For further details please contact me at [email protected].

You may also check the papers of Ralph Skomski and the article "Defect-induced magnetism in undoped wide band gap oxides: Zinc vacancies in ZnO

as an example

G. Z. Xing, Y. H. Lu, Y. F. Tian, J. B. Yi, C. C. Lim, Y. F. Li, G. P. Li, D. D. Wang, B. Yao, J. Ding, Y. P. Feng, and T.Wu, AIP Advances 1, 022152 (2011); doi: 10.1063/1.3609964"

Mircea