Investigation of visible emission and luminescence center evolution in Pr–La:CaF₂ single crystals for laser application

Abstract

A series of Pr,La:CaF₂ single crystals grown using the temperature gradient technique (TGT) method were presented systematically with a detailed spectroscopic investigation. The results indicate that the distinct Pr³⁺–La³⁺ cluster types have replaced the original Pr³⁺–Pr³⁺ clusters after introducing La³⁺ into the Pr:CaF₂ crystal, as demonstrated by density functional theory-based first principles calculation and spectral analysis. This cluster evolution has led to a drastic increase in the Pr³⁺ emission quantum efficiency as the La³⁺ concentration increases. Evaluation of the impacts of multiphonon relaxation and cross-relaxation processes on quantum yields also revealed that cross-relaxation processes persisted in the Pr, La co-doped samples, which led to not high quantum yields as expected. The incorporation of La³⁺ substantially manipulated the local structure of Pr ions in the CaF₂ crystal lattice. Low temperature absorption and selective-site spectroscopy, and time resolved emission spectroscopy were applied to investigate the local structure symmetries of Pr ions in the Pr³⁺,La³⁺:CaF₂ crystal. Despite a lower degree of discrepancy, two types of centers were observed in TRES, all of which showed cubic symmetry of these locations based on the cluster simulation.

---

1. Introduction

Trivalent praseodymium is a particularly fascinating lanthanide ion due to its many visible and infrared transitions. In recent years, there has been an increasing interest in Pr³⁺ doped laser systems due to the development of blue GaN laser diode pump sources, which perfectly match specific Pr³⁺ absorption lines. The green, orange, and red transitions of Pr³⁺ have already been utilized in laser materials like Pr³⁺:LiYF₄ and Pr³⁺:SrAl₁₂O₁₉.^1–4

Among the fluorides, CaF₂ with an optically isotropic fluorite structure has a broad transparency spectrum range that extends into the UV region, high thermal conductivity, and a low maximum phonon energy of around 320 cm⁻¹, which significantly limits non-radiative transitions. These properties make this material useful for a wide range of optical applications. However, the Pr³⁺:CaF₂ crystal as a laser system has been shelved for a long time due to a very negative concentration quenching effect caused by Pr³⁺ ion clustering and certain cross-relaxation energy transfer processes that reduce their emission quantum efficiency. To overcome this disadvantage, it has been suggested to co-dope with non-optically active ions in order to create new clusters around single Pr³⁺ ions, isolating them from one another. Pr:CaF₂ co-doped with Gd³⁺ ions has been studied and continuous-wave laser generation has already been demonstrated, with a maximum output power of 22 mW at 642 nm.⁵ Then in a Pr³⁺,Gd³⁺:SrF₂ crystal, a slope efficiency of 4.4% was reached with a maximum output power of 47 mW at 605.98 nm.⁶ Another promising candidate is Lu³⁺ which also efficiently breaks Pr³⁺ clusters and paves the way towards the development of a Pr³⁺ doped CaF₂ visible laser.⁷ While the spectrum properties and laser performance have improved significantly, there is still uncertainty regarding the sites of Pr³⁺ or Lu³⁺ non-optically active ions. Comparably, we incorporated La for the first time in this research to regulate local structure, mostly because of the similar ionic radii of Pr³⁺ and La³⁺, and the computed findings indicate that Pr³⁺ and La³⁺ may form clusters with a similar degree of ease.

The insertion of trivalent rare-earth ions into the fluorite structure is well known to be accompanied by charge-compensating defects that result in various types of centers consisting of one rare-earth ion or many rare-earth ions within a cluster. Numerous studies have been conducted to investigate the theoretical and experimental aspects of these integration sites. Clustering in rare-earth-doped calcium fluoride has been shown to be substantial even at low dopant concentrations, such as 0.05% Pr³⁺.⁸ The possibility of energetically favorable aggregates or rare-earth (RE) clusters forming in CaF₂ was initially proposed in 1964.⁹ Since then, following a wide number of structural studies based on experimental techniques such as electron paramagnetic resonance spectroscopy (EPR),^10,11 nuclear magnetic resonance (NMR),¹² dielectric relaxation spectroscopy (DRS),¹³ and extended X-ray absorption fine structure (EXAFS)¹⁴ as well as computer simulations.¹⁵ It was concluded that charge compensation could be achieved in several ways depending on the rare-earth size, the lattice parameter, the doping concentration and the sample thermal treatments. However, despite the use of a variety of experimental methodologies, a clear description of these defects has not yet been generated. Tissue and Wright¹⁶ described up to 22 different sites for 0.1% Pr³⁺ in CaF₂, of which only three were assigned to single ions, leaving the remaining 19 sites identified as cluster sites composed of two (pairs or dimers) or three (trimer) ions. Consequently, Pr³⁺ clustering causes the visible emission from ³P₀ in CaF₂ to be extremely weak. In order to expand the usage of rare-earth doped CaF₂ to photonic applications, it is thus highly appealing to find strategies to prevent the development of rare-earth clusters in Pr³⁺:CaF₂. To the best of our knowledge, however, there is no conclusive evidence that these co-dopants significantly hinder the development of rare-earth clusters and generate new luminescence centers.

