I am not sure, because I never did it, but perhaps you can obtain single a magnetic domain applying an external magnetic film during the growth of the monocrystal.

What about synthesis under high-pressure?

Number of structural domains is significantly larger than number of magnetic domains. With the refined Cc-structure there are 24 structural domains possible. Because of magnetoelastic coupling, this can be reduced by cooling in an applied magnetic field. Cooling in half a Tesla or so applied along a cubic [001]-direction makes this the low-T c-axis, yet there are still 8 domains possible. The in-plane orientation of the low-T cell can be fixed by cooling in a magnetic field tilted some 40 deg away from [001]c in direction of [110]c, something like 2 Tesla are necessary. This procedure implies magnetic mono-domain state, but structurally there are still at least two possibilities. Getting structurally monodomain cannot be enforced.

Has the report (I can't remember where I read it) of ferroelectric polarization in Fe3O4 below T_V been established? If so then the structure should be non-centrosymmetric. Does not that make the domain situation even worse?

Cc IS non-centrosymmetric, and that is included in the 24 possible domains. Macroscopic polarization switching is possible, but only at very low T and with frequencies of several 100 Hz (Schrettle PRB 2011) essentially because of residual conductivity. It means even if you had a large single-domain sample it would revert to a multi-domain state with both inversion twin domains ~equally populated pretty fast. We have some time-resolved XRD data on inversion-twin switching.

Yes indeed Cc is a non-centrosymmetric space group. I see the PRB paper of Joly et al. and their Cc structure based on resonace X-ray scattering study. But do I understand the paper of Schrettle correctly who claims that non-centrosymmetry is only at the local (short-range) level?

That's the part (when they start talking about short-range CO) of the Schrettle paper that I don't buy, I don't think their macroscopic data allow such conclusions. The paper you have to look at concerning structure is Senn/Wright/Attfield, Nature 481, 173 (2012). After decades they managed to refine the structure by high-energy XRD on a 40 microm monodomain (almost, 89% of scattering from one domain) crystal , after screening who knows how many crystals of that size to find a sufficiently monodomain one.

I looked at the paper by Senn et al. Heroic work indeed! From Fig. 1 a I see that the higher-order spots from the second crystal is well separated. This will not be so for the lower-order reflections. I doubt profoundly the results of a non-centrosymmetric space group refinement of such a twinned crystal. If the second crystal contribute 11% scattering and for lower order reflections if you cannot separate them from the scattering from the main crystal then the refinement in a non-centrosymmetric space group will not give one any new information. The difference between F^2(hkl) and F^2(-h-k-l) will be within this uncertainty and should not help you at all. (I invite the comments of experienced crystallographers.) But of course it helps to write a paper!

Hi C.,

I do not quite understand your proposal for producing a monodomain single crystal of magnetite. What external magnetic film are you thinking of and how does one apply that to a growing crystal? Can you please explain a bit more.

For your de-twinning question. On the theory side Rob Coe did some nice work on the analysis of the strain tensor: http://dx.doi.org/10.1016/j.epsl.2011.11.021

I think this tells you where/how to squeeze when cooling through the transition.

Experimentally Senn (and I) used a small crystal and a magnetic field. Mark's genius insight was to allow the crystal to re-orient and align itself with the field at room temperature prior to freezing and cooling. The one used for refinement was number 6 and the smallest we tried on that experiment.

For larger (neutron sized) crystals there is the original method by Iizumi. More recently the Compton scattering team in Japan had some success:

http://arxiv.org/pdf/0908.3685.pdf

About structure refinement: F(hkl) and F(-h,-k,-l) are always exactly overlapped in all acentric structures. This is not a problem for refinement unless you want to distinguish whether you have the left or right handed structure.

Mark Senn should be in Grenoble next week if you want to join us for a coffee.

Hi Jon, Thanks a lot for the paper. I spent some time to produce a single-domain single-crystal (neutron size) of manganite but did not succeed. I tried to follow the method of Iizumi. I must now read carefully your article and try to understand why I did not succeed. Now Manuel tells me that even if I produce a single domain crystal it would It "would revert to a multi-domain state with both inversion twin domains ~equally populated pretty fast". Do you agree with his argument? That makes the whole think hopeless and I then don't understand how you could keep the single domain crystal for finite time and and do crystallographic study.

I shall be very pleased to get together with you for a coffee.

Also Jon, could you estimate (not easy though) whether the chage odering in Fe3O4 complete or partial as is invariably the case?

In one of the nicest determinations of the magnetic anisotropy below Tv, Abe t al used the two tricks: cool down in a magnetic field (you select the c monoclinic axis) and and the same time apply stress in an oblique direction (you select one of the two possible twins):

Abe, K., Miyamoto, Y. & Chikazumi, S. Magnetocrystalline Anisotropy of Low Temperature Phase of Magnetite. J. Phys. Soc. Jpn. 41, 1894–1902 (1976).

if you keep the stress applied as they did, it should work.

About the ferroelectric character, in addition to the old 80s work by Kato, there are more recent works by M. Ziese:

Ziese, M. et al. Magnetite (Fe3O4): a new variant of relaxor multiferroic? Journal of Physics: Condensed Matter 24, 086007 (2012).

I would say it is well established, but I have not seen any agreement about the detailed microscopic geometry that gives rise to it.

Thanks Juan.