Analysis of the magnetic dipolar nonradiative decay of the ⁵D₁ level of Eu³⁺ in single-crystalline huntite-type REAl₃(BO₃)₄:Eu³⁺ (RE = Y, Gd, Lu)

Abstract

The intraconfigurational 4f⁶ ↔ 4f⁶ transitions of Eu³⁺ provide sensitive insights into local symmetry and ligand fields, making Eu³⁺ a versatile probe ion for structural elucidation and temperature-dependent optics. In particular, the dynamics of the ⁵D₁ level are of central importance for applications in ratiometric luminescence thermometry but are strongly influenced by the phonon energy of the host compound, selection rules and the average Eu–ligand distance. In Eu³⁺-activated huntite-type borates REAl₃(BO₃)₄ (RE = Y, Gd, Lu), there is an almost trigonal prismatic coordination with a local D₃ symmetry of the RE³⁺ ion, whose subtle distortions vary systematically from RE = Gd to RE = Y to RE = Lu. These structural changes are reflected in a slight elongation of the ⁵D₀ decay time and a decreasing asymmetry ratio R₂, indicating a reduced induced electric–dipole component according to Judd–Ofelt theory. Temperature-dependent photoluminescence and time-resolved measurements determine the intrinsic nonradiative coupling rate between the ⁵D₁ and ⁵D₀ levels to be k_nr(0) ≈ 55 ms⁻¹. As expected, this increases with a shorter Eu–O bond lengths, but in GdAl₃(BO₃)₄, it shows an additional contribution that cannot be explained structurally and is attributed to a local acceleration effect caused by the paramagnetism of the surrounding Gd³⁺ ions. The temperature dependence of the ⁵D₀ decay time also reveals a thermal coupling of the excited states and a high-temperature-induced quenching via the Eu³⁺ ← O²⁻ ligand-to-metal charge transfer (LMCT) state. These results provide a comprehensive understanding of the excited state dynamics of Eu³⁺ in huntite-type borate and, at the same time, illustrate the potential and limitations of these host lattices for Eu³⁺-based luminescence thermometry.

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Introduction

Frequently used luminescent solid-state materials are based on the targeted activation of host compounds containing lanthanoid ions. A particularly popular candidate in this regard is Eu, which is used in both its divalent and trivalent oxidation state. While divalent europium (Eu²⁺) mainly shows broad-band luminescence based on an electric dipole-allowed 4f⁶5d¹ → 4f⁷ transition that can be specifically varied in energy by choosing the host compound,^1–9 Eu³⁺ is much more prominent for its narrow-line luminescence related to intraconfigurational 4f⁶ ↔ 4f⁶ transitions.^10–16 Eu³⁺ primarily exhibits luminescence from its lowest excited ⁵D₀ level to the lower-energy ⁷F_J (J = 0–4) levels in the red spectral range¹⁷ and finds numerous applications in bioimaging^18–20 and solid-state lighting.^21–24

The excited ⁵D₀ level and the ground level ⁷F₀ of Eu³⁺ are both singly degenerate and thus, will not be split any further in a crystal field. As a consequence, the number and relative intensities of observed lines in the absorption and luminescence spectra of Eu³⁺-activated compounds can give insights about the local symmetry of the sites that the Eu³⁺ ions occupy.^24–28 Accordingly, Eu³⁺ can be used for the spectral determination of site symmetry to characterize the environment.^27–32

Among the intraconfigurational 4f⁶ ↔ 4f⁶ transitions of the Eu³⁺ ion, the ⁵D₀ → ⁷F₁ transition and the ⁵D₀ → ⁷F₂ transition are particularly important. The former is a pure magnetic dipolar transition^33–35 and its intensity is largely independent of local symmetry, depending mainly on the refractive index.³⁶ The latter, on the other hand, is an induced electric dipolar transition,^34,35,37,38 according to the Judd–Ofelt theoretical framework,^39,40 and its intensity can be tuned by an appropriate choice of the ligand field environment. The intensity ratio of these two transitions (called asymmetry ratio R₂) is often used to make statements about the local symmetry of the environment and can be even photonically controlled on the nanoscale.^26,41 Recently, the impact of the polarizability of the ligating atoms around Eu³⁺ on the R₂ values, has been also discussed.⁴²

Furthermore, luminescence from the higher-energy ⁵D₁ level (Fig. 1) can be observed, making Eu³⁺ in principle suited for ratiometric luminescence thermometry as well.^44,45 It turns out that the energy gap of ΔE ≈ 1750 cm⁻¹ between the excited ⁵D₁ and ⁵D₀ level is generally useful for high temperatures. In addition to the selected host compound based on their phonon energies,^17,46 also selection rules⁴⁷ and the average Eu–ligand distance may affect the nonradiative decay of the ⁵D₁ level thus having an impact on performance of an Eu³⁺-based luminescence thermometer.^17,46,48

