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Polarisation dependence of magnetic Bragg scattering in YMn$_2$O$_5$

The polarisation dependence of the intensity of elastic magnetic scattering from \ymno\ single crystals has been measured at 25 K in magnetic fields between 1 and 9 T. A significant polarisation dependence was observed in the intensities of magnetic satellite reflections, propagation vector $ \pv=0.5,0,0.25$ measured with both the [100] and [010] axes parallel to the common polarisation and applied field direction. The intensity asymmetries $A$ observed in sets of orthorhombicly equivalent reflections show systematic relationships which allow the phase relationship between different components of their magnetic interaction vectors to be determined. They fix the orientation relationships between the small $y$ and $z$ moments on the \mnfp\ and \mntp\ sub-lattices and lend support to the structure reported by Kim et al. It was found that that $A(hkl)\ne A(\bar h\bar k\bar l)$ which suggests that there is a small modulation of the nuclear structure which has the same wave-vector as the magnetic modulation leading to a small nuclear structure factor for the satellite reflections. The differences $A(hkl)- A(\bar h\bar k\bar l)$ observed indicate shifts in the atomic positions of order 0.005 Å.