Unraveling the local structure and luminescence evolution in Nd3+-doped LiYF4: a new theoretical approach

Yang Xiao a, Xiaoyu Kuang *a, Yauyuen Yeung *b and Meng Ju *c
aInstitute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China. E-mail: kuangxiaoyu@scu.edu.cn
bDepartment of Science and Environmental Studies, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, NT, Hong Kong, China. E-mail: yyyeung@eduhk.hk
cSchool of Physical Science and Technology, Southwest University, Chongqing 400715, China. E-mail: mengju@swu.edu.cn

Received 6th July 2020 , Accepted 26th August 2020

First published on 27th August 2020

Neodymium ion (Nd3+)-doped yttrium lithium fluoride (LiYF4, YLF) laser crystals have shown significant prospects as excellent laser materials in many kinds of solid-state laser systems. However, the origins of the detailed information of their local structure and luminescence evolution are still poorly understood. Herein, we use an unbiased CALYPSO structure searching technique and density functional theory to study the local structure of Nd3+-doped YLF. Our results reveal a new stable phase with the P[4 with combining macron] (No. 81) space group for Nd3+-doped YLF, indicating that the host Y3+ ion site was naturally occupied by the Nd3+ ion impurity. On the basis of our newly developed WEPMD method, we adopt a specific type of orthogonal correlation crystal field to obtain a new set of crystal-field parameters as well as 182 complete Stark energy levels. Many absorption and emission lines for Nd3+-doped YLF are calculated and discussed based on Judd–Ofelt theory, and our results indicate that some of the observed absorption and emission lines are perfectly reproduced by our theoretical calculations. Additionally, we predict several promising transition lines in the visible and near-infrared spectral regions, including the electronic dipole emission lines 4F5/24I9/2 at 808 nm and 2H9/24I9/2 at 799 nm, as well as the magnetic dipole emission lines 4F3/2(27) → 4I11/2(6) at 1047 nm and 4F3/2(27) → 4I11/2(8) at 1052 nm. These transition channels indicate that Nd3+-doped YLF laser crystals have greatly promising laser actions for serving as a solid-state laser material.

1 Introduction

The laser material is the source of laser generation and amplification, and it is also the most basic and core part of laser systems. Recently, various lanthanide-doped crystal materials have exhibited high quantum efficiency, narrowband emission, intense absorption bands, long emission lifetimes and spectral sharpness, making them a potential laser source for quantum memory, optical information storage and high-power fiber lasers.1–5 As a promising laser ion, Nd3+ has gained significant attention due to its unique luminescence properties, such as excellent medium laser amplification, a large absorption cross section, a long optical coherence time, good photostability and high quantum yield photoluminescence.6–11 When the Nd3+ ion is inserted into a host crystal environment, the electronic states of opposite parity in the 4f wave functions can be further mixed, and electronic dipole (ED) transitions can be partly allowed due to the noncentrosymmetric interactions, which provides more opportunities for us to study luminescence properties and applications.8 The Nd3+-doped laser crystals remain highly competitive because they have a high gain cross section and a true four-level laser operation mode (4F3/24I11/2).12 In particular, Nd3+-doped yttrium lithium fluoride (YLF:Nd3+) is a perfectly suitable solid-state laser material, and it shows more potential advantages than other laser materials:13–17 (1) in Nd3+-doped YLF, the product of the fluorescence lifetime τf and the stimulated-emission cross section σ is 1.5 times greater than that in Nd3+-doped YAG and greater than those in other stoichiometric materials, which means that this material is more suitable for high-pulse energy Q-switched lasers. (2) Nd3+-doped YLF exhibits a larger bandwidth at the 4F3/24I11/2 transition line, which shortens the generation of pulses to 2–3 times that for other stoichiometric materials. (3) Nd3+-doped YLF has a strong natural birefringence, which can overwhelm the thermally induced birefringence and eliminate thermal depolarization problems. In summary, these potential advantages of Nd3+-doped YLF make it an excellent solid-state laser material for mode-locked and continuous-wave operation.