This study shows that the co-doping of Pr³⁺ with La³⁺ ions can effectively prevent the formation of Pr³⁺ clusters by forming clusters made up of Pr³⁺ and La³⁺ centers. Compared to singly doped Pr³⁺:CaF₂, a significantly increase in praseodymium visible luminescence is observed in Pr³⁺, La³⁺ co-doped CaF₂, which could potentially lead to visible laser operation. On the other hand, we continued to perform low temperature selective site spectroscopy and time-resolved emission spectroscopy (TRES) to learn more about the new luminescence center. Additionally, a density functional theory (DFT) based first principles calculations were carried out for the Pr³⁺, La³⁺ doped CaF₂, giving us a clear picture of the cluster characters.

2. Experimental setup

2.1 Experiments for crystal growth and spectra properties

0.6 at% Pr³⁺:CaF₂ (0.6Pr) as well as 0.6 at% Pr³⁺,x at% La³⁺:CaF₂ crystals (x = 1, 6, 9, 15, 20; 0.6Pr,1La; 0.6Pr,6La; 0.6Pr,9La; 0.6Pr,15La; 0.6Pr,20La) were fabricated using the TGT method. In addition, a series of 0.05% Pr-doped samples were also grown for the purpose of measuring the radiative lifetimes. The raw materials PrF₃ (99.99%), LaF₃ (99.99%), CaF₂ (99.99%) and PbF₂ (99.99%) were initially added to a growing chamber in a graphite crucible, which was then heated slightly above (∼30–50 °C) the melting point and the solution was homogenized for 24 hours. The pressure within the furnace chamber was maintained below 5 × 10⁻³ Pa during the crystal growth process. For spectroscopic characterization, the as-grown crystals were sliced to a thickness of 2 mm and double-sided polished.

An Agilent UV-VIS-IR spectrophotometer (Cary-5000) was used to detect the absorption of samples. Additionally, an FLS-1000 photoluminescence spectrometer with Red-PMT is used to gather the luminescence spectra under a Xe lamp excited at 443 nm. We used the same excitation and emission slit widths to record the emission spectra. This ensured consistent measurement conditions across different concentration samples, providing reliable results for spectral comparisons. Since each sample was prepared with a thickness of 2 mm, extra care was needed to ensure that they were all identical in shape. The tiny thickness of the samples is crucial to achieving an equal excitation beam profile within each sample since the samples may show differing absorption cross-sections at the excitation wavelength. It is possible to compare the emission intensities of the several samples directly by maintaining the same experimental setup for each sample. We used an optical parametric oscillator powered by the third harmonic (355 nm) of a Nd³⁺:YAG laser to perform emission decays and time-resolved spectra. Low temperature (T = 77 K) measurements were carried out using an East Changing liquid nitrogen cryostat coupled with an East Changing TC 202 temperature controller. Using an inductively coupled plasma optical emission spectrometer (ICP-OES), the actual concentration of Pr³⁺ was determined.

2.2 Computational procedure in VASP

The first-principles calculations based on DFT are performed by the plane-wave basis set method using the VASP code. The interactions between electrons and ions were described by the projector augmented wave (PAW) potential. Furthermore, all computations took the spin polarization into account. The relaxation was verified to have an accuracy of 10⁻⁵ eV using a 1 × 1 × 1 gamma k-grid and a 550 eV cut-off in the plane-wave expansion. To achieve enough precision, the internal coordinates of the 2 × 2 × 2 supercell were refined until the forces exerted on individual atoms approached 0.01 eV Å⁻¹. The formation energy (ΔE) of the cluster was calculated using the following formula:¹⁷

ΔE = (E_tot + E₀) − i·E₁ − (s − v)·E₂ − {[i + (s − v)] − [i − (s − v)²]}·E_corr

where E_tot denotes the total relaxed energy of the centers with notation of i|v|d|s_r-O; i is the number of trivalent substitutional impurities, v is the number of lattice anion vacancies, d is the number of anions that deviated from the normal lattice site, s is the number of interstitials at the nearest (r = 1) or next nearest site (r = 2), and “O” is the shape of the cluster configuration; E₀ is the energy of pure CaF₂ crystal; E₁ and E₂ respectively are the relaxed energy of the centers 1|0|0|0 and 0|0|0|1 in a 2 × 2 × 2 supercell; E_corr is the potential alignment and charge corrections calculated by following equation:
where q is the net charge, α is the Madelung constant of 5.0388, ε is the static electric constant, L represents the supercell dimensions (2 × 2 × 2) of CaF₂ and g is the scaling factor (a value of −0.34 was chosen for the face-centered cubic structure). The computed E_corr for a 2 × 2 × 2 supercell of CaF₂ crystal with a net charge of q = 1 was 0.323 eV.

3. Results and discussion

3.1 Spectroscopic properties

Fig. 1 shows the results of the identification and assignment of the absorption bands in the vis-IR range. The room-temperature absorption spectra of Pr,La:CaF₂ and the singly doped with Pr³⁺ sample were obtained. These spectra are mostly made up of several bands in the entire visible and near-infrared regions that correspond to ³H₄ → ³P₂, ³P₁ + ¹I₆, ³P₀, ¹D₂, ¹G₄, ³F_3,4, and ³F₂ + ³H₆ respectively. The majority of these transitions are electric dipole ones; the only ones with magnetic dipole contribution are ³H₄ → ¹G₄ and ³F_4,3. It is noteworthy to notice that the most powerful transition ³H₄ → ³P₂ corresponds to the 444 nm absorption associated with Pr³⁺ ions. Its bandwidth is approximately ten nanometers greater than that of YLF, making it ideal for pumping with a specific wavelength range.