Fig. 1 Energy level diagram of Eu³⁺. The radiative (blue) and nonradiative decay (black) of the ⁵D₁ level and the radiative decay of the ⁵D₀ (red) level are shown for an idealized temperature of T = 0 K. Energies were taken from the data published by Dieke et al.⁴³

Rare earth aluminum borates in the huntite-type structure represent an interesting class of host compounds for the luminescence of trivalent lanthanoid ions.^49,50 In particular, Yb³⁺- and Nd³⁺-activated REAl₃(BO₃)₄ (RE = Y, Gd) have attractive properties for use in solid-state lasers.^51–55 The optical spectroscopy of huntite borate crystals activated with the Eu³⁺ ion has been investigated in the past by Görller-Walrand et al.^56,57 and by Kellendonk and Blasse.⁵⁸ In this work, we analyze the excited state dynamics of the ⁵D₁ level of Eu³⁺ in the isotypically crystallizing huntite-type series REAl₃(BO₃)₄ (RE = Y, Gd, Lu). We will elaborate on the impact of the varying average Eu–O bond lengths. In addition, a possibly accelerating influence of the paramagnetic nature of Gd³⁺ compared to the other two diamagnetic rare-earth ions on the expectedly magnetic dipolar ⁵D₁ ↔ ⁵D₀ transition will be investigated.

Synthesis and methods

The synthesis of REAl₃(BO₃)₄ (RE = Y, Gd, Lu) single crystals and the instrumentation used for this study are detailed in the SI.

Results and discussion

Structural analysis

The XRD analysis reveals that the Eu³⁺-activated REAl₃(BO₃)₄ (RE = Y, Gd, Lu) compounds crystallize in a trigonal crystal system with the space group R32 (no. 155) in a huntite-type structure that can be considered as a filled version of the calcite (CaCO₃) structure type. The obtained XRD patterns indicate phase purity of the phosphors (Fig. S1). In line with the different ionic radii of the considered rare-earth ions, reflections show a consistently decreasing lattice parameters from Gd³⁺ over Y³⁺ to Lu³⁺ (see Table S1). As expected, the RE–O bond lengths also decrease in this series of rare-earth ions (Table S1).

The crystal structure of REAl₃(BO₃)₄ (RE = Y, Gd, Lu) is depicted in Fig. 2(a).⁵⁹ The RE³⁺ ions occupy six-fold coordinated sites with nearly ideal trigonal prismatic coordination geometry and a local D₃ point symmetry (see Fig. 2(b)). The RE³⁺ cations are shielded from each other by trigonal-planar [BO₃]³⁻ units, resulting in large distances between the nearest RE³⁺ sites (≈5.9 Å), which limits possible decay pathways such as concentration quenching, whilst allowing the detailed study of energy transfer and migration processes when suitable cations are present in the structure.^60–62

Fig. 2 (a) Crystal structure of YAl₃(BO₃)₄ (ICSD: 20223) visualized by VESTA. (b) Coordination of the Y site.

Photoluminescence of Eu³⁺ in REAl₃(BO₃)₄ (RE = Y, Gd, Lu)

The photoluminescence excitation and emission spectra of Eu³⁺ in single-crystalline REAl₃(BO₃)₄ (RE = Y, Gd, Lu) at 81 K are depicted in Fig. 3. The excitation spectra recorded upon monitoring the ⁵D₀ → ⁷F₂ transition of Eu³⁺ at around 613 nm reveal narrow-line transitions to the ⁵D₀ (580 nm) and higher 4f⁶ levels such as the ⁵D₁ (525 nm), ⁵D₂ (460 nm), ⁵L₆ (395 nm) and ⁵D₄ level (360 nm). Additionally, a broad excitation band in the UV range (at around 260 nm) is observed, which can be attributed to the Eu³⁺ ← O²⁻ ligand-to-metal charge transfer (LMCT) state and is commonly observed in complex oxides.^{11,60,63–67} In GdAl₃(BO₃)₄:1% Eu³⁺, additional narrow-line transitions in the UV range at around 310 nm, 300 nm and 270 nm are observed, which are attributed to 4f⁷ ↔ 4f⁷ transitions of Gd³⁺.^47,68,69

Fig. 3 Normalized photoluminescence excitation (left) and emission spectra (right) of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) at 81 K. For excitation spectra, the emission from the ⁵D₀ → ⁷F₂ transition was monitored. Emission spectra were recorded upon excitation into the ⁵L₆ level. The assignment of Eu³⁺-based transitions is exemplarily depicted for the case of LuAl₃(BO₃)₄:1% Eu³⁺.

