Why must it (upper limit) exist?

First, your film has to be made of magnetic material.  If so, then you may expect the magnetization (no matter which units you use) up to the saturation magnetization of a parent bulk material.  This is because a 100 nm thick film may happen to be in single-domain state (that is across its height, not necessarily everywhere).  This is more likely for thinner films, observed spontaneous magnetization will be usually smaller.  The effect depends on the crystallographic orientation of the film, on its magnetocrystalline anisotropy, and on the direction of the field: either in-plane or perpendicularly to the film.

Sometimes, however, surprisingly higher magnetizations were observed.  I'm sorry I have no relevant citation at hand.

Marek,

and how magnetization is limited by the dimensions of film?

Regards,

Eugene.

Eugene,

I don't get the intention of your question.  If you ask for a formula then, sorry, i don't know anything readily applicable.  If you mean the mechanism, then I have already sketched some of them. But you seem to think that thin layer magnetization may happen to be arbitrarily high.  Why? The natural limit is achieved when all magnetic moments in the sample are aligned with external field.  This almost never happens in bulk materials due to the magnetic domains but is easier to achieve in thin layers.

It is bulk, Marek. But what are peculiarities of two dimensionality, if they exist?

Dear Dr. Kislyakov and Dr. Gutowski, thank a lot for your valuable explanations. 

         Why I dont get a magnetization signal from a 1.3µm thick film? The origin of question was instrumentation based I guessed. Can anyone claim that my film's signal is lost when compared with noise coming from glass? If glass prevents it, how can I able to detect signal? By making an another film on a different substrate; i.e. ceramic? Or by using a lock-in amplifier?

Dear Murat,

You don't say what kind of sample you are investigating.  If it is a diamagnet or paramagnet then, indeed, the signal from thin layer may be very weak, below your detection limit.  But 1.3 µm thick ferromagnet should produce easily detectable signal, be it in a VSM or SQUID apparatus.  A simple Hall probe may be not an adequate sensor, even for ferromagnetic materials.

@Eugene:  Maybe there is nothing special of 2D dimensionality, but.  If the layer is thin, then the surface effects (where translational symmetry is clearly broken) "occupy" a significant part of the sample's volume.  That is why they can be spotted and play non-neglible role thus making the results differing from those obtained for bulk samples.  How "thick" is a surface?  From some experiments it may be estimated as  1-1.5 magnetic layers, thus not even a 1 lattice constant.

Thank You, Marek.

I tried to rise up questions of dimensionality in magnetism.

Regards,

Eugene.

Eugene, it may be useful to divide an answer up according to the characteristics of the specimens. In strictly localized moment magnets, dimensionality hardly affects the magnitude of the magnetic moments of magnetic sites.

In metallic magnets, the magnitude of the moment at given exchange energy depends on the band width. At surfaces (and interfaces) this can be smaller due to the reduced number of neighbors. Magnetic moments at surface sites of metallic ferromagnets may therefore be larger than those "inside" the solid. This belongs to the scenarios invoked for explaining the enhanced magnetization of very small metallic magnetic particles, for example (larger surface to volume ratio).

Reduced dimensionality may bring about other aspects in thin films, though. Enhanced thermal demagnetization has been reported to be induced by interaction with metallic supports - and we believe to have seen this kind of effect on (pretty thin, though, (5 ML)) Fe films on Pt support. That would imply a reduced magnon dispersion relation due to that interaction. And then, of course, at strictly 2D the Mermin Wagner theorem (-> fluctuations) has an implication for magnetization.

Coming back to the original question: you will hardly find any atom or ion with a magnetic moment of more than, say, 10 Bohr magnetons (check e.g. Sm). This will give you a hard upper limit of the per-atom magnetization. The highest moment atoms have a significant contribution of orbital magnetic moment, though. incorporating these elements in solids bears the risk of (partial) quenching of the orbital moment. Based on spin alone, Gd is the element with the highest moment (half filled f shell plus maybe a little extra moment from the 5d/6s,p electrons resulting in 7+x Bohr magnetons per atom).

Given a composition and/or density of a material of interest to you, you can transform this to whatever units, as Marek indicated.

Edit:

Whether you get signal from a film of 100nm thickness, depends on the method and sensitivity (and the material, of course). But the rough answer for more ore less state of the art instrumentation and ferromagnetic materials would be: yes, easily. Most magnetometers do not detect magnetization but the total magnetic moment of the sample (to the extent it is aligned with the field). So, a 5*5mm^2 specimen will generate 25 times the signal of a 1*1mm^2 specimen of the same characteristics and thickness.

By going through the literature you will find that people have e.g. found and investigated the phenomenon of the spin reorientation transition in thin films. You will see that this usually tales place at film thicknesses of a couple atomic layers, which is way below 100 nm.

Thank You, Kai.

@ Murat: what was your experiment (method) and what film material did you look at? As someone mentioned before, without external field the film may have formed domains (to reduce the stray field energy) and the net moment of the sample may therefore be very small. 

Hello Dear researchers.

I have just found an article concerning my bulk samples. The problem I confused is arbitrary unit of y axis at page 4. In addition I have no sign of emu or emu/g despite the figure caption claims that it is a magnetization measurement in squid.

I made thin films of these bulk samples. That is why I wonder.

Kindly regards.

Published version of article. I submitted here to see if some changes are made or not. But figure 3 is same (Page 3).

Thanks.

So this is about superconducting diamagnetism. Ideally, a superconductor expells the magnetic flux from its volume, and then the quantity plotted in the graphs would amount to -1. It is not important what the magnitude of magnetization actually is, but to what extent the external magnetic field is shielded. How much field was applied is given in the paper. This shielding is due to superconducting currents at the specimen surface (type I superconductors, ore more complex (type II, I havent checked what applies here)).

In order to observe this, Your samples must (a) be superconducting (b) be cooled to below Tc. See Fig. 4 for the transition temperatures.

The induced moment of a superconducting specimen will always be negative with respect to the external field, no matter what direction you apply it. therefore the choices made in Fig. 3 make perfectly sense to me.

Edit:

Most samples in that study are only superconducting under pressure. So, besides sufficient cooling, applying the required pressure is also important (check Fig. 4 again). The "critical" parameters (composition, pressure, temperature) might turn out to be different in thin films compared to bulk material, but your films are not what I would perceive as "very thin".

Actually, when you do get a magnetic signal from your sample(s), it should scale with (superconducting) sample volume.

Edit 2:

Actually this is a nice example for demonstrating the need to concisely formulate questions and to include all relevant aspects. My entire previous answer and much of the foregoing thread is nearly pointless for the real question and material of the TO/OP. 

Thanks a lot Mr. Fauth , Gutowski and Kislyakov.

Kai,

while the essence of your last comment is correct, then your interpretation of "-1" in Fig.3 is in error.  The authors present magnetization, not susceptibility, in arbitrary units.  A superconductor below critical temperature, and in case of type II superconductors below first critical field as well, is a perfect diamagnet.  More precisely, they show the total magnetic moment of their sample, as you have already mentioned.  Presenting such results in emu/g does not make much sense as the magnetic moment is by no means material specific in case of superconducting material.  Inside a superconductor the equality 0=B=µ0H+M holds, thus M=-µ0H (or just M=-H in cgs units, here the number -1 enters, as susceptibility).  This means nothing else but strict proportionality between the measured signal and the external field (and the sample volume, of course).  Anyway, this also means that one may expect the signal to be 103-104 times weaker than for ferromagnetic sample of similar size.