Fig. 1 Absorption spectra of the Pr,La:CaF₂ crystal.

The excitation and emission channels in the Pr-doped crystal are shown in Fig. 2. After excitation to the ³P₂ level at ca. 443 nm, the electrons undergo non-radiative relaxation to populate the lower-lying steady-state levels (³P₀, ³P₁, ¹I₆). This relaxation process subsequently leads to the observed emission spectrum, which consists of six bands in the visible region. The emission bands located at 483, 524, 606, 639, 702, and 721 nm correspond to the transitions from the ³P₀ or ³P₁ level to the ³H₄, ³H₅, ³H₆, ³F₂, and ³F_3,4 levels, respectively. The comprehensive analysis of this emission spectrum provides valuable insights into the energy level structure and radiative transitions of the Pr³⁺ ions within the CaF₂ host crystal.

Fig. 2 The excitation and emission channels in the Pr-doped CaF₂ crystal.

The identification and assignment of the emission bands in the visible region have been performed and it can be seen in Fig. 3(a) under excitation at 443 nm. The emission intensity of the ³P₀ → ³H₆ transition increases with the La concentration up to more than several hundred times the initial value for the Pr³⁺ singly doped sample, which is clear evidence of the breaking of Pr³⁺–Pr³⁺ clusters by co-doping. In contrast, the extremely weak Pr³⁺ emission seen in Pr³⁺:CaF₂ compared to Pr,La:CaF₂ shows that the majority of Pr³⁺ ions are aggregated together and that the Pr³⁺ emission is suppressed within these clusters. The initial Pr³⁺–Pr³⁺clusters are therefore replaced in the matrix host by Pr³⁺–La³⁺ clusters which prevent the onset of the cross relaxation process quenching the Pr³⁺ luminescence.⁷ Plotting the integrated emission intensity of ³P₀ → ³H₆,³F₂ against La³⁺ concentration in Fig. 3(b) reveals that the rise follows a cumulative distribution function curve, reaching an asymptotic value. Thus, the incorporation of La³⁺ as a co-dopant somehow modifies the clustering structure of Pr³⁺ ions with the consequence of preventing the formation of Pr³⁺ clusters. The visible region quantum efficiency of the ³P₀ level increases drastically with the La³⁺ concentration simultaneously as shown in Fig. 3(d). For all samples, emission intensities were integrated across the wavelength range of 570 to 660 nm. Fig. 3(c) shows the ratio I₂/I₁ between the integrated intensities, with sample “1” being 0.6% Pr³⁺:CaF₂ and sample “2” being the Pr,La:CaF₂ samples. Between the two samples, an intensity ratio of 231 (I₂/I₁) is seen, indicating that 0.6Pr³⁺,20La³⁺:CaF₂ is 231 times brighter compared to 0.6Pr³⁺:CaF₂. Since the absorption coefficients (α = σ_absN) at the pumping wavelength are 1.6 cm⁻¹ and 1.5 cm⁻¹ in 0.6% Pr³⁺:CaF₂ and 0.6Pr³⁺,20La³⁺:CaF₂, respectively, this finding cannot be explained by differences in absorption.

Fig. 3 (a) Emission spectra of Pr^{3+ 3}P₀ level when excited at 443 nm. (c) Normalized spectra have an integrated intensity equal to one for sake of clarity. The gray boxes represent the integral areas. (b) and (d) ³P₀–³H₆,³F₂ integrated emission intensity and quantum efficiency of the Pr,La:CaF₂ sample versus La³⁺ co-dopant concentration.

The primary distinction between the rare-earth incorporation sites in different hosts leads to this outcome. Unlike single-site fluoride hosts with a uniform distribution of dopants within the lattice such as LiYF₄,¹⁸ strong emission quenching due to the clustering effect of Pr³⁺:CaF₂ is to be expected. In conclusion, the Pr³⁺ emission recorded in 0.6Pr:CaF₂ exclusively arises from a minority of “isolated” Pr³⁺ ions, which can be identified as corresponding to the C_4v single ion sites when compared with the literature.¹⁶ The short distance between the Pr³⁺ ions in clusters clearly favor cross-relaxation processes. For Pr³⁺ ions, there are many cross-relaxation pathways that include the energy transfer between an excited Pr³⁺ ion in the ³P₀ multiplets and a Pr³⁺ ion in the ³H₄ ground state resulting in decay non-radiatively through multiphonon emission or emission of an infrared photon.¹⁹ Therefore, the co-doping of Pr³⁺ with La³⁺ has been shown to be an effective way to avoid the formation of Pr³⁺–Pr³⁺ clusters.

