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Chiral multiferroic langasites have attracted attention due to theirdoubly-chiral magnetic ground state within an enantiomorphic crystal. We reporton a detailed resonant soft X-ray diffraction study of the multiferroicBa$_3$TaFe$_3$Si$_2$O$_{14}$ at the Fe $L_{2,3}$ and oxygen $K$ edges. Below$T_N$ ($\approx27K$) we observe the satellite reflections $(0,0,\tau)$,$(0,0,2\tau)$, $(0,0,3\tau)$ and $(0,0,1-3\tau)$ where $\tau \approx 0.140 \pm0.001$. The dependence of the scattering intensity on X-ray polarization andazimuthal angle indicate that the odd harmonics are dominated by theout-of-plane ($\mathbf{\hat{c}}$-axis) magnetic dipole while the $(0,0,2\tau)$originates from the electron density distortions accompanying magnetic order.We observe dissimilar energy dependences of the diffraction intensity of thepurely magnetic odd-harmonic satellites at the Fe $L_3$ edge. Utilizingfirst-principles calculations, we show that this is a consequence of the lossof threefold crystal symmetry in the multiferroic phase.

Crystal Symmetry Lowering in Chiral Multiferroic Ba$_3$TaFe$_3$Si$_2$O$_{14}$ observed by X-Ray Magnetic Scattering