I could offer the analysis of magnetoelastic effect using phenomenological theory and representation analysis. In one of our works we analyzed magnetoelectricity in CuCl2. I think something similar could be done for magnetoelastic effects in difluorides.

That would be great Nikita. Please have a look at the papers. Tanushri Saha Dasgupta and the collaborators have already done some calculations (recent PRB) on Difluorides only on the volume magnetostriction but these are first principle calculations. You have different approaches. I shall be much interested in some calculations on hexagonal manganites as well.

Nikita: We discivered an isostructural phase transition mediating magnetoelectric coupling in BiFeO3 solid solutions. It was published in PRL in 2008 and dealt with (Bi,Ba) (Fe,Ti) O3 using powder XRD . We reconfirmed this using powder neutron diffraction also using FRMII data and published in PRB. We used Tapan's very low resolution powder data to show magnetoelastic couplings at low temperatures in this solid solid solution system which was controversial in pure BiFeO3.But you need really high resolution data to capture such effects, either SXRD or neutron powder diffraction.Please have a look at our papers on BiFeO3 solid solutions and also in Pb(Fe0.5Nb0.5)O3 ( the latter was published in APL)which also shows strong magnetoelastic effect.

The external magnetoelastic effect or magnetostriction in hexagonal manganites are rather large and can be easily detected by medium resolution neutron or X-ray diffraction. These are the relative changes in the lattice parameters close to the magnetic ordering temperature. For example in YMnO3 Delta V/V_0 = -3.25 \times 10^{-4}. What one would like also to measure is the internal magnetostriction, i.e. shifts in atom positions inside the unit cell. This is more difficult to measure for magnetic structures with k = 0 where magnetic and nuclear reflections arise at the same reciprocal points in general. If you refine the crystal and magnetic structures with the neutron data then you will find that magnetic and structural parameters are strongly correlated. The guys who use Fulprof blindly do not usually look at the correlation matrices and come out with nonsensical results. I have tried to avoid these correlations by collecting data on a spallation neutron source where one can measure data up to a very high Q. One can then refine the high-Q data to get structural information and the low-Q for the magnetic refinements. This helps to avoid strong correlation between structural and magnetic parameters. We did not succeed completely because of the very small internal magnetostriction effects. We did better with polarized neutron diffraction on a single crystal of the multiferroic YMn2O5. This is a very difficult problem. I would like to share the experience with other workers in this field.

Dear Prof. Chatterji,

I looked at your papers on difluorides and hexagonal manganites. As I understand, you study how the structural parameters change upon magnetic phase transitions and find the changes in the lattice constants as well as in atomic positions.

This can be analyzed theoretically if you like using the representation analysis and Landau theory of phase transitions. One needs to know the crystal structure and the appearing magnetic structure. One can then find the mechanical representation for all the atoms and with the help of Landau theory see how these degrees of freedom interact with the magnetic structure. This is of course similar to magnetoelectrics where the magnetic structure couples to polar distortions, except that here it couples to elastic or some other deformations.

Also since some difluorides show distorted rutile structure and hexagonal manganites distorted P6_3/mmc structure one can perform the analysis above starting from the respective praphases and not from the crystal structures in which the magnetic ordering occurs. This will not necessarily simplify the analysis but will make it more consistent. We used this approach lately to study some magnetoelectrics (MnWO4, CuO, and others).

Dear Prof. Pandey,

I looked through the papers on BiFeO3 solutions. In 0.8BFO-0.2BTO for example (PRB 83, 054406) you measure the jumps in structural parameters around 100 – 250K. At these temperatures there are magnetic phase transitions but as I know their nature is not clear. I have to say that the representation analysis in this paper is a little bit strange (although probably correct), because you explicitly use the wave vectors k and –k, whereas k=0.

You also find jumps at 625K. The “main” magnetic phase transition occurs at 520K, whereas some magnetic ordering persists up to 625K. This temperature is close to the magnetic phase transition temperature in pure BFO. Therefore, I would think that the remains of magnetic ordering above 520K are connected with the presence of BFO-rich regions in the sample. One is then tempted to connect the structural jump with the magnetic phase transition. However, in order for a jump to occur upon magnetic phase transition one needs a discontinuous magnetic phase transition. In pure BFO it is of second order as I know. A more careful study of the phase transition at 625K is needed in order to confirm its discontinuity and in order to find out the critical degree of freedom. But one can of course speculate that the magnetic phase transition is of first order and build the respective theory.

Thus, overall the picture is unclear. The G-type ordering in BFO couples probably most strongly to the antiphase octahedra rotations through the trilinear interaction of the form eta*M*L. This should result in the peculiarities of the oxygen positions after the magnetic phase transition occurs. The coupling to polarization is not trivial (i.e. not of the form P^2*L^2) when an incommensurate modulation occurs. Unfortunately, I didn’t analyze how the G-type magnetic ordering couples to the rhombohedral distortion.

Have you explicitly determined the crystal structures above and below 625K?