To date, the development of Nd3+-doped YLF laser crystals in practical applications has a rich history. Yang et al.18 reported a broadband vacuum ultraviolet (VUV) fluorescence of Nd3+-doped YLF for the first time. They found a large Stokes shift greater than 5000 cm−1 in the VUV excitation spectra. Shortly afterward, they measured the detailed VUV excitation spectra of Nd3+-doped YLF, and their results showed a strong excitation peak near 1200 Å, which leads to an overlap of the host-lattice absorption.19 Subsequently, Malinowski et al.20 investigated the anti-Stokes fluorescence of Nd3+-doped YLF using tunable-pulsed-laser spectroscopy based on time-resolved measurements. They determined the detailed atomic energy level structure of Nd3+ ions and observed the fluorescence lines (356–417 nm) from the 4D3/2 and 2P3/2 excited states. To analyze the electron paramagnetic resonance (EPR) spectra of Nd3+-doped YLF, an effective spin-Hamiltonian approach was proposed by Guillot-Noël et al. to explain the general features of EPR, and then, they discovered the evidence of ferromagnetically coupled Nd3+ ion pairs.21 Very recently, Watanabe et al.22 measured the 4f3 → 4f25d1 absorption spectra of Nd3+-doped YLF using a synchrotron radiation light source. Their results indicated that the 4f3 → 4f25d1 absorption spectra have no significant temperature dependence at several different temperatures. On the theoretical side, Collombet et al.23 studied the 4f3 → 4f25d optical transitions of Nd3+-doped YLF using crystal-field theory. Additionally, the crystal-field parameters and some energy level structures of YLF:Nd3+ have been studied by several groups.24–29 Although the partial luminescence properties have been studied, the complete energy levels and luminescence mechanisms of Nd3+-doped YLF remain unknown. In particular, there is no systematic theoretical research on the microstructure for Nd3+-doped YLF laser crystals.

In this work, we first explored the local structure and electronic properties of YLF:Nd3+ by crystal structure analysis using the Particle Swarm Optimization30–36 (CALYPSO) method and density functional theory (DFT) calculations. Next, we determined the 182 complete energy levels of YLF:Nd3+ and analyzed the luminescence evolution based on our newly developed Well-Established Parametrization Matrix Diagonalization (WEPMD) method.37–42 Several potential emission channels of Nd3+-doped YLF were predicted, indicating that this system is a good laser material, especially for near-infrared (NIR) lasers.

2 Computational methods

Our structure searching simulations were performed by using the CALYPSO method, which is based on a global minimum search obtained through ab initio total-energy calculations.30–36 The most important characteristic of this method is that the crystal structure can be predicted for a given chemical ratio and external conditions, and the CALYPSO method has been successfully validated for various known systems.43,44 Our structural predictions were performed with the systems YLF and Nd3+-doped YLF under ambient pressure. Among all the predicted structures, the 50 lowest-lying structures were collected as the candidate structures with the lowest energy. The subsequent geometric optimizations and electronic structure calculations were performed using the generalized gradient approximation (GGA) of the DFT method in the Vienna Ab initio Simulation Package (VASP).45–49 The valence electron configurations were 4f45s25p66s2, 4d15s2, 1s22s1, and 2s22p5, corresponding to Nd, Y, Li, and F, respectively. Because the 4f3 configuration of Nd3+ systems has strong correlation effects, the standard DFT functional cannot eliminate the influence of the electronic correlations. To consider the strong correlation effects of Nd3+-doped YLF, we carried out the GGA with an onsite Coulomb repulsion parameter U, mainly because the present GGA+U approach is well suited to describing strongly correlated systems. Here, Knížek et al. have obtained a precise U value of 6.8 eV for Nd.50

To explore the luminescence mechanisms of the stimulated absorption and emission processes, the f-shell energy level of the [NdF8]5− ligand complex for Nd3+-doped YLF was analyzed by using our developed WEPMD method that involves higher-order interactions essential for reproducing the energy level schemes for rare earth ions. The reliability of this method was verified in our previous study.37–42,51,52 The lanthanide ion of neodymium (4f3) is surrounded by eight fluorine ions in the coordination sphere of [NdF8]5−, forming a slightly distorted dodecahedron with S4 symmetry, so its Hamiltonian (H) consists of two parts: the isolated free-ion Hamiltonian (HA) and the crystal-field (CF) Hamiltonian (HCF). The parametric Hamiltonian can be expressed as24–28

H = HA + HCF(1)
image file: d0cp03748f-t1.tif(2)
image file: d0cp03748f-t2.tif(3)
Detailed descriptions of these terms were given in our previous studies.51,52 It is worth noting that the Hartree–Fock-determined ratios P4 = 0.75P2, P6 = 0.50P2, M2 = 0.56M0 and M4 = 0.38M0 constrain the Pj and Mn parameters.