The emission spectra show narrow bands in the orange and red range, which are typical for luminescence from the ⁵D₀ level to the lower energetic ⁷F₁, ⁷F₂, ⁷F₃ and ⁷F₄ levels. The number of emission bands (2 for the ⁵D₀ → ⁷F₁, 2 for the ⁵D₀ → ⁷F₂, 4 for the ⁵D₀ → ⁷F₃, and 4 for the ⁵D₀ → ⁷F₄ transition) indicates a D₃ point symmetry for Eu³⁺,²⁵ in excellent agreement with the local structure of the distorted [REO₆]⁹⁻ (RE = Y, Gd, Lu) trigonal prisms (Fig. 2). In addition to the emission from the ⁵D₀ level, also weak emission from the higher-energetic ⁵D₁ level into the ⁷F₀, ⁷F₁, and ⁷F₂ levels (520–570 nm) can be detected. The comparably weak emission from the ⁵D₁ level can be explained by rapid multiphonon relaxation due to the high cut-off phonon energy in REAl₃(BO₃)₄ (ħω_cut ≈ 1400 cm⁻¹).⁷⁰ The excitation spectra reveal an energy gap of ΔE ≈ 1750 cm⁻¹ between the ⁵D₁ and ⁵D₀ level of Eu³⁺ in these compounds (see SI), which is in agreement with other works.^{44,48,71–73}

Fig. 4 depicts the measured decay curves of the ⁵D₁- and ⁵D₀-based emission of Eu³⁺ in REAl₃(BO₃)₄ (RE = Y, Gd, Lu) at 81 K, respectively. The luminescence intensity stemming from both excited levels in the 1 mol%-activated borates show single exponential decay clearly justifying the assumption of negligible cross-relaxation or additional interaction processes among the Eu³⁺ ions at that temperature, which is consistent with the structure and the associated high RE–RE distances of more than 5 Å. The decays remain single exponential even at temperatures up to 823 K (see Fig. S4 in the SI). Cross-relaxation involving the ⁵D₁ level is often manifested by a fast component at short delay times in the decay curve, especially at higher temperatures.^71,74–76

Fig. 4 Photoluminescence decay curves with single exponential fits (black) of the ⁵D₁-based (left, µs range) and the ⁵D₀-based emission (right, ms range) of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) at 81 K.

Due to the high energy gap between the ⁵D₀ and the ⁷F₆ level (Fig. 1), the decay of the ⁵D₀ level can be assumed to be purely radiative. The ⁵D₀ level of Eu³⁺ in REAl₃(BO₃)₄ (RE = Y, Gd, Lu) can be characterized by a decay time of just above 1 ms (see Table 1) at 81 K, which is consistent with Eu³⁺ in other host compounds.^{11,65,77–79} The measured decay time of the ⁵D₀ level in REAl₃(BO₃)₄:1% Eu³⁺ shows a measurable increase from RE = Gd over RE = Y to RE = Lu. Inspection of the local coordination geometry of the [REO₆]⁹⁻ entities (see Fig. 5) according to single-crystal (RE = Gd, Y) or Rietveld refined (RE = Lu; Fig. S1) structural data reveals that the angle between the two planes defined by O3^v–O3ⁱ–O3^iv and O3^v–O3ⁱ–O3ⁱⁱⁱ (Table 2) decreases from Gd over Y to Lu (34.5° → 30.0° → 26.1°), suggesting a gradual evolution of the (distorted) trigonal prism geometry towards a (distorted) octahedral one (from Gd to Lu). According to Judd–Ofelt theory,^39,40 a stronger induced electric dipolar character of the radiative transitions of Eu³⁺ should be detectable in non-centrosymmetric site symmetries (represented by the trigonal prismatic coordination geometry), inducing a decrease in the ⁵D₀ observed lifetime. Also, this interpretation goes in line with the decreasing splitting between the two Stark components of the ⁷F₁ level (see ⁵D₀ → ⁷F₁ transition in the emission spectra of Fig. 3 or ⁵D₁ ← ⁷F₀ transition in the excitation spectra of Fig. S3 in the SI), which gradually decreases along that series of rare earth ions, as a |J = 1〉 level retains its triple degeneracy in the limiting case of octahedral symmetry. Additional confirmation is gained from the asymmetry ratio R₂, which can be derived from the emission spectrum as^26,42

and decreases from RE = Gd over RE = Y to RE = Lu (see Table 1) in REAl₃(BO₃)₄:1% Eu³⁺ thus suggesting a more dominant magnetic dipolar nature of the 4f⁶ ↔ 4f⁶ transitions of Eu³⁺ along this series.