The ratio of intensities I₂/I₁ is directly correlated with the ratio of emitting center concentrations N₂/N₁. N_i is the concentration of emitting centers in sample i. Since the fraction of emitting centers in Pr–Pr clusters is so low, we will disregard it in this instance and go into further explanation in the following section. Effective emitting centers are denoted by N_i and are restricted to isolated Pr ions that do not quench for consideration. As long as the concentration of excited ions is low to prevent any depletion of the ground state, it is possible to precisely define the connection between emission strength and the number of emitting centers.⁷ The rate equation for the concentration of luminescence centers in the excited state n(³P₀) changes into:

In the steady-state regime (dn(³P₀)/dt = 0), the concentration of emitting centers in the excited state n(³P₀) is then simply given by

n(³P₀) = σ_absϕN_Prτ(³P₀) (3-2)

where N_Pr represents the total concentration of emitting centers, σ_abs is the absorption cross-section; ϕ is the excitation photon flux and τ(³P₀) is the emitting level lifetime. On the other hand, the emission intensity is proportional to the concentration of emitting centers in the excited state n(³P₀) as follows:where τ_rad is the level emission radiative lifetime and β is the branching ratio of the transition (or transitions) under consideration. Given that the photon flux Φ is constant for all samples, one may calculate the ratio of emitting center concentrations as a function of the intensity ratio I₂/I₁ by combining eqn (3-2) and (3-3):

Table 1 provides a summary of the experimentally measured values required to perform the computations in eqn (3-4). By capturing the complete ³P₀ emission spectrum from 480 nm to 800 nm and correcting for the experimental spectral response, the branching ratio β of the red (³P₀ → ³F₂) and orange (³P₀ → ³H₆) transitions was determined. Since the ³P₀ → ¹D₂,¹G₄ infrared transition contributes very little to the total emission spectrum, it was not considered.²⁰ Subsequently, the branching ratio β was computed by dividing the spectral integral of the emission spectrum by the spectral integral of the red and orange transitions of interest.

Table 1 Spectroscopic parameters applied in eqn (3-4) computations in the Pr,La:CaF₂ sample. The red (³P₀–³F₂) and orange (³P₀–³H₆) transitions branching ratio is denoted by β; the effective absorption cross-section is represented by σ_abs; τ and τ_rad are the measured and radiative lifetime of the ³P₀ level respectively

Sample	β	σ abs (10^−21 cm^2)	τ(^3P0) (μs)	τ rad(^3P0) (μs)	I 2/I1	N 2/N1
0.6Pr:CaF2	0.38	1.15	122	172	—	—
0.6Pr 1.0La	0.469	1.16	34	54	67	58
0.6Pr 6.0La	0.466	1.17	36	55	190	157
0.6Pr 9.0La	0.462	1.18	36	55	202	167
0.6Pr 15La	0.462	1.20	38	55	218	169
0.6Pr 20La	0.462	1.20	38	55	231	180

---

The luminescence kinetics of Pr³⁺ ions in the investigated materials is strongly related to the presence of La³⁺. Fig. 3(a) compares semilog plots of ³P₀ luminescence decay curves recorded at room temperature for the CaF₂ crystal containing 0.6 at% Pr³⁺ sample series. The lifetimes were determined by normalizing to unity the decay curves at t = 0 and by integrating the entire decay curves.²¹ In the 0.6Pr:CaF₂ sample, the decays approximately follow a double-exponential trend over two orders of magnitude and has a fast decay component apparently as a consequence of strong cross relaxation interaction between the Pr³⁺–Pr³⁺ cluster with a time constant substantially exceeding the time range covered in our experiments. What is going on in this sample is that, due to the formation of clusters in this host, we find two main species of Pr ions, one is in the form of a Pr cluster which do not emit light at all due to strong quenching corresponding to the short part (0.58 μs), and the other one which are isolated Pr ions giving the long lifetime part (142 μs). The calculated proportion of the short lifetime φ, quantum yield of luminescence in the cluster η_cluster and the proportion of cluster R_cluster can be expressed as the following formulas:

where A_s and A_l are the fitting constants of the equations; τ_s and τ_l are the short lifetime and long lifetime part, respectively; σ_r and σ_nr are the transition rates of radiative and non-radiative processes. The calculated proportion of short lifetime φ is 0.01 in 0.6Pr:CaF₂, and quantum yield of luminescence in the cluster η_cluster is about 0.01 (τ_s = 0.58 μs shown in Fig. 4(a), τ_rad = 54 μs in Fig. 4(c)). As a result, the proportion of the cluster R_cluster is 50% in 0.6Pr:CaF₂.

Fig. 4 ³P₀ fluorescence decay curves of the Pr,La:CaF₂ crystal under pulsed excitation at 443 nm. (a) 0.6Pr and 5.0Pr doped CaF₂ samples, (b) 0.6% Pr sample series , (c) 0.05% Pr sample series.

By adding lanthanum, the non-emitting Pr³⁺–Pr³⁺ clusters were replaced by Pr–La luminescence centers, which begin to dominate the decay and emit, providing an approximate lifetime of 36 μs as shown in Fig. 4(b). We believe that there is still some quenching in these clusters due to the low quantum efficiency as shown in Fig. 3(d) and the longer lifetime of 0.05Pr,5La:CaF₂.

