Spectroscopy of f-f transitions, crystal-field calculations, and magnetic and quadrupole helix chirality in DyFe${}_3$(BO${}_3$)${}_4$

Abstract

Recently, quadrupole helix chirality and its domain structure was observed in resonant x-ray diffraction experiments on DyFe${}_3$(BO${}_3$)${}_4$ using circularly polarized x rays [T. Usui et al., Nature Materials 13, 611 (2014)]. We show that this effect can be explained quantitatively by calculating the quadrupole moments of the Dy${}^{3+}$ ions induced by the low-symmetry ($C_2$) crystal-field (CF) component. In this work, the CF parameters for the Dy${}^{3+}$ ions in the $P{3}_{1}21$ ($P{3}_{2}21$) phase of DyFe${}_3$(BO${}_3$)${}_4$ are obtained from CF calculations based on the analysis of high-resolution temperature-dependent optical spectroscopy data. We also consider the helix chirality of the single-site magnetic susceptibility tensors of the Dy${}^{3+}$ ions in the paramagnetic $P{3}_{1}21$ ($P{3}_{2}21$) phase and suggest a neutron diffraction experiment to reveal it.

9 pages, 5 figures, 4 tables