Table 1 Measured decay time τ of the ⁵D₀ level, the asymmetry ratio R₂ according to eqn (1) and the intensity ratio of the ⁵D₂ ← ⁷F₀ and ⁵D₁ ← ⁷F₀ excitation transitions (Fig. 3) of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) at T = 81 K

Compound	τ(^5D0)/ms	R2	I(^5D2/^5D1)
YAl3(BO3)4:1% Eu^3+	1.35 ± 0.01	5.568 ± 0.003	8.872 ± 0.001
GdAl3(BO3)4:1% Eu^3+	1.25 ± 0.01	5.644 ± 0.003	10.885 ± 0.001
LuAl3(BO3)4:1% Eu^3+	1.38 ± 0.01	5.266 ± 0.002	8.807 ± 0.001

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Fig. 5 Coordination environment of the RE³⁺ ion in REAl₃(BO₃)₄ (RE = Y, Gd, Lu). Relevant bond lengths and angles are reported in the SI (Fig. S2 and Table S2).

Table 2 Definition of a distorted octahedral surrounding by the angle between the two planes defined by O3^v–O3ⁱ–O3^iv and O3^v–O3ⁱ–O3ⁱⁱⁱ according to Fig. 5 in REAl₃(BO₃)₄ (RE = Y, Gd, Lu). Relevant bond distances and angles are reported in the SI (Fig. S2 and Table S2)

Compound	Angle/° between the planes O3^v–O3^i–O3^iv and O3^v–O3^i–O3^iii
GdAl3(BO3)4	34.5(1)
YAl3(BO3)4	30.0(1)
LuAl3(BO3)4:1% Eu^3+	26.1(1)
Ideal octahedron	0

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Next to the established asymmetry ratio R₂, the intensity ratio of the excitation transitions ⁵D₂ ← ⁷F₀ and ⁵D₁ ← ⁷F₀ may also give additional independent confirmation on this hypothesis (see Fig. 3), as the former of the two transitions also has induced electric dipolar character according to Judd–Ofelt theory.^39,40 It should be noted, however, that line strengths in photoluminescence excitation spectra are only a good estimate for oscillator strengths (normally only accessible from absorption spectra) in the limit of low optical densities.⁸⁰ Given the low absorbance of 4f⁶ ← 4f⁶ transitions as well as the low activator fraction of only 1 mol% of Eu³⁺, this seems to be a reasonable approximation. In fact, the intensity ratio of the indicated excitation transitions in REAl₃(BO₃)₄:1% Eu³⁺ does follow the same trend as R₂ (see Table 1). This parallel course of the two independent ratios thus strongly indicates the validity of the proposed structure–property correlation.

Excited-state dynamics of the ⁵D₁ and ⁵D₀ levels of Eu³⁺

In contrast to the ⁵D₀ level, the ⁵D₁ level in this set of compounds decays within around 17 µs (see Fig. 4). This much faster decay can be attributed to the additional contribution of multiphonon relaxation from the ⁵D₁ into the ⁵D₀ level. In the following, the small differences in the intrinsic nonradiative coupling rate between the ⁵D₁ and ⁵D₀ level of Eu³⁺ in REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) will be analyzed in more detail. For that purpose, temperature-dependent luminescence spectra were recorded for all three Eu³⁺-activated borates upon excitation into the ⁵L₆ level at 395 nm (Fig. 6). The emission intensity of the ⁵D₁-based transitions increases with rising temperature, which suggests a gradual thermal population of the ⁵D₁ level. The temperature-dependent luminescence intensity ratio (LIR) can give valuable insights here and tested against a temperature-dependent steady-state model. As the energy gap between the ⁵D₁ and the ⁵D₀ levels (ΔE ≈ 1750 cm⁻¹) cannot be bridged just by one cut-off phonon mode, but will also need a participation of at least one other (optical) phonon mode, the steady-state LIR can be modeled using the following equation¹⁷with I_j (j = 1, 2) as the intensities of the emission from the lower (⁵D₀ ≡ |1〉) and higher energetic (⁵D₁ ≡ |2〉) excited levels with degeneracies g₁ = 1 and g₂ = 3, respectively, C as the pre-factor, which is the ratio between the Einstein coefficients A_j0 for spontaneous emission from the two levels, k_1r and k_2r as total radiative rates of the respective levels, α as a feeding factor, which describes the fraction of population from the pumped excited auxiliary level (here: ⁵L₆) into the higher excited level ⁵D₁, k_nr(0) as the intrinsicnonradiative coupling rate between the two excited levels, and 〈n_k〉 (k = 1, 2) as the thermal phonon occupation factors of a regarded mode k with energy ħω₂,with k_B as the Boltzmann constant and T as the absolute temperature. The phonon energies are constrained by the restriction . It can be shown that the generalized model (1) evolves into a classic Boltzmann distribution if the terms connected with k_nr(0) are much larger than those containing the radiative rates, which is the case at sufficiently high temperatures.⁴⁶

Fig. 6 Temperature-dependent emission spectra of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) after excitation into the ⁵L₆ level (left) and the resulting luminescence intensity ratio with fit according to eqn (2) (right). The ⁵D₁-based emission is depicted in the inset.