The radiative lifetimes are usually derived using the Judd–Ofelt theory. However, this calculation does not give satisfying results in the case of Pr³⁺ doped multisite systems since one should isolate for each Pr³⁺–La³⁺ cluster a separate set of absorption spectra.²¹ Therefore, we derived the ³P₀ radiative lifetimes by adding enough of the La³⁺ ions so as to avoid any possible cross-relaxation processes. The content of La ions is several hundred times that of Pr, it can be assumed that at this time Pr is completely evenly distributed within the lattice. In addition, since the ion radius of La is comparable to the Pr ion, there should be a comparable agglomeration tendency, and the cluster structure properties should develop similarly. This hypothesis will be detailed by DFT calculation in the next section. Consequently, this estimation of the radiative lifetime is valid provided that energy transfer does not exist in Fig. 3(b). The radiative lifetime for the 0.6Pr sample series presented in Table 1 should correspond to the lifetime of the 0.05Pr,10La sample displayed in Fig. 3(b). The radiative lifetime in 0.6Pr:CaF₂ is expected to be equal to the lifetime in 0.05Pr:CaF₂.

The significant number of non-emitting Pr³⁺ clusters in 0.6Pr:CaF₂ is confirmed by the results in Table 1, which show that the number of Pr³⁺ emitting centers is 180 times bigger in 0.6Pr,20La:CaF₂ than in 0.6Pr:CaF₂ for an approximately equivalent concentration of Pr³⁺ ions. The quantum efficiency of ³P₀ and the calculated N₂/N₁ are shown as a function of La³⁺ concentration in Fig. 5(a). When co-doping Pr³⁺ with La³⁺ in CaF₂, the number of luminescence centers increases drastically, along with the quantum efficiency, demonstrating that the co-dopant allows previously non-emitting Pr³⁺ centers to generate visible emission by taking the place of Pr³⁺ ions inside the Pr³⁺ clusters. Nonetheless, the quantum efficiency of Pr,La:CaF₂ is not as high as expected, there maybe some process caused the energy dissipation of ³P₀ level. The following modified exponential energy-gap law of Van Dijk and Schuurmans could be used to compute the multiphonon relaxation rate,²² given that the energy gap between ³P₀ and ¹D₂ is roughly 3500 cm⁻¹:

W_MPR (T = 0 K) = β_elexp[−α(ΔE − 2ℏω_max)] (3-6)

The total radiative rate of the ³P₀ state is calculated with the radiative lifetime as shown in Fig. 5(b), which is typically 2 × 10⁴ s⁻¹ for fluoride such as LiYF₄.²³ We conclude that the multiphonon relaxation rate is 10² s⁻¹, which is 200 times smaller than the radiative rate. Consequently, the multiphonon relaxation mechanism is insufficient to explain the approximately 40% quantum efficiency. On the other hand, the large energy of visible photons requires considering the possibility of excited state absorption (ESA) into energy levels of the 4f¹5d¹ configuration of Pr³⁺. The energetic position and splitting of the 4f¹5d¹ states depend much stronger on the crystal field. In the CaF₂ host, it provides comparably low crystal field strengths, which results in an energetically higher position of the lower edge of the 4f¹5d¹ absorption band.²⁴ Therefore, ESA into these levels from the upper laser level is not likely for the usual pump wavelengths of Pr³⁺:CaF₂. On the other hand, the Stark multiplets ³P₀, ³P₁, ³P₂ and ¹I₆ of Pr³⁺ are energetically separated by less than 2000 cm⁻¹. Thus, the Boltzmann population of the levels ³P₂ and in particular ³P₁ must be considered at room temperature, and thermal excitation inevitably plays an important role in lowering the QE.²⁵

Fig. 5 (a) Emission quantum efficiency of ³P₀ at room temperature and calculated N₂/N₁versus La³⁺ concentration; (b) evolution of the radiative transition rate, cross relaxation rate and ³P₀–¹D₂ multi-phonon relaxation rate as a function of La³⁺ concentration in 0.6% Pr³⁺,xLa³⁺:CaF₂ (x = 1, 6, 9, 15, 20).

To summarize, Fig. 5(b) displays the radiative transition rate, cross relaxation rate, and multiphonon relaxation rate. The cross relaxation rate is calculated by the formula, W_CR = 1/τ − 1/τ_rad − W_MPR, using the experimental and radiative lifetime. It is evident that the insertion of La³⁺ as a co-dopant causes a dramatic drop in the cross relaxation rate and an increase in the radiative transition rate. The cross relaxation rate can still approach an order of 10⁴ s⁻¹, which is equal to the intrinsic radiation rate, even though it has decreased by a far larger amount than the intrinsic transition rate. The cross relaxation rate that follows is essentially constant. This study demonstrates unequivocally that not all Pr³⁺ ions become emission centers when co-doping with 20% La³⁺, that is, partially Pr–Pr clusters are replaced by Pr–La clusters.

3.2 Investigation of the variations in luminescence centers using low temperature spectroscopy and computational simulation

3.2.1 Low temperature selective-site excitation and TRES. As previously discussed, the addition of Lu³⁺ or Yb³⁺ as co-dopants appears to generate new cluster centers containing both codopants.⁷ The analysis of low temperature absorption spectra offers essential information about these cluster centers. The low temperature absorption spectra of 0.6Pr:CaF₂ and 0.6Pr,1.0La:CaF₂ samples are shown in Fig. 6(a). The transition of ³H₄–³P₂ is of particular significance, since it is usually used for optical excitation of Pr³⁺ emission. The absorption spectrum of the singly Pr³⁺ doped sample is clearly different from the spectra recorded for the co-doped samples. The spectrum of the singly doped sample is characterized by several tiny peaks at 468 nm for the ³H₄–³P₂ transition, but the spectrum of the co-doped sample has a broad peak at the same wavelength. In case of the 0.6Pr:CaF₂ sample, absorption spectra is dominated by 443.54 nm. As can be easily spotted, after co-doping with La³⁺, new absorption lines at 440.66 nm emerge, which significantly increase while the line at 443.54 nm decrease. The contrast between the absorption spectra clearly demonstrates a distinct arrangement of the Pr³⁺ ions in the singly doped Pr³⁺:CaF₂ crystal. These new lines are related to the new absorption center caused by the Pr–La cluster.

