Terahertz optical activity near crystal field transitions of Tm3+ ions in magnetoelectric alumoborates

Abstract: Crystal field (CF) excitations in the ground multiplet $^3H_6$ of Tm$^{3+}$ ions were investigated using terahertz transmission spectra of magnetoelectric TmAl$3$(BO$_3$)$_4$ and Tm${0.05}$Yb${0.1}$Y${0.85}$Al$_3$(BO$_3$)$_4$. These excitations were identified as mainly magnetic dipole transitions from the ground singlet A$_1$ to the next excited doublet E, split by the crystal field of the D$_3$ symmetry. The fine structure of the modes was resolved at low temperatures. It manifested differently in lightly doped and in pure Tm borates, consistent with different distortions of the local crystal field with the D$_3$ symmetry. Strong natural optical activity was observed near the CF transitions resulting in a polarization plane rotation up to 25 degrees. The optical activity is quantitatively described by contributions of magnetic and electric dipole transitions to dynamic magnetoelectric susceptibility and taking into account the classification of local distortions.

• The paper demonstrates that THz optical activity in Tm alumoborates arises from crystal field transitions and shows intrinsic magnetoelectric coupling.
• It employs advanced spectroscopy and modeling to resolve fine structure and quantify Bi-induced impurity effects in the material.
• Results indicate significant polarization rotation (>20°) at low temperatures, highlighting prospects for tunable THz optical devices.

Terahertz Optical Activity and Crystal Field Fine Structure in TmAl₃(BO₃)₄ Magnetoelectrics

Introduction

This paper presents a comprehensive experimental and theoretical investigation of terahertz (THz) optical activity associated with crystal field (CF) transitions within the $3H_6$ ground multiplet of Tm$^{3+}$ ions in magnetoelectric alumoborates, specifically in TmAl₃(BO₃)₄ and Tm-doped YAl₃(BO₃)₄. The study focuses on zero-field measurements, highlighting the manifestations of fine structure resulting from local lattice distortions, particularly those induced by Bi$^{3+}$ impurities incorporated during crystal growth from Bi-containing flux. The work quantifies the contributions of magnetic- and electric-dipole transitions to the dynamical magnetoelectric (ME) susceptibility and demonstrates the potential of THz natural gyrotropy as an incisive probe of local symmetry in noncentrosymmetric rare-earth compounds.

Experimental Approach

Single crystals of TmAl₃(BO₃)₄ and Tm₀.₀₅Yb₀.₁Y₀.₈₅Al₃(BO₃)₄ were synthesized using a Bi₂Mo₃O₁₂-Li₂MoO₄-B₂O₃ flux technique, which is known to induce partial substitution of rare-earth sites with Bi. The crystals were oriented along principal axes and probed in transmission and polarization-rotation geometries via a quasi-optical backward-wave-oscillator (BWO) system in the 0.3–1.17 THz spectral range (10–39 cm$^{-1}$), at temperatures down to 4 K. Careful analysis of rotating-analyzer spectra provided direct access to polarization rotation (optical activity) and ellipticity associated with CF transitions.

Crystal Field Spectroscopy and Fine Structure

Both pure and diluted samples revealed a strong resonance in the vicinity of 25–33 cm$^{-1}$, attributed to predominantly magnetic-dipole $A_1 \to E$ transitions of Tm$^{3+}$ in $D_3$ symmetry CF environments. Spectra exhibited well-resolved fine structure at low temperature. In TmAl₃(BO₃)₄, the transition mode split into multiple components, corresponding to three types of Tm$^{3+}$ sites defined by their proximity and the nature of local distortions—most notably the presence of Bi$^{3+}$ impurities. By contrast, only a single broadened pair of transitions is observed in the diluted system, reflecting dominant random deformation and reduced probability for Tm–Bi interaction.

A cluster model, incorporating three distinct Tm$^{3+}$0 environments around a Bi$^{3+}$1 impurity, was required to accurately reproduce both transmittance and gyrotropy spectra in the pure compound. This model fitted a Bi concentration of $^{3+}$2, compatible with independent spectroscopic evaluations for borates grown from similar fluxes. For the diluted material, random lattice deformations governed the E-doublet splitting, and the distribution of local strains was quantitatively extracted.

Magnetoelectric Optical Activity

A pronounced natural optical activity was detected at the $^{3+}$3 CF transitions, with polarization rotation angles reaching up to 25° in zero magnetic field. This gyrotropy is symmetry-allowed for the noncentrosymmetric $^{3+}$4 space group and arises from interference between magnetic-dipole and electric-dipole transition pathways contributing to the dynamic ME susceptibility tensor $^{3+}$5. The experimental rotation angle, as well as the temperature and site-dependent intensity patterns, were quantitatively reproduced using the extracted transition dipole matrix elements.

The result that rotation angles exceeding 20° at intramultiplet CF transitions can occur in the absence of an applied field is highlighted as a strong numerical demonstration of intrinsic ME coupling in this material class. This result places rare-earth alumoborates alongside antiferromagnetic electromagnets and other multiferroics where dynamical ME effects have been more commonly observed.

Implications and Prospects

The results underscore that local structural deviations—especially those arising from growth-related impurities or stress—can play a deterministic role in the formation of gyrotropic fine structure. The ability to unambiguously relate spectral features in the THz regime to the occupation and splitting of CF levels provides a methodology for detailed characterization of rare-earth site environments in magnetoelectrics. As the THz regime directly probes low-lying CF states that mediate ME coupling, these findings facilitate a more granular understanding of the microscopic mechanisms underpinning functional properties in noncentrosymmetric quantum materials.

Practical implications extend to the design of tunable optical elements, such as THz polarization rotators or isolators, exploiting the large natural optical activity and sensitivity to local symmetry breaking. From a theoretical perspective, the work reinforces the importance of incorporating ensemble averaging over impurity-induced and random lattice distortions for quantitative modeling of optical and ME response functions.

Looking forward, systematic exploration of other rare-earth ions and controlled defect engineering may yield further insights into the interplay between local structure and macroscopic ME phenomena. Moreover, these results provide a basis for dynamic control of gyrotropy via external field tuning if combined with additional functional constituents in similar material platforms.

Conclusion

This study provides a rigorous analysis of terahertz optical activity and crystal field fine structure in Tm-containing magnetoelectric borates, unequivocally establishing the influence of local symmetry breaking and impurity incorporation on both ME coupling and gyrotropy. By deconvolving the contributions of different classes of local site distortion via experimental and modeling efforts, the work demonstrates that THz natural optical activity offers a powerful probe for fundamental and applied investigations of noncentrosymmetric rare-earth systems.