3 Results and discussion

3.1 Electronic structure

To explore the ground-state structure of the YLF crystal, we first predicted the crystal structure of YLF with a chemical composition of Li[thin space (1/6-em)]:[thin space (1/6-em)]Y[thin space (1/6-em)]:[thin space (1/6-em)]F = 4[thin space (1/6-em)]:[thin space (1/6-em)]4[thin space (1/6-em)]:[thin space (1/6-em)]16 via the CALYPSO method at ambient pressure. Noticeably, the tetragonal phase with the standardized I41/a symmetry was successfully discovered by using the structure search method, and the experimental structure was successfully reproduced, which strongly supports the validity of the CALYPSO method. To further explore the stabilized structure of YLF:Nd3+, we performed structural prediction simulations of Nd3+-doped YLF up to 96 atoms per cell with the chemical composition of Nd[thin space (1/6-em)]:[thin space (1/6-em)]Li[thin space (1/6-em)]:[thin space (1/6-em)]Y[thin space (1/6-em)]:[thin space (1/6-em)]F = 1[thin space (1/6-em)]:[thin space (1/6-em)]16[thin space (1/6-em)]:[thin space (1/6-em)]15[thin space (1/6-em)]:[thin space (1/6-em)]64. When Nd3+ ions are doped into the YLF crystal, we uncovered a novel phase transition in which the crystallographic symmetry of the ground-state structure changes from I41/a (tetragonal phase) to P[4 with combining macron] (tetragonal phase). For Nd3+-doped YLF, the host Y3+ ion site was naturally occupied by the Nd3+ ion impurity, with the same tetragonal phase as the YLF crystal. The stabilized structures of the YLF and YLF:Nd3+ crystals are presented, as shown in Fig. 1. The local polyhedron [YF8]5−/[NdF8]5− is found to have S4 point group symmetry, and each Y/Nd ion is surrounded by eight F ions. We also list the lattice parameters, interatomic distances and angles in the stabilized structures of YLF and Nd3+-doped YLF in Table S1 (ESI). We can clearly see that the geometry of this local polyhedron [YF8]5−/[NdF8]5− is slightly distorted, as deduced from the disparity between the Y–F and Nd–F bond lengths.
image file: d0cp03748f-f1.tif
Fig. 1 Predicted stabilized structures of (a) YLF and (b) YLF:Nd3+.

As shown in Table S1 (ESI), we also found slight variations in the lattice parameters between YLF (a = b = 10.439 Å, c = 10.812 Å) and Nd3+-doped YLF (a = b = 10.467 Å, c = 10.859 Å), which indicates a minor increase in the lattice parameters. Moreover, the optimized lattice parameters, interatomic distances and interatomic angles of pure YLF crystals are perfectly consistent with the experimental results,53 which validates the feasibility of the CALYPSO method. The atomic coordinates for the stabilized structure of Nd3+-doped YLF are listed in Table S2 (ESI). To fully demonstrate the rationality of the stabilized structure of Nd3+-doped YLF, many metastable structures were also identified using structural search methods. According to their energies from low to high, we list the first three metastable structures, as shown in Fig. S1 (ESI). The unit cell volume, lattice constants, and the corresponding relative energies are also listed in Table S3 (ESI). Interestingly, when the energies of isomers (a), (b) and (c) are very close to the energy of the stabilized structure, their space groups are consistent with that of the stabilized structure, but the doping sites of the Nd3+ ion are completely different.

As shown in Fig. 2, the phonon spectra for the stabilized structures of YLF and YLF:Nd3+ were recorded to perform an iterative assessment of dynamical stability. It can be clearly seen that no imaginary frequencies were found, indicating that the ground states of YLF and YLF:Nd3+ are dynamically stable under ambient conditions. To further prove the correctness of the ground state structure, the XRD patterns of pure YLF and YLF:Nd3+ are simulated as shown in Fig. 3, and the available experimental XRD data of YLF are also shown in Fig. 3 for comparison.54 We can clearly see that the distribution of the peaks and the overall intensities are extremely similar between the simulated and experimental XRD spectra of pure YLF, which indicates the accuracy of our identified stabilized structure as well as the validity of our structural search for Nd3+-doped YLF. Compared to that of the pure YLF crystal, the XRD spectrum of Nd3+-doped YLF has no obvious extra diffraction peaks when the doping concentration of Nd3+ ions reaches 6.25%. However, we can clearly see that the position of the diffraction peaks has changed slightly, where all the diffraction peaks of the Nd3+-doped YLF crystal shift finely toward lower angles compared to those of the pure YLF crystal. For simplicity, we have amplified only the (101) diffraction peak in the 2θ range of 18° to 20°, as shown in Fig. 3. Compared to the pure YLF crystal, the diffraction peaks of the YLF:Nd3+ crystal obviously shift to smaller diffraction angles. Similar to our previous structural analysis, the volume of the unit cell increases slightly due to the substitution of Y3+ ions by the slightly larger ionic radius Nd3+ ions in the host lattice. On the basis of Bragg's law:

image file: d0cp03748f-t3.tif(4)
where λ denotes the wavelength of the incident X-ray beam, n is an integer, and θ represents the Bragg angle. The spacing between the planes in the atomic lattice is described by the distance d. According to Bragg's formula, θ decreases as the distance d increases. That is, if the unit cell volume of YLF:Nd3+ increases slightly (d increases), then the Bragg angle θ is slightly decreased. Similar results have been observed by Dou et al. in their experiments.55 Hence, the rationality of our ground structure predicted by CALYPSO is further confirmed by relevant theoretical and experimental arguments, and this ground structure also provides a reliable basis for us to study the doping mechanism of the microstructure.

image file: d0cp03748f-f2.tif
Fig. 2 Calculated phonon spectra of (a) YLF and (b) YLF:Nd3+.

image file: d0cp03748f-f3.tif
Fig. 3 Comparison of the simulated X-ray diffraction patterns of (b) YLF and (c) YLF:Nd3+ with the experimental XRD pattern of (a) YLF.

The electronic properties of pure YLF and Nd3+-doped YLF were investigated by analyzing their electronic band structures and total and partial density of states (TDOS and PDOS), as shown in Fig. S2, S3 (ESI) and Fig. 4. In Fig. S2(a) (ESI), the GGA calculation shows that the band gap of YLF is calculated to be 7.81 eV, which well matches the previous theoretical result (Eg = 7.54 eV)56 but is smaller than the experimental value (Eg = 10.1 eV).57 This is typical for the DFT calculation using the GGA method, which will underestimate the band gap. To provide a more accurate description of the band gap of pure YLF than the standard DFT functional, we recalculated the band structure using the modified Becke–Johnson (BJ) method using the Wien2k package,58 as shown in our previous studies.52 A slightly higher value of 9.65 eV is obtained, which is in excellent agreement with the experimental value of 10.1 eV. For Nd3+-doped YLF, the standard GGA method may not accurately describe the electronic structure due to the addition of impurity Nd3+ ions with localized f states. To eliminate the effect of strongly correlated electron potentials for the Nd3+ 4f shell, the band structure and the TDOS and PDOS of YLF:Nd3+ were calculated using the GGA+U method. We obtained a band gap of 3.78 eV for the YLF:Nd3+ system, as shown in Fig. S2(b) (ESI), which is far smaller than the band gap of pure YLF of 7.81 eV (obtained using the GGA method).

image file: d0cp03748f-f4.tif
Fig. 4 Total and partial density of states of (a) YLF and (b) YLF:Nd3+ calculated using the GGA+U method.

This result indicates that the addition of impurity Nd3+ ions to YLF significantly reduces the band gap, whereas the Nd3+-doped YLF still possesses an insulator character with a relatively flat top of the valence band (VB). To further deepen the understanding of the contribution of each orbital to the electronic states and the bonding characteristics, we plot in Fig. 4 the TDOS and PDOS for pure YLF and Nd3+-doped YLF. It is evident that the states closest to the conduction band (CB) in the range of 7.8 to 10.0 eV are dominated by the d orbital. Additionally, the PDOS of Nd3+-doped YLF reveals that the occupied states between the bottom of the CB and the top of the VB are completely ascribed to the Nd3+ 4f orbital, which indicates that the impurity Nd3+ ions lead to a dramatic reduction in the band gap. We also calculated the band structure using the BJ method to obtain a more accurate band gap value of YLF:Nd3+. As shown in Fig. S3 (ESI), the result also showed an insulator system with a band gap value of 4.12 eV.