Fig. 6 (a) Absorption spectra of 0.6Pr:CaF₂ and 0.6Pr,1.0La:CaF₂ samples measured at 77 K; (b) comparison of absorption, emission and excitation spectra of the 0.6Pr,1.0La:CaF₂ sample. Blue lines are the absorption spectra. Black and red lines are the emission spectra that were excited via the absorption line marked with asterisk of the appropriate color. Green and olive traces represent the excitation lines that were measured observing emission from the lines marked by green or olive asterisks respectively. All the measurements have been done at 77 K.

According to the symmetry considerations, splitting of the manifolds with J = 4 is 4 for cubic symmetry. For manifolds with J = 0, it has a single Stark level. Nevertheless, only the lowest Stark level of ³H₄ is occupied at low temperatures (77 K). In the event of a single site structure, a single absorption line is thus expected for the ³H₄–³P₀ transition. The symmetry of the Ca²⁺ site in CaF₂ is cubic (O_h) but due to the presence of interstitial F_i⁻ ions that balances the charge mismatch between Pr³⁺ and Ca²⁺, the local symmetry drops to C_3v or C_4v.¹⁷ In the case of the Pr–Pr or Pr–La cluster, the symmetry can even be lower. The absorption spectra of 0.6Pr:CaF₂ and 0.6Pr,1.0La:CaF₂ contains roughly 19 and 9 lines, clearly confirming the presence of many sites. Each sharp line can be associated with a specific site with a well-defined symmetry while the broad line evidences a strong inhomogeneous broadening most likely related to Pr–La clusters.²⁶

Then we utilized the 0.6Pr 1.0La sample on the selective spectrum displayed in Fig. 6(b), which shows that the 0.6Pr,1.0La sample has at least two distinct Pr³⁺ sites. Emission spectra excited at 440.66 nm show a new peak at 480.8 nm, whereas red traces show only the same peak at 484 nm when excited at 443.54 nm, demonstrating that the incorporation of La³⁺ as a co-dopant modifies the clustering structure, i.e. producing more new luminescence centers.²⁷

In order to get better insight into luminescence processes present in that crystal, a series of liquid nitrogen time-resolved emission spectrum (TRES) measurements were performed. Recording the time-resolved emission spectrum with a time frame beginning at the end of the decay at 100 μs allows one to isolate the emission spectrum associated with the slowest center, as shown in Fig. 7(b and e). The emission spectra integrated with different time gating are shown in Fig. 7(b). As can be easily seen, there is a distinct difference between green and other traces. This is due to the presence of several luminescence centres that should differ in decay kinetics. On the other hand, the decay curves displayed in Fig. 7(c) exhibit a few differences with almost identical lifetimes, which the DFT computation may account for given the little variations in the cluster configurations. The shorter the lifetime of the centre, the less pronounced it is in the spectra gathered longer after excitation pulse. The green spectrum is a mixture of long and short living centres. Black and red traces show emission spectra of long-lived centres. The emission spectrum of this first cluster (Fig. 7(b)) is characterized by an increased emission peak integrated from 100–200 μs at 480.8 nm, which is consistent with the fact that the slowest decay was recorded at this wavelength (Fig. 7(c)). Another time window set during the first 20 μs of the decay gives a very different emission spectrum. This new spectrum exhibits a prominent emission peak at 484 nm which is characteristic of the second Pr³⁺–La³⁺ cluster.

Fig. 7 Pr³⁺ time-resolved spectra in 0.6Pr,1.0La:CaF₂ at 77 K. (a–c) Excited at 443.54 nm. (d–f) Excited at 440.66 nm. Colors from red to blue represent the logarithmic PL intensity from high to low. The time-resolved emission spectra (b and e) obtained with different time gates after pulse excitation. Time-resolve decays (c and f) at wavelengths of 480.8, 484, 487 and 492 nm.

The existence of two types of Pr³⁺–La³⁺ clusters is convincingly confirmed by investigating the ³P₀ time-resolved emission spectra in the co-doped samples at a low temperature. In 0.6Pr,1.0La:CaF₂, we observed the ³P₀ decay at two distinct excitation wavelengths: 443.54 nm (Fig. 7(c)) and 440.66 nm (Fig. 7(f)). The decays (τ_{ex443.54,em480.8} = 41 μs) and (τ_{ex440.66,em480.8} = 33 μs) are different, suggesting the coexistence of two distinct clusters.