At very low temperatures, the LIR remains constant indicating that the two excited ⁵D₁ and ⁵D₀ levels of Eu³⁺ are decoupled in that regime (Fig. 6). Once low energetic phonon modes can be thermally activated, the LIR shows a slight drop as a consequence of thermally stimulated nonradiative relaxation of the ⁵D₁ level in favor of an accelerated population of the ⁵D₀ level. If the overall nonradiative absorption transition from the ⁵D₀ to the ⁵D₁ level can compete with the radiative decay k_1r of the ⁵D₀ level, the LIR rises again and the two excited levels get into thermal equilibrium, which manifests in a Boltzmann behavior of the temperature-dependent LIR.¹⁷ For the investigated borates REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu), the radiative rate of the ⁵D₀ level k_1r was fixed to the experimentally obtained values (Fig. 4), and the feeding factor was set to α = 1, as no emission from higher energetic levels is observed in the luminescence spectra at 81 K (Fig. 3). The cut-off phonon energy was set to ħω_max = 1400 cm⁻¹ (ref. 70) and the number of additional phonons to p₂ = 1.

The model can describe the LIR very accurately and the fit yields physically reasonable results (Fig. 6). The obtained energy gap is in the range of ΔE ≈ 1650 cm⁻¹ and is generally fits in quite good agreement with the effective gap extracted from the excitation spectra (≈ 1750 cm⁻¹) (see SI). The logarithmic LIR changes its slope at high temperatures (T > 650 K), which is unusual for classic Boltzmann thermalization (see Fig. 6). We attribute this behavior to the involvement of the Eu³⁺ ← O²⁻ LMCT state (see Fig. 3) that can act as a crossover quenching pathway for the Eu³⁺ luminescence.^17,81,82 This hypothesis is confirmed by the observable decrease of the decay time of the ⁵D₀ level above 650 K (see Fig. 8), which will be discussed in more detail below. The influence of the LMCT state limits the applicability of the fitting model (1) at high temperatures. Thus, the limited temperature range for Boltzmann behavior of the LIR may also be the reason why the extracted energy gap from the fit does not fully match the spectroscopically extracted one from the excitation spectra at 81 K (see SI).

The intrinsic nonradiative rate according to the fits to eqn (2) are very similar and all in the range of k_nr(0) ≈ 55 ms⁻¹, which is generally plausible given the fact that the cut-off (optical) phonons are typically dominated by localized ligand-related vibrations. This places the rate within the expected range for host compounds with high cut-off phonon energies, such as aragonite-type LaBO₃ (k_nr(0) = 74 ms⁻¹).¹⁷

The range of application for a luminescent thermometer is largely defined by the so-called onset temperature T_onset, at which two thermally coupled levels are in thermal equilibrium.⁴⁶ This equilibrium is defined by the kinetic condition of competitve nonradiative multiphonon absorption compared to the radiative rate of the lower energy state, which equals for our Eu³⁺-activated borates.¹⁷ The solution to this condition is numerical and yields onset temperatures in the range of T_onset ≈ 400 K. This means that the onset temperatures for REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) are in a similar range to other Eu³⁺-based phosphors with high phonon energies, like LaBO₃:0.5% Eu³⁺ (T_onset = 402 K)¹⁷ and LaPO₄:0.5% Eu³⁺ (T_onset = 396 K).¹⁷ It should be noted that the onset temperatures heavily depend on the phonon energy ħω₂ obtained from the fit to eqn (2) and the associated thermal phonon occupation factor 〈n₂〉. This can result in significant differences. Thus, the onset temperature can only serve as an estimate to judge the performance of a luminescent thermometer.

A comparison of the individual intrinsic nonradiative rates in REAl₃(BO₃)₄ (RE = Y, Gd, Lu) shows no discernible trend (Table 3). It has been demonstrated by Ermolaev and Sveshnikova in the case of molecular emitters⁸³ as well by some of us in microcrystalline β-NaREF₄:0.5% Eu³⁺ (RE = La, Y, Lu)¹⁷ that the intrinsic nonradiative rate of Eu³⁺ should decrease with increasing average RE–ligand distance as vibrational coupling becomes weaker then.¹⁷ The estimated values for the nonradiative transition rates k_nr(0) according to the fits of the temperature-dependent LIR between the ⁵D₁ and ⁵D₀-based emission to eqn (2) does not readily allow such conclusions based on the large error margins of the values. Out of that reason, we performed time-resolved measurements of the luminescence decay of the ⁵D₁-based emission at 81 K to enhance the precision of the found values and motivate the validity of the order of magnitude estimated from the fit to eqn (2). At that temperature, nonradiative absorption from the ⁵D₀ to the ⁵D₁ level is negligible and thus, the total decay rate k₂ of the ⁵D₁ level contains the radiative contribution k_2r as well as the intrinsic nonradiative relaxation contribution k_nr(0) to the ⁵D₀ level⁴⁶

k₂ = k_2r + g₁ × k_nr(0) (4)

