High-resolution spectroscopy , crystal-field calculations , and quadrupole helix chirality of DyFe 3 ( BO 3 ) 4

High-resolution polarized transmission spectra of DyFe3(BO3)4 single crystals were investigated in broad spectral (10-23000 cm-1) and temperature (3.5-300 K) ranges. Energies of the dysprosium levels in the paramagnetic and antiferromagnetic phases were determined. On the basis of these data and preliminary calculations in the frameworks of the exchange-charge model, we determined the crystal-field and Dy-Fe exchange interaction parameters of the Dy3+ ions at sites with the point C2 symmetry corresponding to the enantiomorphic P3121 and P3221 space groups. The values of electronic quadrupole moments of the Dy3+ ions were calculated, which enabled us to interpret results of the work [Usui et al., Nature Mater. 13, 611 (2014)] on the observation of domains of different quadrupole chirality in DyFe3(BO3)4. The crystals DyFe3(BO3)4 belong to the family of multiferroic rare-earth iron borates that crystallize in the trigonal R32 structure of the natural mineral huntite. With decreasing the temperature to TS=285 K, DyFe3(BO3)4 undergoes a structural phase transition from the R32 phase to the enantiomorphic space-group pair P3121 and P3221. It has been shown recently by resonant x-ray diffraction that, below TS, single-crystal samples of DyFe3(BO3)4 contain macroscopic domains which differ by right-handed (P3121) or left-handed (P3221) helical structures of electronic quadrupole moments of the Dy3+ ions [1]. Quadrupole moments at the Dy sites are induced by a low-symmetry C2 component of the crystal field that appears below TS and distorts the electronic density distribution in the Dy3+ ions. It is possible to calculate values of these moments on the base of the crystal-field (CF) parameters. A limited available information on the CF levels of Dy3+ ions in DyFe3(BO3)4 prevents from doing CF calculations in the frame of the C2 symmetry CF Hamiltonian with 15 parameters. We have measured temperature-dependent transmission spectra of DyFe3(BO3)4 single crystals corresponding to optical transitions from the ground multiplet to all the excited multiplets up to about 22200 cm-1 and to the far-infrared transitions within the ground multiplet. Almost all of the spectral lines observed in the absorption spectra of both the * Corresponding author: popova@isan.troitsk.ru DOI: 10.1051/ , 0 (2017) 713203041 EPJ Web of Conferences epjconf/201 SPECTROSCOPY.SU 2016 132 3041 © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). paramagnetic and antiferromagnetic (T< TN=39 K) phases of DyFe3(BO3)4 were unambiguously identified and the corresponding energies of excitations of the Dy3+ ions were determined. This dataset formed a basis for the CF calculations and modeling of exchange interactions. Here, we confine ourselves with the paramagnetic phase. The spectrum of a Dy3+ ion in a dielectric crystal can be described using the Hamiltonian H=HFI+HCF, where HFI is the free-ion Hamiltonian but CF , p p q q p q H C B is the CF Hamiltonian determined by 15 independent CF parameters p q B ( p q C are the spherical tensor operators of rank p). The initial values of the CF parameters were calculated in the framework of the exchange-charge model [2]. Then, the energies of transitions between the levels of the Dy3+ ions, obtained from the numerical diagonalization of the Hamiltonian H operating in the total space of 2002 states of the electronic 4f9 configuration, were compared with the measured optical spectra of DyFe3(BO3)4 in the paramagnetic phase, and the initial CF parameters were varied to fit the experimental data. Values of the six CF parameters ( 2 0 404, B 4

The crystals DyFe3(BO3)4 belong to the family of multiferroic rare-earth iron borates that crystallize in the trigonal R32 structure of the natural mineral huntite.With decreasing the temperature to TS=285 K, DyFe3(BO3)4 undergoes a structural phase transition from the R32 phase to the enantiomorphic space-group pair P3121 and P3221.It has been shown recently by resonant x-ray diffraction that, below TS, single-crystal samples of DyFe3(BO3)4 contain macroscopic domains which differ by right-handed (P3121) or left-handed (P3221) helical structures of electronic quadrupole moments of the Dy 3+ ions [1].Quadrupole moments at the Dy sites are induced by a low-symmetry C2 component of the crystal field that appears below TS and distorts the electronic density distribution in the Dy 3+ ions.It is possible to calculate values of these moments on the base of the crystal-field (CF) parameters.A limited available information on the CF levels of Dy 3+ ions in DyFe3(BO3)4 prevents from doing CF calculations in the frame of the C2 symmetry CF Hamiltonian with 15 parameters.
We have measured temperature-dependent transmission spectra of DyFe3(BO3)4 single crystals corresponding to optical transitions from the ground multiplet to all the excited multiplets up to about 22200 cm -1 and to the far-infrared transitions within the ground multiplet.Almost all of the spectral lines observed in the absorption spectra of both the paramagnetic and antiferromagnetic (T< TN=39 K) phases of DyFe3(BO3)4 were unambiguously identified and the corresponding energies of excitations of the Dy 3+ ions were determined.This dataset formed a basis for the CF calculations and modeling of exchange interactions.Here, we confine ourselves with the paramagnetic phase.
The spectrum of a Dy 3+ ion in a dielectric crystal can be described using the Hamiltonian H=HFI+HCF, where HFI is the free-ion Hamiltonian but CF , p p q q p q H C B

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is the CF Hamiltonian determined by 15 independent CF parameters p q B ( p q C are the spherical tensor operators of rank p).The initial values of the CF parameters were calculated in the framework of the exchange-charge model [2].Then, the energies of transitions between the levels of the Dy 3+ ions, obtained from the numerical diagonalization of the Hamiltonian H operating in the total space of 2002 states of the electronic 4f 9 configuration, were compared with the measured optical spectra of DyFe3(BO3)4 in the paramagnetic phase, and the initial CF parameters were varied to fit the experimental data.i ) are found with lower accuracy because they little influence the multiplet splittings.However, just this CF component determines some specific properties of RE iron borates in the P3121 (or P3221) phase, in particular, the anisotropy of the magnetic spectroscopic factors of Kramers doublets of the Dy 3+ ions in the ab-plane and the quadrupole helix chirality in DyFe3(BO3)4 [1].
The low-symmetry C2-component of the crystal field distorts the electronic density distribution in the Dy 3+ ions and induces non-zero non-axial components of the electronic quadrupole moment at the dysprosium sites.The quadrupole helix chirality appears due to rotations of the local C2 symmetry axis by 2π/3 and 4π/3 at the 3a dysprosium sites shifted relative one another along the c-axis by c/3 and 2c/3, respectively.The results of calculations of the average values of the quadrupole moment components at different temperatures T (kB is the Boltzman constant) using the set of the CF parameters given above agree satisfactorily with the experimental data presented in Ref. [1] (see Table 1) and confirm supposition [1] that changes of  This paper was supported by the Russian Science Foundation (14-12-01033).

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with temperature are mainly induced by redistribution of populations of CF sublevels of the Dy 3+ ion ground multiplet.