Yes, you are right. Usualy the Curie temperature depends on the size of the ferromagnet nanoparticles. The less is the average dimension, the less is the Curie temperature. The same is valid for thin films.

Nanoparticles of materials that are magnetically ordered in a certain way in the bulk, can display a complete different behavior. A classic example is superparamagnetism that is observed in magnetite nanoparticles .....

Curie temperature of material is inverse proportional to distances between magnetic particles such as Fe. Then in every structures if the correlation of particles became less by... they have less magnetic power & decrease their curie temperature.

The Fe atoms in (double) chains on CuN do not interact via direct exchange, so these are physically very different systems. Nevertheless, the trend you suscpect is, overall speaking, correct.

In a finite size cluster with ferromagnetic next neighbor exchange interaction, the surface atoms have fewer such neighbors to interact with (reduced coordination number) and therefore a reduced exchange field. On average, therefore the Weiss mean field is therefore reduced. This tacitly assumes unchanged atomic moments. In reality, the local moments at the cluster surface are likely to be enhanced (due to the very same origin - reduced number of neighbors reduces the d-band width and thus is likely to enhance the density of states at the Fermi level, often resulting in larger magnetic moments), so there are competing effects.

Superparamagnetism mentioned by Paolo above occurs below the Curie temperature. It is the smallness of magnetic anisotropy energy in that case (due to the smallness of the particle volume) which prevents the magnetically ordered spins from being tied to the atomic lattice. As you go through the Curie temperature, the susceptibility will drastically be reduced.

This is certainly a very interesting question in magnetism and nano-magnetism.

From an experimental point of view, the measurement of the superparamagnetic limit is very challenging because the clusters need to be deposited on surfaces (and then coated) of embedded in a matrix before their magnetic behavior can be studied. For the sizes we are talking about (few nm), the influence of the surrounding capping, surface or matrix is very important in the sense that they affect the magnetic properties of the clusters…. Probably the challenge here is to find a matrix that modifies only slightly the magnetic properties of the clusters in order to be able to claim that the measured superparamagnetic limit is close to the one of free clusters.

@Yves, you're right to mention this as a challenge. Nevertheless, the superparamagnetic limit (->"blocking temperature", in itself a notion to use with care, "uncoupling" of magnetic structure from atomic structure) and Curie temperature ("uncoupling" of exchange-coupled moments) are not the same thing.

Experimentally, I would think that in most cases determining the Curie temperature is even more challenging than determining the blocking temperature.

I agree with Yves and Kai. The measurement of a size-dependent quantity is also challenging because real specimens are polydispersed! We do not have a single transition temperature, but a distribution of values. A proper modelling taking into account the true size distribution is therefore needed. Plus, the smaller the size, the higher the surface effects as already mentioned by Kai: we know that atoms on the surface are more mobile and do not have the same neighborhood as those in the bulk, so I would expect a difference between bulk and core for each different particle. I suspect that magnetostriction-related phenomena also play a role on nanoparticles, influencing the kinetics of the process near Curie temperature (and again the size distribution will play a role).

I guess it's going to be hard to give a precise account of the temperature effects on spin ordering if a proper modelling of the microstructure of the various nanoparticles is not done together with that of the magnetic effects (and this includes modelling the surroundings as pointed out by Yves).

Progress is being made experimentally. But that is still FAR away from looking at the Curie temperature.

http://prl.aps.org/abstract/PRL/v108/i5/e057201

http://prl.aps.org/abstract/PRL/v107/i23/e233401

Older, but also VERY interesting:

http://prl.aps.org/abstract/PRL/v95/i23/e237209

For those of you with access to Physik Journal (Membership journal of the German Physical Society) [and proficient of German], here's a little review on the first two papers, written for the non-specialist.

http://www.pro-physik.de/details/articlePdf/1881009/issue.html

Acc. Chem. Res., 2008, 41 (2), pp 179–189, gives a nice review on the scaling laws for monodispersed magnetic nanoparticles and their applications in nanomedicine

Size dependent Curie temperature can be corelated with the size dependent magnetization. It is observed that for smaller size of particles they exhibit dead surface layer which causes in less magnetization due to reduced exchance interaction. This reduced exchange interaction in smaller size will definetly reduce the Curie temperature as well.

I disagree with the assertion in Sagar Shirsath's comment. Magnetic dead layer formation is not generally an intrinsic or generic feature of magnetic nanoparticles and - as far as I can tell - certainly not in iron nanoparticles. Dead layers may nevertheless result from interaction with foreign material.

The following two papers from my/our own work are on Fe sub-10nm particles of fairly different sizes, deposited with low kinetic energy onto a well defined copper surface. The average per-atom moments exceed that of bulk iron in both cases.

http://onlinelibrary.wiley.com/doi/10.1002/pssb.200945607/abstract

http://link.springer.com/article/10.1140%2Fepjd%2Fe2007-00271-9

The next paper shows that small Fe clusters may even be driven nonmagnetic by contact with another surface, graphite in this case.

http://www.sciencedirect.com/science/article/pii/S0009261404008322

Here is another example with graphite, a study of graphite encapsulated Co particles (much larger than our Fe clusters above). Here, the magnetic properties can indeed be rationalized by the assumption of dead surface layers, as mentioned by Sagar Shirsath.

http://www.sciencedirect.com/science/article/pii/S0009261401007163

None of the above do discuss the Curie temperature, though, which was the subject of the original question. Unfortunately, the methods employed in our work do not offer a simple route to reaching sufficiently high temperatures, such that the Curie temperature could be evaluated.