Upon selective pumping of the excited ⁵D₁ level (λ_ex = 525 nm) of Eu³⁺ in the huntite-type borates under investigation at a sufficiently low temperature (in order to prevent any thermalization among the excited levels), the ratio of the radiative rate of the ⁵D₁ level to the nonradiative rate can then be derived from the ratio of the luminescence intensities of the transitions stemming from the ⁵D₁ (⁵D₁ ≡ |2〉) and ⁵D₀ (⁵D₀ ≡ |1〉) level, respectively,⁴⁶By rearranging eqn (4) as a function of k_2r, substituting it into eqn (5), and transforming it to a function of k_nr(0), we thus obtaineqn (6) relates k_nr(0) to the total cumulative intensity of all radiative transitions from a given level |i〉. In practice, often only one particular transition with intensity I_iJ is considered. This can be accounted for by inclusion of the branching ratio β_i→J of a given transition from the respective level |i〉 into a lower energetic level |J〉, resulting in ref. 46with²⁶The emission spectra upon selective excitation into the ⁵D₁ level are depicted in Fig. 7. As for the spectra measured upon excitation into the ⁵L₆ level (Fig. 3), the Eu³⁺-related emission from the ⁵D₀ level dominates, which indicates a comparably fast nonradiative decay from the ⁵D₁ level to the ⁵D₀ level compared to its radiative rate. Nevertheless, weak emission in the range of 550–565 nm can be observed, which is attributed to the ⁵D₁ → ⁷F₂ transition. Consequently, the nonradiative rate can be calculated if the branching ratio for the ⁵D₁ → ⁷F₂ transition is known. The branching ratios for the ⁵D₁ → ⁷F₂ (β_1→2) and the ⁵D₀ → ⁷F₂ (β_0→2) transitions were calculated from the emission spectra shown in Fig. 3 and are listed in Table 3. The intensities were determined from the emission spectra in Fig. 7c.

Table 3 Measured decay rate of the ⁵D₁ level (k₂), branching ratios of the ⁵D₁ → ⁷F₂ (β_1→2) and ⁵D₀ → ⁷F₂ (β_0→2) according to eqn (8), the intrinsic nonradiative rate k_nr(0) according to eqn (7) and k_nr(0) obtained from the LIR, radiative rate of the ⁵D₁ level (k_2r) according to eqn (4) and (10) of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu)

Compound	k2/ms^−1	β1→2	β0→2	knr(0)/ms^−1	knr(0) (LIR)/ms^−1	k2r from eqn (4)/ms^−1	k2r from eqn (10)/ms^−1
YAl3(BO3)4:1% Eu^3+	56.09 ± 0.01	0.2999	0.5990	55.16 ± 0.03	53 ± 8	0.93 ± 0.01	0.90 ± 0.05
GdAl3(BO3)4:1% Eu^3+	57.18 ± 0.01	0.3220	0.6084	56.23 ± 0.04	54 ± 8	0.95 ± 0.01	0.98 ± 0.03
LuAl3(BO3)4:1% Eu^3+	57.41 ± 0.01	0.3439	0.5962	56.47 ± 0.01	60 ± 5	0.94 ± 0.01	0.92 ± 0.04

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Fig. 7 Left: Normalized photoluminescence emission spectra of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) upon excitation into the ⁵D₁ level at 81 K. The inset depicts the ⁵D₁-based emission.