3.2 Crystal-field levels

To understand the energy level splitting of YLF:Nd3+, we analyzed the Stark levels and CFPs using the WEPMD method. According to our structural search, we obtained the stabilized structure of YLF:Nd3+, which forms a local [NdF8]5− unit with S4 site symmetry. Under the CF interaction of the Nd3+-doped YLF, the energy levels will split into many Stark levels. The 155 Stark levels observed experimentally were used throughout the fitting process28 and are summarized in Table S4 (ESI).

By using Novák's novel method,59 the initial values of the CFPs were obtained through ab initio calculations in the Wien2k program. First, we used 16 free-ion parameters for fitting on the basis of fixed CFPs, and the results (fit 1) are listed in Table 1. The fit 1 results show that the root-mean-square (rms) is only 29.7 cm−1, which indicates that the CFPs calculated are reliable. Subsequently, the CFPs were no longer fixed during further fitting to accurately describe the CF splitting of YLF:Nd3+. As shown in Table 1 (fit 2), an rms deviation of 20.1 cm−1 was obtained by further fitting. This result is better than that of a previous study (26.1 cm−1) reported by Åberg et al.26 However, the Stark levels of the 2H(2)11/2 multiplet show large discrepancies between the theoretically calculated value and the experimental value, as shown in the bold section of Table S4 (ESI). To the best of our knowledge, for Nd3+ ions in other hosts,24,60 the Stark levels of the anomalous 2H(2)11/2 multiplet are also poorly fitted because the one-electron CF often limits the fitting process of these energy levels. To further improve the anomalous splitting of the 2H(2)11/2 multiplet, different types of correlation crystal fields were tested by using crystal-field theory. We finally found that the orthogonal correlation crystal field (OCCF) could most effectively improve the anomalous 2H(2)11/2 multiplet by introducing OCCF operators. According to the correlation crystal-field Hamiltonian, the corresponding OCCF operators can be expressed as61,62

image file: d0cp03748f-t4.tif(5)
and the detailed implications of these parameters were described in our previous study.41 For Nd3+-doped YLF, the rms deviation is reduced to 15.7 cm−1 by using the OCCF operators, as shown in Table 1 (fit 3). Additionally, it is obvious that the Stark levels of the 2H(2)11/2 multiplet have a small error between the calculated and experimental values, as shown in the bold section of Table S4 (ESI). These results indicate that our WEPMD method based on the OCCF could perfectly remove the 2H(2)11/2 multiplet. Hence, the Stark energy levels calculated by us are in good accordance with the experimental values, and 27 experimentally unknown Stark energy levels are also predicted. It is hoped that our prediction will provide useful information for experimental exploration.

Table 1 Free-ion and CF parameters for Nd3+-doped YLF (cm−1)
Parameters Present work Previous work
Fit 1 Error Fit 2 Error Fit 3 Error Other26 Other28
E av 24[thin space (1/6-em)]400 2 24[thin space (1/6-em)]407 2 24[thin space (1/6-em)]398 1 24[thin space (1/6-em)]411
F 2 72[thin space (1/6-em)]849 27 72[thin space (1/6-em)]891 23 72[thin space (1/6-em)]761 17 72[thin space (1/6-em)]930 72[thin space (1/6-em)]939
F 4 52[thin space (1/6-em)]374 52 52[thin space (1/6-em)]503 44 52[thin space (1/6-em)]315 33 52[thin space (1/6-em)]379 52[thin space (1/6-em)]491
F 6 35[thin space (1/6-em)]625 34 35[thin space (1/6-em)]526 31 35[thin space (1/6-em)]649 15 35[thin space (1/6-em)]169 35[thin space (1/6-em)]489
ζ 873 1 875 0.6 876 0.4 874 873
α 21 0.1 21 0.1 21 0.1 21 21
β −572 5 −573 2 −573 2 −560 −572
γ 1468 10 1461 9 1464 5 1520 1478
T 2 261 9 237 8 291 6 275 217
T 3 39 2 42 0.4 41 0.4 96 44
T 4 89 3 78 0.8 79 1.1 142 86
T 6 −279 3 −290 1 −287 3 −295 −285
T 7 343 6 328 6 342 4 352 318
T 8 234 8 224 6 266 4 175 205
M 0 0.6 0.1 1.3 0.1 1.5 0.1 0.7
P 2 180 24 227 10 247 9 186
B 0 2 [513] 385 4 365 5 367 372
B 0 4 [−722] −978 9 −976 13 −762 −974
ReB44 [−1093] −1259 5 −1179 7 1313 −1116
B 0 6 [1] −9 6 −45 7 −0.2 −20
ReB46 [−835] −1007 6 −1024 6 1031 −1020
Im[thin space (1/6-em)]B46 [166] 318 12 244 22 161 200
G 0 2 162 32
G 0 4 508 15
Re[thin space (1/6-em)]G44 654 20
G 0 6 3 0.4
Re[thin space (1/6-em)]G46 290 49
Im[thin space (1/6-em)]G46 −92 15
N exp 155 155 155 149 155
N p 16 22 25 19
σ 29.7 20.1 15.7 26.1

