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

Chiral multiferroic langasites have attracted attention due to their doubly-chiral magnetic ground state within an enantiomorphic crystal. We report on a detailed resonant soft X-ray diffraction study of the multiferroic Ba$_3$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 $(0,0,tau)$, $(0,0,2tau)$, $(0,0,3tau)$ and $(0,0,1-3tau)$ where $tau approx 0.140 pm 0.001$. The dependence of the scattering intensity on X-ray polarization and azimuthal angle indicate that the odd harmonics are dominated by the out-of-plane ($mathbf{hat{c}}$-axis) magnetic dipole while the $(0,0,2tau)$ originates from the electron density distortions accompanying magnetic order. We observe dissimilar energy dependences of the diffraction intensity of the purely magnetic odd-harmonic satellites at the Fe $L_3$ edge. Utilizing first-principles calculations, we show that this is a consequence of the loss of threefold crystal symmetry in the multiferroic phase.