The nonradiative rates determined via k₂ and the branching ratios from eqn (7) are in excellent agreement with the values determined from the LIR and confirm the physical plausibility of the fitting parameters (Table 3). In addition, a clear trend in the RE–ligand distance dependence can be analyzed much more carefully given the higher precision of the nonradiative transition rates obtained from time-resolved spectroscopy. In fact, k_nr(0) slightly increases from YAl₃(BO₃)₄:1% Eu³⁺ to LuAl₃(BO₃)₄:1% Eu³⁺ as expected according to the Ermolaev–Sveshnikova model⁸³ and in line with our earlier findings in β-NaREF₄:0.5% Eu³⁺ (RE = La, Y, Lu).¹⁷ However, a slightly higher nonradiative rate persists in GdAl₃(BO₃)₄:1% Eu³⁺ than in YAl₃(BO₃)₄:1% Eu³⁺ despite a larger ionic radius of Gd³⁺ than Y³⁺ in sixfold coordination (r(Gd³⁺) = 1.08 Å, r(Y³⁺) = 1.04 Å)⁸⁴ analogously to the intrinsic nonradiative coupling strengths estimated from the temperature-dependent LIR (Fig. 6 and Table 3). Additional confirmation of the physical validity of this effect can be qualitatively assessed from the emission spectra depicted in Fig. 7. The relative intensity of the ⁵D₁ → ⁷F₂ transition in GdAl₃(BO₃)₄:1% Eu³⁺ compared to that of the ⁵D₀ → ⁷F₂ transition upon excitation into the ⁵D₁ level is indeed slightly smaller than in YAl₃(BO₃)₄:1% Eu³⁺ implying a slightly faster nonradiative decay responsible for the observation of ⁵D₀-based emission in that experiment (Fig. 7). Consequently, it can be concluded that the nonradiative decay rate k_nr(0) coupling the excited ⁵D₁ and ⁵D₀ levels of Eu³⁺ is indeed slightly larger in GdAl₃(BO₃)₄:1% Eu³⁺ than in YAl₃(BO₃)₄:1% Eu³⁺ despite a shorter expectable average Eu–O bond length in the latter host compound. We ascribe this observation to the magnetic dipolar nature of the nonradiative ⁵D₁ ↔ ⁵D₀ transition and a local accelerating effect by the paramagnetic nature of neighboring Gd³⁺ ions. A very detailed investigation of this phenomenon on a wider scope of compounds is currently ongoing and will be part of a future study.

Besides the nonradiative decay from ⁵D₁ to ⁵D₀ level governed by multiphonon relaxation, radiative relaxation of the ⁵D₁ level remains to be discussed. By determining k_nr(0) from eqn (5), the radiative rate k_2r can be simultaneously extracted by means of eqn (2). In all three Eu³⁺-activated borates, it is in the order of 1 ms⁻¹ (see Fig. 4) and thus, within the reported range for the ⁵D₁ level.^17,75,85 An alternative method to indirectly assess the radiative rate k_2r of the ⁵D₁ level is a complementary analysis of the ⁵D₀-related luminescence decay curves at elevated temperatures (Fig. 8). Over the entire temperature range, the decay curves can be fitted with a single-exponential model. The decay rates remain constant up to a temperature of just over 250 K, then show a gradual increase up to 700 K, and increase even more strongly above those temperatures. Over the entire temperature range, no structural phase transitions of the huntite-type borates REAl₃(BO₃)₄ (RE = Y, Gd, Lu) is observable,^86–88 which indicates that this temperature dependence must be a consequence of thermally activated processes. Multiphonon relaxation cannot be responsible for the observed temperature dependence of the decay rate of the ⁵D₀ already detectable above 400 K, given the very high energy gap to the lower ⁷F₆ level (around 12390 cm⁻¹)⁴³ that would require at least 9 cut-off modes in the borate hosts (see Fig. 8). The slight increase in the decay rate of the ⁵D₀ level just above 250 K can be attributed to the onset of thermal coupling between the ⁵D₁ and ⁵D₀ levels, consistent with the observed minimum of the LIR at that temperature (Fig. 6) and the onset temperature (Table 3), above which the LIR follows Boltzmann behavior. In that temperature range, the ⁵D₀ and ⁵D₁ will decay with a thermally averaged decay rate 〈k(T)〉⁸⁹

The stronger increase in the rate above 700 K is also in good agreement with the LIR, which no longer follows the usual course above 650 K (see Fig. 6). This may be related to the influence of the Eu³⁺ ← O²⁻ LMCT state, which depopulates the 4f⁶ levels of Eu³⁺ via a thermally activated crossover and induces quenching.^82,90,91 Due to this process, eqn (9) is extended by a Mott–Seitz expression describing the crossover relaxation,⁹² resulting inwith a connected intrinsic crossover rate k_x(0) and ΔE_x as the effective barrier between the ⁵D₀ level and the crossing point with the potential energy curve of the LMCT state. The temperature-dependent decay rates of the ⁵D₀-based level can be fitted well by eqn (10) (Fig. 8). The fitted energy gaps between the ⁵D₁ and ⁵D₀ levels using eqn (10) are in the range of 1700 cm⁻¹ and in excellent agreement with the spectrally determined energy gaps (≈1750 cm⁻¹). In turn, the fitted crossover barrier ΔE_x (see Fig. 8 for exact value) is much below the anticipated value according to the excitation spectra of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) (Fig. 3). However, as the crossover process only becomes relevant at very high temperatures (>700 K), only four independent data points can be effectively used to estimate the crossover rate k_x(0) and barrier ΔE_x, which results in relatively large errors and thus, only offer limited insights. Higher temperatures could help make more precise statements and justify the validity of the model according to eqn (10) for the whole temperature range. By determining k_nr(0) from eqn (7), the radiative rate k_2r can be obtained by rearranging eqn (4). This is in the range of about 1 ms⁻¹ (Table 3) and generally matches the values estimated by eqn (10).