In case you cannot access our papers via the publishers' pages, feel free to contact me for reprints.

Thanks to all of you for great answers. It seems, though, that there is no clear answer yet!

Here is one article which might be of use to check the curie temperature(APPLIED PHYSICS LETTERS 88, 153117 2006 ). People have observed an enhancement of Curie temperature in the case of Fe nanoparticles.

Very Interesting discussion

I would like to add some other queries which are somehow related to this debate. 

I have read many articles with this kind of statements

1. “Superparamagnetic nanoparticles with low/high Curie temperature” Is it right to use “Curie temperature” term for superparamagnetic materials?

2. “Curie temperature increases with applied magnetic field” If it then Curie temperature is not materials property? If not then what does it mean?

@Varun, #1

we have to distinguish between the blocking temperature and  the Curie temperature, respectively. The 'problem' arises primarily due to the frequent 'definition' of ferromagnetism being linked to the appearance of hysteresis in magnetization curves. A better approach is to consider the presence of spontaneous magnetization, and the correlation between moments at different atomic sites. Then, e.g. if

=1

for all times and for all pairs (i,j) of sites in the particle, you would have a ferromagnetic state independent of the fact whether the total particle moment does exhibit orientation fluctuations or not.

Hysteretic behavior may appear (well) below the blocking temperature, which itself depends on the time scale of the experimental probe (magnetometers typically being slow ones, Mößbauer very fast in comparison).

The Curie temperature then would denote the temperature at which the above correlation function breaks down.

@Varun, #2

I'd be interested in knowing where you took that phrase from.

But then, yes, the phase transition is not independent of an applied field:

will depend on temperature and applied field. As a matter of fact, the phase transition between the paramagnetic and the ordered state gets smeared out by an applied field. That represents a typical challenge for measuring the "intrinsic" Curie temperature ("intrinsic" meaning: with no external field) in magnetometers, where you do need an applied field, in general (it's also a good reason for keeping that field small). There are procedures, though, to find TC from magnetization curves taken at different temperatures around TC.

Metamagnetic transitions provide another example of field dependent magnetic ordering.

I would say  "ordering temperature" might be better way to explain than writing it is Curie temperature. As in the case of thin films, where dimensionality come into picture,  Curie temperature is not at all a constant, but thickness dependent. I would always use it as "ordering temperature".

@ Dear Prof Kai

Thank you very much for kind explanation. 

Curie Temp may be size dependent, thickness dependent, defect dependent, and can be depend on the way of synthesis but can not be dependent on field. I totally agreed with Prof. Kai Faut that phase transition depends on applied magnetic field. However, in this case it will be better to use phase transition temperature or magnetic ordering temperature instead Curie temp.

Dr Ramesh @  to write ordering temperature is always safe but in your case (thickness dependence) you can use Curie temperature too.

"Ordering temperature" simply is more general, since the considerations are also true for other types of magnetic order than ferromagnetic. The correlation function above then "simply" looks different.

From theoretical poin of view is quite reasonable that magnetic ordering temperature depends on np size. There is a nice reference reporting experimental results on this. Please see Fig. 6 of Physica B 354 (2004) 71–79, by Chuan-bing Rong et al.

@ Franz J. Giessibl

Bulk Iron has a Curie temperature around 1043 K. To understand the magnetic order, we need to predict exactly the Curie temperature. In my works [1, 2] one can find how to calculate the Curie temperature of iron.

Here I try to answer the question why in the iron nanoparticles there are two phases, namely paramagnetic (smaller nanoparticles with critical length of ~9 nm [3]) and ferromagnetic (nanonparticles of the larger size >9 nm)?

If we assume that the lattice constant in iron nanoparticles is 2.866 Å and covalent Iron radii of 1.32 Å (low spin) and 1.52 Å (high spin) and the groups of 38 iron atoms collide with each other elastically. Groups of 38 iron atoms have a length of 37*2.866x10-10m=10.6 nm which is the critical length [3].

For ferromagnetic iron nanoparticles the condition must be fulfilled:

TC=(pi*h2/4kB)*(1/(sqrt(38MFe*38MFe)*(2.866 Å-1.32 Å-1.52 Å)2))=1049 K

For longer sizes of iron nanoparticles the multiple of 38 iron atom groups can fulfill the above condition, for nanoparticles with sizes smaller than 10 nm the above condition is not fulfilled and they therefore remain paramagnetic.

References:

[1] S. Mushkolaj arXiv:0810.4265 (2008).

[2] S. Mushkolaj J. Mod. Phys. 5, 12, 1124-1138, (2014).

[3] J. Carvell, E. Ayieta, A. Gavrin, Ruihua Cheng, V. R. Shah and P. Sokol, J. Appl. Phys. 107, 103913 (2010).