Hexagonal manganites RMnO3 (R = Y, Dy, Ho, Er, Tm, Lu etc.) are multiferroic materials with ferroelectric transition at about 1000 K whereas the magnetic transition is at about 100 K. Unlike the orthorhombic manganites, here the cause of ferroelectricity is geometric and is not due to the magnetic ordering through inverse D-M effect. These hexagonal manganites show strong magnetostriction of the lattice parameters (external magnetostriction) near the magnetic phase transition and this can be easily measured by NPD or by XRPD. We have measured the external magnetostriction by NPD on D20 at ILL. But our attempt to measure small displacements in atomic coordinates and bond distances below T_N (internal magnetostriction) did not give any conclusive results from these NPD data. The inherent problem is probably the strong correlations between magnetic and structural parameters for the magnetic structure with propagation vector k = 0. For these structures, the magnetic reflections are on top of nuclear reflections and give rise to strong correlations. We tried to solve the problem by measuring neutron diffraction intensities up to a very high Q with a diffractometer (POWGEN) on a spallation source (SNS) and refine the magnetic structure with the low-Q data and the nuclear structure with high-Q data, but even this strategy did not succeed. Has anyone any better suggestions or explanations?
Are there any diffraction data from a synchrotron available for the same temperature range?
Sure synchrotron powder diffraction data would contain no magnetic reflection and thus help to get pure structural data. But unfortunately I do not have them as yet. I have to write ESRF proposal.
I also agree that using synchrotron X-ray powder diffraction will help. The O positions will not be too precise with X-ray data of course and have to be refined with neutron data starting with the X-ray values.
@Tapan Chatterji. Can you please explain the physical reason which prevent from precise determination of O positions. (Almost similar comment I got for one of my manuscript).
The answer is very simple. Here we are concerned with the atomic positions of relatively heavy rare-earth element like Ho (atomic number Z = 67) , transition element Mn (Z = 25) and the lighter O (Z = 8). Now you know the X-ray atomic scattering factor f is proportional to the total number of electrons or the atomic number Z. Again X-ray diffraction intensity is proportional to the square of the atomic scattering factor or Z^2. Z^2 for Ho, Mn, and O are 4489, 625 and 64 and therefore f^2 of these Ho, Mn, and O are in the ratio 70:10:1. So O will scatter X-rays 70 times less than Ho and 10 times less than Mn. So the X-ray scattering from HoMnO3 will dominated by Ho and Mn atoms and O will scatter very little. So you see O positions will not be determined very well by X-ray diffraction. Now neutron scattering lengths (which plays the same role as atomic scattering factor for neutrons) of Ho, Mn and O are 8.08, -3.73, and 5.80 and therefore neutron diffraction intensities for these atoms will in the ratio 65:14:34 or 4.6:1:2.4. So for neutron diffraction O will scatter very well. That is why for rare earth manganites neutron diffraction is better suited for determining the atomic positions, especially the O positions.
Now Brajesh do some home work. Go to the library and read the books:
Neutron Diffraction, G.E.Bacon, Oxford (1975)
Magnetic Neutron Scattering, ed. Tapan Chatterji, Elsevier (2006).
If you do not understand something then just ask me.
There are other reasons for which neutron diffraction is preferred than X-ray diffraction. Unless you are very careful you may not be getting proper powder average in X-ray diffraction whereas in neutron diffraction one is likely to get better powder average because of the use of a larger amount of sample. So often the positional parameters are not as accurate as you get in neutron diffraction. (I know my ESRF friends will not agree with me about this). Powder X-ray diffraction do not give any information about the magnetic structure.
You can however measure the lattice parameters and their temperature evolutions very accurately and quickly by synchrotron X-ray diffraction. This is very useful for phase transition studies.
Thank you so much sir. I know those facts but never understand by such an illustrative example. From book Magnetic Neutron Scattering, ed. Tapan Chatterji, which is available in my library, where I read chapter 2 which is very useful to understand magnetic structure especially antiferromagnet. I need to read chapter 1 book also.
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