3.3 Electric and magnetic dipole transitions

To deeply probe the luminescence properties and light–matter interactions of YLF:Nd3+, the Judd–Ofelt (J–O) theory was used to calculate the ED and magnetic dipole (MD) transitions based on our best results of fit 3. The J–O theory was introduced in the study of 4f–4f transitions by B. R. Judd63 and G. S. Ofelt,64 and it is widely used for trivalent lanthanide ions doping various host crystals because it can accurately describe the transition properties by introducing the J–O parameters. Ryan et al.65 obtained the effective J–O parameters (Ω2 = 0.362 × 10−20 cm2, Ω4 = 4.02 × 10−20 cm2 and Ω6 = 4.84× 10−20 cm2) for the Nd3+-doped YLF crystal by least-squares fitting, and the refractive index (n = 1.45)65 was also used in our calculations. The relevant expressions used in the calculations of Nd3+-doped YLF are given in the Appendix section (ESI). We first calculated the ED absorption lines and the corresponding radiative decay rates (AED and AMD), wavelengths (λ) and line oscillator strengths (SED) from the ground to excited state levels of Nd3+-doped YLF. In Table S5 (ESI), we list only some of the absorption lines in the visible and NIR regions (380–2500 nm). It is evident that the line oscillator strength shows a maximum at the absorption line 4I9/24F5/2 transition (808 nm), and this important characteristic of peak absorption at 808 nm may lead to wide application in the field of laser diodes.66–68 Surprisingly, the absorption line 4I9/24F5/2 transition has strong absorption at approximately 808 nm, which has been measured experimentally.69,70 Our theoretical calculation is in excellent agreement with the experimental result, which indicates that our WEPMD method is very accurate and reliable, as the results for both the theory and experiments are consistent. In addition, we also calculated the spontaneous emission transitions in Nd3+-doped YLF, and the experimental results are listed for comparison in Table S6 (ESI). Noticeably, the spontaneous emission lines 4F3/24I9/2, 4I11/2, 4I13/2 and 4I15/2 occur at 882, 1056, 1335 and 1840 nm, respectively. The total radiative lifetime of 4F3/24I9/2–15/2 transitions is 469 μs, and the radiative decay rates AED of these lines are 852.8, 1060.7, 210.0, and 10.6 s−1, respectively. Obviously, these corresponding values are in good agreement with the experimental values measured by Ryan et al.,65 providing reliable support for our present simulation of ED transitions. Additionally, we can clearly see that the 4F5/24I9/2 (808 nm) emission line has a large branching ratio (β), and the corresponding ED transition intensity is 1776.8 s−1. Due to its relatively large β and strong ED oscillator strength, the 4F5/24I9/2 emission line may be a good candidate for laser output and be beneficial for probing the potential laser action. It is worth noting that most of the MD radiative decay rates (AMD) are very small. However, the emission line 2H9/24I9/2 transition at 799 nm has a relatively strong radiative decay (AMD = 3.6 s−1) among all MD transitions. In Fig. 5, we show the two promising emission transitions of 2H9/24I9/2 and 4F5/24I9/2 by presenting their energy level transition diagrams. It should be noted that we also show the important transition diagram of the absorption line 4I9/24F5/2 transition using a green line. For the Nd3+-doped YLF crystal, the emission line of the 2H9/24I9/2 transition has a strong MD contribution that may create a condition beneficial for the exploration of magnetic light–matter interactions.
image file: d0cp03748f-f5.tif
Fig. 5 Energy level diagram for the Nd3+-doped YLF crystal. The calculated ED transitions that produce emission wavelengths at 799 and 808 nm are shown.