3.2.2 Rare-earth cluster simulation of Pr³⁺ and La³⁺. When rare-earth ions are introduced into CaF₂, they will replace the Ca²⁺ ions and interstitial F_i⁻ ions will work as charge compensation. There are multiple nonequivalent sites for the charge compensation F_i⁻ ions to occupy. Subsequently, the 1|0|0|1₁ (C_4v) and 1|0|0|1₂ (C_3v) configurations with F⁻ ions at the nearest and next-nearest sites of rare-earth ions respectively emerge.²⁸ These monomers further aggregate to form clusters. Based on ref. 29, the rare-earth clusters in the CaF₂ crystal are modeled and then fully relaxed. Fig. 8(a) and Table 2 display the possible clusters that are thermodynamically stable. Three groups of centers were identified: the first group consists of monomer centers, while the other groups are clusters with distinct local sublattices, namely cubic and square antiprisms. Within the Pr³⁺:CaF₂ crystal, the nearest center C_4v configuration is more stable than C_3v, which is in agreement with the idea that large rare-earth ions like Pr³⁺ form small clusters.¹⁶ Simultaneously, the nearest site center for La³⁺ that has almost the same ion radius as Pr³⁺ exhibits greater stability and conformity with the available data.²⁸ Formation energy of the clusters were plotted and illustrated in Fig. 8(b). The binding energy curve exhibits a piecewise variation as the number of Pr³⁺ increases. Low-order clusters with cubic sublattices are more easily generated than higher-order square antiprisms due to their binding energy slope (−2.27 eV) being significantly larger than that of high-order clusters (−1.46 eV).

Fig. 8 (a) The thermodynamically stable clusters in Pr³⁺ doped CaF₂ crystals, and these centers are divided into three groups: “A”, “B”, and “C” stand for cubic monomers, cubic sublattice clusters, and square antiprism structure clusters, respectively. (b) The formation energy of the thermodynamically stable centers depends on the number of rare earth ions. The cyan triangles and blue circles represent two different types of cubic cluster configurations with distinct binding energies.

Table 2 Formation energy of the thermodynamically stable Pr³⁺ and La³⁺ clusters in CaF₂ crystals. The formation energy of La³⁺ centers is taken from ref. 28

Symbols	Pr^3+ centers (eV)	La^3+ centers (eV)
1|0|0|11	−0.951	−0.896
1|0|1|21	−2.005	−1.158
2|0|2|21	−2.019	−2.393
2|0|1|31	−2.774	−3.056
3|0|1|31	−3.819	−4.488
3|0|2|41	−5.748	—
4|1|0|41	−6.720	−5.513

---

Additionally, [Pr³⁺–La³⁺] clusters were simulated and shown in Fig. 9(a). Pr³⁺ and La³⁺ also have a tendency to group together to form [mLa³⁺–nPr³⁺] clusters. When more Pr³⁺ ions were added to the host, the bonding energy of the [Pr³⁺–La³⁺] clusters dropped linearly as shown in Fig. 9(b). It is observed that the formation energy of the Pr–La center is lower than that of the Pr³⁺ or La³⁺ clusters on the condition that m + n ≤ 2, indicating that the former are more stable than the latter. On the other hand, when m + n > 2, the formation energy of the Pr–La center is significantly larger than that of the Pr³⁺ or La³⁺ clusters indicating that self-clusters may form at high concentrations.

Fig. 9 (a) The thermodynamically stable [Pr³⁺–La³⁺] centers in CaF₂ crystals. (b) The formation energy of Pr³⁺ and La³⁺ clusters in relation to the quantity of Pr³⁺ ions present in each cluster.

In this part, to further elucidate the evolution of the local cluster structures in the Pr:CaF₂ crystals, we have carried out first-principles calculations. The results reveal that the cluster configurations are predominantly based on the cubic sub-lattice structure, and the higher-order prism configurations are not as stable, as evidenced by the shallower slope in the second stage of the binding energy trends. Interestingly, the cluster characteristics in the Pr–La co-doped samples still maintain the features of the cubic sub-lattice-based structure, which also helps explain the similarity in the lifetimes of the two Pr–La centers observed in the time-resolved spectroscopy.

4. Conclusion

The investigation of Pr³⁺,La³⁺ co-doped CaF₂ samples shows a drastic increase of the number of luminescent Pr³⁺ ions as opposed to singly doped Pr³⁺:CaF₂ where non-luminescent Pr³⁺ clusters predominate. An increase in Pr³⁺ luminescence by a factor of 231 is observed in 0.6Pr,20La:CaF₂, suggesting that the clusters encompassing Pr³⁺ and La³⁺ ions have replaced Pr³⁺ clusters. Two types of Pr³⁺–La³⁺ clusters is convincingly confirmed by investigating the ³P₀ time-resolved emission spectra in the co-doped samples at a low temperature. The computational results revealed that that the addition of La³⁺ to the Pr³⁺:CaF₂ crystal results in clusters of [mLa³⁺–nPr³⁺], with the formation energy decreasing with m + n. The first coordination shell of Pr³⁺ maintains a cubic structure, and the formation energy of the Pr–La center is larger than that of Pr³⁺ or La³⁺ clusters, suggesting self-cluster formation at high concentrations.

Data availability

The data that support the findings of this study are available from the corresponding author, L. Su, upon reasonable request.

Conflicts of interest

There is no conflict of interest in this manuscript.

Acknowledgements

This work has been financially supported by the National Key Research and Development Program of China (2021YFE0104800), the National Natural Science Foundation of China (61925508, 62205359), and the Science and Technology Commission of Shanghai Municipality (23511102700). This work was also supported by the CAS Project for Young Scientists in Basic Research (YSBR-024).

