That will depend on the kind of application considered. 

Kai Fauth,thank you for your response. I know what you have said, but what is the minimum value of the polarization even for small applications? That is my question. From ...... and above value can be used for different applications. Who can fill the gap

I once read a paper long ago on people involved in designing FRAM (ferroelectrica random access memories) for electronic memory applications, and I remember reading that a few micro coulombs per cm square should be enough. The sensing electronics is so advanced that it can handle detecting such a small charge. Remember in high density memory cells, the cell size is very small (microns x microns), and the detected switched charge is very small. The whole question with any ferroelectric material which is used for any device application, is always related to reliabiligty, and most important, its switched polarisation charge should be repeatably reproduced after the material has undergone a millions of switching cycles.

And when it comes to device applications besides the simple polarisation charge property of a ferroelectric, several other properties are also of immense interest. To summarie the answer to your question, in micro electronics, a charge of few micro coulombs can be easily detected for any useful device application.

K. Sreenivas

K. Sreenivas, thank you very much for your immediate response with detail discussion

When it comes to small objects, do mind that small charges (as in previous post) is not equivalent to small energies- on the contrary!

likewise, in magnetism we would have to differentiate between applications involving small moments on the one hand and small magnetization (definition: dipole moment per volume) on the other.

I still have a couple "problems" with the original question and potential answers, though.

• What would you consider an application? If You were to invent a particular detector employing some small magnetization ferromagnetic element but that detector would (for the time being) only make sense in a cutting edge research lab.... would you consider this an application  of that material?  (I would)
• This said, I would tend to think it actually makes little sense to answer the question - at least as it stands. That is, because if I were to put forward any number for the minimum magnetization today, it may be obsolete tomorrow! The lower limit of usable ferromagnetic polarization in an application is probably more fundamentally limited by our imagination than by some value.
• You could ask instead what the smallest value of ferromagnetic magnetization is in current applications. Better specify the type of application you have in mind. Then, someone more knowledgeable / better informed than me might come up with up-to-date information.
• Last but not least thank you for asking the question. Thinking about an adequate answer has stimulated me to taking a different look into a problem where we have been stuck for a couple of years.  It might indeed make sense for us to look for a ferromagnetic material with small magnetization....

Kai Fauth, thenk you for you comments and you have got what I want to ask "what the smallest value of ferromagnetic magnetization is in current applications?"

We know that for Electromagnets, Cores for inductors, Transformers and Relays applications we should have to use soft ferromagnetic materials with low coercivity and low remanence while for Magnetic recording media and permanent magnet applications we should have to use hard ferromagnets with high coercivity and high remanence. Eventhough the value of the remanence depends on the type of the applications that we need, what is the value of this small remanence even for small applications??

What do you understand by "small application"?

Now, remnant magnetization and coercive field come into play as do properties like "magnetically soft or hard", while the original question was 'only' about magnetization. There are so many more applications than transformers and electric motors. (my $0.02: the more specific your question the higher the chances of receiving useful answers)

Think of potential applications involving dilute magnetic semiconductors (where I don't know about actual devices). (Ga,Mn)As is ferromagnetic with Mn just being of the order of 1% (not at ambient temperature). Magnetization then is really small. But for applications involving (spin) transport what counts often is just the vicinity of the Fermi level. 

And would ferrimagnets be included in the topic of your question?

))))