Numerical investigations have manifested that the contributions of MD oscillator strengths and MD transition rates are relatively weak compared to those of ED transitions, but a few emission lines still exhibit large MD oscillator strengths and transition rates in the near-infrared range. Table S7 (ESI) shows the MD emission lines from the 4F3/2(27,28) manifold to the 4I9/2, 4I11/2, 4I13/2 and 4I15/2 manifolds. On the one hand, the emission transition 4F3/24I9/2 in the near-infrared spectrum was measured by Zhang et al.71 They found that two emission line 4F3/2(R2) → 4I9/2(Z5) and 4F3/2(R1) → 4I9/2(Z5) transitions occur at 903 nm and 908 nm, respectively. These emission transitions are perfectly reproduced by our theoretical calculations at 904 and 908 nm, which correspond to the emission lines 4F3/2(28) → 4I9/2(5) and 4F3/2(27) → 4I9/2(5), respectively. On the other hand, the transition of 4F3/24I13/2 produced two relatively strong emission lines at 1313 and 1321 nm reported by Huang et al.17 In Table S7 (ESI), we can clearly see that 4F3/24I13/2 produces a total of 14 MD emission lines, and the two emission lines 4F3/2(28) → 4I13/2(13) and 4F3/2(27) → 4I13/2(13) have relatively strong transition intensities, occurring at 1313 and 1321 nm, respectively. Amazingly, these results indicate that the two experimental emission lines at 1313 and 1321 nm are once again perfectly reproduced by our theoretical calculations. Most notably, the transition intensities of most of these MD emission lines are very weak, where the two emission lines of 4F3/2(27) → 4I11/2(6) at 1047 nm and 4F3/2(27) → 4I11/2(8) at 1052 nm exhibit the strongest oscillator strengths. Obviously, the two strongest MD emission lines stem from the transition 4F3/24I11/2, and the MD emission lines occur in the range of 1.0–1.1 μm. For Nd3+-doped YLF laser crystals, the emission wavelengths of the two promising transition lines can provide potential attractive applications, i.e., the emission line at 1047 nm may be helpful for skin wound healing, and the emission line at 1052 nm may be used as a master oscillator in Nd3+-doped glass amplifiers.72,73Fig. 6 shows the promising laser transition 4F3/24I11/2, in which we draw its emission lines from the 4F3/2(27,28) levels to the 4I11/2 manifold using blue lines, and the two significant emission lines of 4F3/2(27) → 4I11/2(6) at 1047 nm and 4F3/2(27) → 4I11/2(8) at 1052 nm are presented by using red lines. Based on the perfect consistency between the theoretical and experimental results, our predictions can provide useful assistance for experimental studies, especially on laser materials.

image file: d0cp03748f-f6.tif
Fig. 6 Calculated magnetic dipole emission lines from the 4F3/2(27,28) manifold to the 4I11/2(6,7,8,9,10,11) manifold.

4 Conclusions

To summarize, a new stable phase with the P[4 with combining macron] space group of Nd3+-doped YLF is uncovered based on the CALYPSO method with DFT calculations. The electronic band structure calculations suggest that the insulator band gap of the system decreases significantly after doping with the impurity Nd3+ ions, which is mainly attributed to the contribution of the Nd3+ 4f orbital. By using our developed WEPMD method, we adopted the OCCF parameters to obtain a new set of CFPs, which can describe the CF splitting of Nd3+ ions in the YLF crystal more accurately. All 182 Stark levels were accurately identified, 27 of which were not measured in previous experiments. We predicted two potential laser channels of 4F5/24I9/2 at 808 nm and 2H9/24I9/2 at 799 nm with strong ED transition intensities. Two promising laser transitions of 4F3/2(27) → 4I11/2(6) at 1047 nm and 4F3/2(27) → 4I11/2(8) at 1052 nm with greater oscillator strength were determined. These results could serve as a useful guide for exploring the luminescence evolution of other rare-earth-doped laser materials.

Conflicts of interest

There are no conflicts to declare.


Financial support was provided by the National Natural Science Foundation of China (No. 11874043 and 11904297), the Fundamental Research Funds for the Central Universities (SWU118055), and Dean's Research Grants of the Faculty of Liberal Arts and Social Sciences, EdUHK.


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Electronic supplementary information (ESI) available: Structures of the optimized metastable, Stark energy levels, and electric and magnetic dipole transitions of Nd3+-doped LiYF4. See DOI: 10.1039/d0cp03748f
These two authors contributed equally to this work.

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