High-resolution spectroscopy of Pr3+ions in YAl3(BO3)4:Pr3+. Crystal-field, hyperfine,and electron-deformation interactions

Optical transmission spectra of YAl3(BO3)4 crystals doped with the Pr3+ ions in concentrations 1 and 2.5 at. % were studied by high-resolution (up to 0.05 cm-1) Fourier spectroscopy, including in magnetic field parallel to the trigonal c axis of the crystal. The g factors of several crystal-field doublets of Pr3+ were determined. The crystal-field calculations performed using the exchange-charge model and high-resolution spectroscopy data allowed us to obtain a physically reasonable set of crystal-field parameters. The observed splitting of a number of doublets in zero magnetic field is explained by the presence of random lattice deformations. Simulation of the profiles of observed deformational doublets was carried out taking into account both hyperfine and electron-deformation interactions. The width of the distribution function of random strains was estimated. The main sources of random strains in YAl3(BO3)4:Pr3+ crystals are discussed.

💡 Research Summary

The authors present a comprehensive high‑resolution spectroscopic study of praseodymium‑doped yttrium aluminum borate (YAl₃(BO₃)₄, abbreviated YAB) crystals. Two series of samples were investigated: one with 1 at.% Pr³⁺ and another with 2.5 at.% Pr³⁺, grown by the solution‑melt method using different fluxes (Bi₂Mo₃O₁₂, K₂Mo₃O₁₀, and a mixed K₂O/MoO₃/B₂O₃ flux). Transmission spectra were recorded in the 2000–23 000 cm⁻¹ range with a Fourier‑transform spectrometer at a resolution of 0.05 cm⁻¹, over temperatures from 5 K to 300 K, and in three polarization configurations (unpolarized, π, σ).

A magnetic field of 0.595 T parallel to the trigonal c‑axis was applied to a subset of the measurements. Zeeman splittings of three narrow singlet‑to‑doublet transitions were resolved, allowing the experimental determination of the longitudinal g‑factors (g‖ ≈ 7.9, 10.1, 9.0). These values agree well with those calculated from crystal‑field (CF) theory using an exchange‑charge model, confirming the reliability of the derived CF parameters.

The CF Hamiltonian was constructed in the full 4f² manifold (dimension 546, accounting for the nuclear spin I = 5/2 of the sole stable isotope ¹⁴¹Pr). It includes the free‑ion electrostatic and spin‑orbit terms, configuration‑mixing corrections, Zeeman interaction, magnetic‑dipole hyperfine, electric‑quadrupole hyperfine, and an electron‑deformation term. The exchange‑charge model treats both point‑charge contributions from surrounding ions and covalent overlap (exchange charges) on the Pr³⁺–O²⁻ bonds. By fitting the experimentally observed CF level energies (43 levels identified) the authors obtained a physically reasonable set of CF parameters B_q^k.

A striking feature of the spectra is the appearance of doublet line shapes for transitions involving the non‑Kramers Γ₃ doublets, even though the hyperfine splitting (six components for I = 5/2) is too small to be resolved at the experimental resolution. The authors attribute this “deformation doublet” to random low‑symmetry lattice strains that lift the degeneracy of the Γ₃ doublets. They model the strain distribution as a Gaussian with a characteristic width, assume each individual hyperfine component has a Lorentzian profile (half‑width 0.053 cm⁻¹), and sum over all components to reproduce the observed line profiles. The simulated spectra match the experimental ones very well, allowing extraction of the strain distribution width.

Quantitatively, the deformation splitting Δ varies with Pr concentration and flux. For the 1 % samples (regardless of flux) Δ≈0.5 cm⁻¹, whereas for the 2.5 % sample Δ≈0.9–1.5 cm⁻¹, indicating a concentration‑dependent contribution. The authors propose a linear relation Δ(x) = β x + Δ_i, where β scales with the size mismatch between Pr³⁺ and Y³⁺ (Ω_Pr ∝ r_Pr − r_Y) and Δ_i≈0.48 cm⁻¹ represents an intrinsic strain component independent of flux.

The origin of the random strains is discussed in detail. Flux components introduce extrinsic defects: Bi³⁺ can substitute for Y³⁺, Mo⁶⁺ for Al³⁺, and K⁺ may occupy interstitial sites, all creating local distortions. Additionally, intrinsic defects such as vacancies and dislocations generated during crystal growth contribute to the strain field. The additive nature of these contributions explains why the deformation splitting for the 1 % samples is essentially the same across different fluxes, while the higher‑doped crystal shows a larger total strain due to the additive effect of the higher Pr concentration and the specific K₂Mo₃O₁₀ flux.

Overall, the work delivers a self‑consistent set of CF parameters for Pr³⁺ in YAB, quantifies the hyperfine and electron‑deformation interactions, and provides a realistic model for strain‑induced line broadening. These results are valuable for the design of YAB:Pr³⁺ based nonlinear optical devices, self‑frequency‑doubling lasers, and quantum‑information platforms where long coherence times and precise control of the spectroscopic environment are essential.