Notes and references

1. D.-T. Marzahl, F. Reichert, P. W. Metz, M. Fechner, N.-O. Hansen and G. Huber, Appl. Phys. B: Lasers Opt., 2014, 116, 109–113.
2. Z. Yang, S. Z. Ud Din, P. Wang, C. Li, Z. Lin, J. Leng, J. Liu, L. Xu, Q. Yang and X. Ren, Opt. Laser Technol., 2022, 148, 107711.
3. Z. Yang, Q. Yang, X. Ren, Y. Tian, Y. Zu, C. Li, S. Z. U. Din, J. Leng and J. Liu, Opt. Express, 2022, 30, 2900–2908.
4. L. B. Zhou, J. Y. Zou, W. X. Zheng, T. Zhang, B. Xu, X. D. Xu, A. A. Lyapin and J. Xu, Opt. Laser Technol., 2022, 145, 107471.
5. H. Yu, D. Jiang, F. Tang, L. Su, S. Luo, X. Yan, B. Xu, Z. Cai, J. Wang, Q. Ju and J. Xu, Mater. Lett., 2017, 206, 140–142.
6. C. Xu, W. Wang, Z. Zhang, F. Ma, D. Jiang, A. Strzep, W. Zheng, B. Xu, H. Kou, J. Xu and L. Su, Opt. Laser Technol., 2024, 168, 109768.
7. D. Serrano, A. Braud, J. L. Doualan, P. Camy and R. Moncorgé, J. Opt. Soc. Am. B, 2012, 29, 1854–1862.
8. D. R. Tallant, D. S. Moore and J. C. Wright, J. Chem. Phys., 2008, 67, 2897–2907.
9. M. J. Weber and R. W. Bierig, Phys. Rev., 1964, 134, A1492–A1503.
10. S. D. McLaughlan, Phys. Rev., 1966, 150, 118–120.
11. S. A. Kazanskii, A. I. Ryskin, A. E. Nikiforov, A. Y. Zaharov, M. Y. Ougrumov and G. S. Shakurov, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 014127.
12. R. J. Booth, M. R. Mustafa and B. R. McGarvey, Phys. Rev. B: Solid State, 1978, 17, 4150–4159.
13. J. Fontanella and C. Andeen, J. Phys. C: Solid State Phys., 1976, 9, 1055.
14. F. Ma, Z. Zhang, D. Jiang, Z. Zhang, H. Kou, A. Strzep, Q. Tang, H. Zhou, M. Zhang, P. Zhang, S. Zhu, H. Yin, Q. Lv, Z. Li, Z. Chen and L. Su, Cryst. Growth Des., 2022, 22, 4480–4493.
15. J. Corish, C. R. A. Catlow, P. W. M. Jacobs and S. H. Ong, Phys. Rev. B: Condens. Matter Mater. Phys., 1982, 25, 6425–6438.
16. B. M. Tissue and J. C. Wright, Phys. Rev. B: Condens. Matter Mater. Phys., 1987, 36, 9781–9789.
17. F. Ma, F. Su, R. Zhou, Y. Ou, L. Xie, C. Liu, D. Jiang, Z. Zhang, Q. Wu, L. Su and H. Liang, Mater. Res. Bull., 2020, 125, 110788.
18. A. Sottile, E. Damiano and M. Tonelli, Opt. Lett., 2016, 41, 5555–5558.
19. G. P. Morgan, D. L. Huber and W. M. Yen, J. Lumin., 1986, 35, 277–287.
20. B. Zandi, L. D. Merkle, J. B. Gruber, D. E. Wortman and C. A. Morrison, J. Appl. Phys., 1997, 81, 1047–1054.
21. S. Normani, A. Braud, R. Soulard, J. L. Doualan, A. Benayad, V. Menard, G. Brasse, R. Moncorgé, J. P. Goossens and P. Camy, CrystEngComm, 2016, 18, 9016–9025.
22. J. M. F. v. Dijk and M. F. H. Schuurmans, J. Chem. Phys., 1983, 78, 5317–5323.
23. S. Khiari, M. Velazquez, R. Moncorgé, J. L. Doualan, P. Camy, A. Ferrier and M. Diaf, J. Alloys Compd., 2008, 451, 128–131.
24. H. Tanaka, S. Kalusniak, M. Badtke, M. Demesh, N. V. Kuleshov, F. Kannari and C. Kränkel, Prog. Quantum Electron., 2022, 84, 100411.
25. S.-h. Huang, X.-j. Wang, B.-j. Chen, D. Jia and W. M. Yen, J. Lumin., 2003, 102–103, 344–348.
26. R. H. Petit, P. Evesque and J. Duran, J. Phys. C: Solid State Phys., 1981, 14, 5081.
27. S. A. Payne, J. A. Caird, L. L. Chase, L. K. Smith, N. D. Nielsen and W. F. Krupke, J. Opt. Soc. Am. B, 1991, 8, 726–740.
28. J. Liu, Y. Wang, Z. Zhang, Z. Zhang, D. Jiang, F. Tang, H. Kou, F. Ma and L. Su, Opt. Mater. Express, 2023, 13, 2288–2301.
29. C. R. A. Catlow, J. Phys. C: Solid State Phys., 1973, 6, L64.

---