To discuss commensurate/incommensurate phases you need at least two systems with different periods. In magnetic crystals we have an atomic structure with period A and a magnetic structure with period B. In general, these two do not coincide leading to incommensurate effects. The best way to observe these phases is neutron diffraction which measures the neutron scattering intensity as a function of the wave vector Q. The diffraction peaks are called the Bragg reflections. For atomic structure we will see the peaks at Q_L=2Pi/A and the magnetic structure will produce the reflections at Q_m=2Pi/B. When A=B, we say that our magnetic phase is commensurate (with the atomic lattice structure). What is important, the wave vector depends on temperature and effectively plays a role of the order parameter Q(T). It means that by heating/cooling your sample you can change its atomic or magnetic configuration. Usually, the low temperature phase is more stable and commensurate. With increasing the temperature it may render incommensurate (with respect to the initial phase) simultaneously changing its atomic or magnetic configuration which will manifest itself in the changes (shifts) of the Bragg reflections. You can also modify the period of magnetic structure by applying magnetic field or pressure. All these may result in a cascade of phase transitions in your sample.

Now, regarding multiferroic RMn2O5. This is a very rich material and it exhibits very many different phase transitions (and not just magnetic) due to its nontrivial magnetic structure. There are five magnetic interactions between neighboring spins through the Mn4+–Mn4+ path, and the Mn3+–O–Mn4+, Mn3+–O–Mn3+, and Mn4+–O–Mn4+ bonds. These competing interactions (in the presence of a rare-earth ion R=Bi,Y) bring about different ordered phases described by magnetically modulated wave vectors Q_m=(Qx,Qy,Qz). For example, at low temperatures, one of the phases is antiferromagnetic with Q_m=(1/2,0,1/4). For this multiferroic, this phase is chosen as a reference point for commensurability. With increasing the temperature, commensurability is violated and the system transfers to another magnetic state with Q_m=(Qx,0,Qz) where Qx=1/2+Dx and Qz=1/4+Dz. The values of the period deviations (Dx and Dz) are usually small but still big enough for their observation via the neutron diffraction. Interestingly enough, in response to the above magnetic ordering, the lattice modulation vector Q_L is exactly 2Q_m for all phases. More info about this interesting material you can find in the attached review (I guess this is the one you mentioned in your question).

To discuss commensurate/incommensurate phases you need at least two systems with different periods. In magnetic crystals we have an atomic structure with period A and a magnetic structure with period B. In general, these two do not coincide leading to incommensurate effects. The best way to observe these phases is neutron diffraction which measures the neutron scattering intensity as a function of the wave vector Q. The diffraction peaks are called the Bragg reflections. For atomic structure we will see the peaks at Q_L=2Pi/A and the magnetic structure will produce the reflections at Q_m=2Pi/B. When A=B, we say that our magnetic phase is commensurate (with the atomic lattice structure). What is important, the wave vector depends on temperature and effectively plays a role of the order parameter Q(T). It means that by heating/cooling your sample you can change its atomic or magnetic configuration. Usually, the low temperature phase is more stable and commensurate. With increasing the temperature it may render incommensurate (with respect to the initial phase) simultaneously changing its atomic or magnetic configuration which will manifest itself in the changes (shifts) of the Bragg reflections. You can also modify the period of magnetic structure by applying magnetic field or pressure. All these may result in a cascade of phase transitions in your sample.

Now, regarding multiferroic RMn2O5. This is a very rich material and it exhibits very many different phase transitions (and not just magnetic) due to its nontrivial magnetic structure. There are five magnetic interactions between neighboring spins through the Mn4+–Mn4+ path, and the Mn3+–O–Mn4+, Mn3+–O–Mn3+, and Mn4+–O–Mn4+ bonds. These competing interactions (in the presence of a rare-earth ion R=Bi,Y) bring about different ordered phases described by magnetically modulated wave vectors Q_m=(Qx,Qy,Qz). For example, at low temperatures, one of the phases is antiferromagnetic with Q_m=(1/2,0,1/4). For this multiferroic, this phase is chosen as a reference point for commensurability. With increasing the temperature, commensurability is violated and the system transfers to another magnetic state with Q_m=(Qx,0,Qz) where Qx=1/2+Dx and Qz=1/4+Dz. The values of the period deviations (Dx and Dz) are usually small but still big enough for their observation via the neutron diffraction. Interestingly enough, in response to the above magnetic ordering, the lattice modulation vector Q_L is exactly 2Q_m for all phases. More info about this interesting material you can find in the attached review (I guess this is the one you mentioned in your question).

@Sergei Sergeenkov I have a little objection to your definition of incommensurate magnetic structure. We don't usually call incommensurate to a magnetic structure where simply QL and Qm (as you defined them) are different. If the magnetic periodicity is a multiple of the atomic periodicity (typically aM=2aL in a ferromagnetic arrangement of spins along a) the magnetic structure is still commensurate to the lattice but a sublattice of the first. Magnetic peaks will be at different positions of the Bragg peaks, usually at 2theta values consisten with fractional indices. QL=Qm only in the case of a ferromagnetic lattice or some particular AFM or ferrimagnetic lattices but in these particular cases magnetic peaks will show up in systematically absent positions of the atomic lattice. In general if the magnetic sublattice vectors (e1M, e2M, e3M) can be built by a linear transformation of the atomic lattice vectors (aL, bL, cL) eiM=m*aL+n*bL+o*cL where m, n and o are integer values for the three i=1,2 and 3 then the magnetic lattice will be commensurate with the atomic one. Incommensurate magnetic arrangements are observed when the magnetic lattice is not a sublattice of the nuclear one (cannot be built by the definition given before). There are many incommensurate lattices but the definition of incommensurate is related to the impossibility to build a rational relation between the magnetic and the nuclear periodicity vectors more generally thatn QLQm.

By Powder XRD or ND, we get intensity as function of 2theta. Can you please suggest how to convert this type of graph into Q maps.(in some papers I used to see this type of map using XRD also). Please suggest reference/book to get some basic idea.

It's very simple, no need for book here Q = 2*pi/d = 4*pi*sin(theta)/lambda, get any worksheet progam that can do that conversion on your 2theta column and you'll get your graph in Q units. Many Rietveld programs do it for you automatically (e. g. GSAS in liveplot window Options/X-units/Q).

The only posible controversial issue with converting CuKalpha data into Q or d units is that you have peaks originated in 2 different wavelengths in your pattern (Kalpha1=1.5406 Å an Kalpha2=1.5440 Å, unless you use a monochromator that strips Kalpha2) so when you convert to Q using just lambda average (1.5418 Å) neither your Kalpha1 nor your Kalpha2 peaks will be located in the correct Q values. It may be a good idea if you have a nice splitting (e.g very narrow peaks) to use Kalpha1 for the conversion and then ignore the Kalpha2 peak (since that will be off place). But for peaks at low angles this option will have them slightly off and using Kalpha average is better. In any case and just for comparison purposes you should be very clear in the selection of lambda for your equation and consider it when doing the comparison with other (neutron or X-ray) data.

Eventually it would be advisable to do a mathematical substraction of Kalpha2 component, but as said, just for display/comparision purposes, NEVER EVER use such data for a refinement!!!!

Best of luck!

Thank you very much. Its really clear and easy. I use GSAS for powder XRD and till now I never did NPD for magnetic structures. Sometimes for thin films (or single crystals) I see the map (Q_x,Q_y) to explain their magnetic structures or propagation vector which decides whether structure is G, A, C or some helical structure. (please correct me If I am wrong in framing the question). Can you please tell how this type of mapping done.