Fig. 8 Temperature-dependent decay curves of the ⁵D₀-based emission of REAl₃(BO₃)₄:1% Eu³⁺ (RE = Y, Gd, Lu) (left) and obtained decay rates as a function of temperature with a fit to eqn (10) (right).

Conclusions

In this work, the luminescent properties of Eu³⁺ in single-crystalline huntite-type REAl₃(BO₃)₄ (RE = Y, Gd, Lu) were investigated. Narrow-band emission in the red spectral range is observed, which can be attributed to emission from the ⁵D₀ level to the lower-energy ⁷F_J (J = 0–4) levels. The splitting of the emission indicates a local D₃ symmetry of the [REO₆]⁹⁻ coordination entities in REAl₃(BO₃)₄. The relative angular position of the six oxygen ligands correlates well with the trend in the decay times of the ⁵D₀ level, as well as the observed splitting of the ⁵D₁ or ⁷F₁ crystal field levels, respectively and with the different asymmetry ratio (R₂) values. In addition, weak narrow-band emission is observed in the green spectral range, which can be traced back to emission from the ⁵D₁ level. The comparatively weak emission from the ⁵D₁ level is in agreement with the energy gap law and the high cut-off phonon energy of REAl₃(BO₃)₄. The intrinsic nonradiative rate from the ⁵D₁ level into the ⁵D₀ level was determined both from the luminescence intensity ratio and time-resolved studies on the photoluminescence from the ⁵D₁ level. Both methods yield a rate in the range of k_nr(0) ≈ 55 ms⁻¹. The intrinsic nonradiative transition rate k_nr(0) connecting the ⁵D₁ and ⁵D₀ level of Eu³⁺ tends to increase with decreasing average Eu–O bond length as could be demonstrated upon comparison between YAl₃(BO₃)₄:Eu³⁺ (k_nr(0) = (55.16 ± 0.03) ms⁻¹) and LuAl₃(BO₃)₄:Eu³⁺ (k_nr(0) = (56.47 ± 0.01) ms⁻¹). However, there is not the expected net decrease in the corresponding nonradiative transition rate in GdAl₃(BO₃)₄:Eu³⁺ (k_nr(0) = (56.23 ± 0.04) ms⁻¹) compared to the Y congener, which we attribute to a local accelerating effect by the paramagnetic nature of neighboring Gd³⁺ ions. A very detailed investigation of this phenomenon on a wider scope of compounds is currently ongoing and will be part of a future study. The decay rate of the ⁵D₀ level shows a temperature dependence that reveals additional thermally activated processes. It is shown that the temperature dependence is due to the strong thermal coupling between the ⁵D₀ and ⁵D₁ levels, through which both decay with a thermally averaged rate, as well as crossover relaxation via the Eu³⁺ ← O²⁻ ligand-to-metal charge transfer state. The models describing the temperature-dependent steady-state and time-resolved excited state dynamics demonstrated in this work thus offer the possibility of a detailed understanding of the excited state dynamics of the ⁵D₁ and ⁵D₀ levels of Eu³⁺ in REAl₃(BO₃)₄ (RE = Y, Gd, Lu). Nevertheless, further measurements should be carried out at higher temperatures to better understand and validate the models and, in particular, the relaxation process through the charge transfer state. Analysis of other Eu³⁺-activated host compounds at various temperatures also offers the possibility of verifying a more universal application of the presented model and can allow to assess the general applicability of Eu³⁺ as a targeted luminescent thermometer.

Conflicts of interest

There are no conflicts to declare.

Data availability

Source data generated in this study, which are presented in the main text and supplementary information (SI), are provided as a Source Data files via the Zenodo repository under the accession code https://doi.org/10.5281/zenodo.18346446. Source data is also available from the corresponding authors upon request. Supplementary information is available. See DOI: https://doi.org/10.1039/d5ma01480h.

Acknowledgements

M. S. gratefully acknowledges a scholarship of the “Young College” of the North-Rhine Westphalian Academy of Sciences, Humanities, and the Arts as well as funding by the Strategic Research Fund of the HHU Düsseldorf. The authors from the University of Verona (L. C., M. B., F. P.) thank the Facility “Centro Piattaforme Tecnologiche” (CPT) for access to the Rigaku SmartLab SE powder diffractometer.

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Footnote

† Dedicated to our friend Luís Carlos on the occasion of his 60th birthday.

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