We present the results of temperature- and polarization-dependent high-resolution optical spectroscopy studies of $\mathrm{DyF}{\mathrm{e}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ performed in spectral ranges $40-300\mathrm{c}{\mathrm{m}}^{-1}$ and $3000-23000\mathrm{c}{\mathrm{m}}^{-1}$. The crystal-field (CF) parameters for the $\mathrm{D}{\mathrm{y}}^{3+}$ ions in the $P{3}_{1}21$ ($P{3}_{2}21$) phase of $\mathrm{DyF}{\mathrm{e}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ are obtained from calculations based on the analysis of the measured f-f transitions. Recently, quadrupole helix chirality and its domain structure was observed in resonant x-ray diffraction experiments on $\mathrm{DyF}{\mathrm{e}}_3{\left(\mathrm{B}{\mathrm{O}}_3\right)}_4$ using circularly polarized x rays [T. Usui, Y. Tanaka, H. Nakajima, M. Taguchi, A. Chainani, M. Oura, S. Shin, N. Katayama, H. Sawa, Y. Wakabayashi, and T. Kimura, Nat. Mater. 13, 611 (2014)]. Using the obtained set of the CF parameters, we calculate temperature dependencies of the electronic quadrupole moments of the $\mathrm{D}{\mathrm{y}}^{3+}$ ions induced by the low-symmetry ($C_2$) CF component and show that the quadrupole helix chirality can be explained quantitatively. We also consider the temperature dependencies of the bulk magnetic dc-susceptibility and the helix chirality of the single-site magnetic susceptibility tensors of the $\mathrm{D}{\mathrm{y}}^{3+}$ ions in the paramagnetic $P{3}_{1}21$ ($P{3}_{2}21$) phase and suggest the neutron and resonant x-ray diffraction experiments in a magnetic field to reveal the helix chirality of field-induced magnetic moments.

• Received 24 November 2016
• Revised 5 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.125131