A common way is using first principles theoretical calculations, such as the density function theory (DFT). Many papers are being published with such results, and the following is an example of a calculation to determine the electronic structure of the manganite perovskites:

http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.76.960

However one should be careful and selective when searching for papers because there are quite a few non-reliable works out there, especially on these subjects. As is usually the case, going to well-known journals (e.g. APS' journals) is a decent, preliminary filter.

Dear Lior Kornblum,

Thanks for your answer.  First principles theoretical calculations is a powerul tool to determine the magnetic structure. But even I know the spin structure of a compounds, for example Γ2 Γ4, it is still defficult for me to imagine the complete picture of the magnetic structure. Where can I start in this area??

I am not sure if you are asking in the context of a literature survey or you want to do calculations by yourself. If YFeO3 is indeed the material of interest, I do not see many works on its magnetic state, but this one might be worth a look

http://dx.doi.org/10.1016/j.matchemphys.2012.12.086

If you are talking about your own research, I'd suggest doing a thorough literature survey on this and then collaborate with an expert of DFT of such materials.

Dear Lior Kornblum,

Thank you for your answer. I do not want to do calculations by myself, it is difficult for me. I mean that I am lack of basic knowledge about the magnetic structure, but I do not know where to start. Is there any books or other materials introducing the magnetic structure?

In my experience good results are often published in scientific papers first, and after a few years (or decades) they will find their way into review papers, book chapters and books. Therefore I think that if you have a specific material in mind (YFeO3? something else?) then I'd start with google scholar and look for scientific papers on its magnetic structure. If you mean books on magnetic structure in general then I'm not familiar with such myself.

Dear Lior Kornblum,

Thank you very much, I will try it with google scholar.

Is your question more like "how is it done" (by theory or experiment)  or more like "what has been found for my specific material of interest" ?

For crystalline materials (large enough single crystals) neutron scattering is a great method, for example. More recently, x-ray scattering methods (using synchrotron radiation) have gained quite some popularity.

Specific problems have lead to various methods. Surface spin structures, for example, have been successfully investigated with spin resolved scanning probe methods. Magnetization profiles at interfaces have been probed using x-ray reflectometry etc etc.

When looking for basics, start with text books on magnetism. They generally do discuss some of the more frequently occurring magnetic structures and the interactions which are at their origin. I do like "Magnetism" by Siegmann & Stöhr (Springer, 2006).

Dear Kai Fauth,

Thank you for response.More like the latter. I mean that I am confused when I came across the spin structure like Γ2 etc in the literature discussing my specific material of interest.

The text book "Magnetism" is very helpful.

Thanks a lot !