A probe of the radiation field magnetic component based on octahedral Yb³⁺ in the CaNbGa garnet – CNGG – single crystal

Abstract

In a disordered Yb³⁺-doped CaNbGa garnet – CNGG – single crystal, it is shown that octahedral Yb centers exist up to a solubility limit of about 5 × 10¹⁸ cm⁻³ in addition to the well known dodecahedral Yb which incorporates to a much larger density ∼10²¹ cm⁻³. Despite the low density of the octahedral Yb, the presence of a symmetry center for this garnet site forbids electric dipole (ED) transitions, thus magnetic dipole (MD) spectroscopic contributions are observed with an intensity similar to that of ED ones. Because of the easy growth of this garnet, the potential application of these two contributions for probing the magnetic field component radiated by plasmonic structures is discussed on the basis of time-resolved spectroscopy, since ED Yb³⁺ photoluminescence is about one order of magnitude faster than MD ²F_5/2 → ²F_7/2 (ΔJ = +1) emissions for the 0.3 at%Yb:CNGG crystal. Channels appropriated for room temperature operation can be excited at λ_EXC = 960.3 nm, while sensed at λ_EMI = 1022 nm for the short-lived ED reference channel and λ_EMI = 998, 1011, 1068 or 1080 nm for the long-lived MD signal channel.

---

1. Introduction

Energy levels of trivalent lanthanides (Ln³⁺) are characterized by ^2S+1L_J multiplets further split by the crystal field (CF) of a host in m_J levels. Intraconfigurational electronic transitions between these multiplets are most often induced by light–matter interactions mediated by electric fields through forced electric dipole (ED) transitions, but also include magnetic dipole (MD) interactions, particularly notable for transitions between multiplets with ΔJ = 0 or ±1.¹ Although it is usually assumed that MD transitions are ∼10⁵ times weaker than ED ones, their relative intensity in fact depends on the specific selection rules. In hosts where ED transitions are weak or even strictly forbidden, as when Ln³⁺ are incorporated at sites with a center of symmetry, the intensity of MD transitions can be dominant.

Stimulated by recent advances in optical plasmonic-based metamaterials and nanophotonics, a variety of ways to exploit MD transitions of Ln³⁺ have been proposed: theoretically, as the building blocks for homogeneous negative index materials,² or experimentally, as probes for the study of local magnetic fields in metamaterials, in a very simple approach that consists of placing the MD probe at the metamaterial surface, and if this resonance frequency corresponds to the spectral range of the field enhancement, spectral changes in intensity or shape may be observed in comparison with other magnetic dipoles outside the system or with some reference ED emission in the same system.^3–7 Furthermore, experimental studies by using the competition between ED and MD processes have shown the way for achieving a strong enhancement of MD emission⁸ and also to broadly tune the emission spectra.⁹

For the above indicated sensing purposes, previous studies have involved mainly the visible ⁵D₀ → ⁷F₁ MD transition of Eu³⁺, in probing systems based on Eu-doped Y₂O₃ thin films,^7–9 dispersions of Eu-doped organic systems in polymeric thin films,^3,4,6 or Eu-doped Y₂O₃ NPs (about 60 nm).¹⁰ The specific advantage of using Eu³⁺ is the coexistence of the nearly pure MD ⁵D₀ → ⁷F₁ (λ ≈ 590 nm) transition and the ED ⁵D₀ → ⁷F₂ (λ ≈ 615 nm) transition used as the reference. Other Ln³⁺ emissions which have been tested with the same aim are mixed MD–ED transitions in the near-infrared (NIR) range, for instance the overlapping ⁴F_9/2 → ⁶F_11/2 + ⁶H_9/2 (λ ≈ 734 nm) emissions of Dy³⁺,¹¹ the also overlapping ¹G₄ → ³H₅ (λ ≈ 784 nm) and ³H₄ → ³H₆ (λ ≈ 800 nm) emissions of Tm³⁺,¹¹ or the ⁴I_13/2 → ⁴I_15/2 (λ ≈ 1.5 μm) transition of Er³⁺,¹² in all cases by using the corresponding doped Y₂O₃ thin films.

The near-infrared (NIR) range from 800 to 1100 nm has several advantages over other spectral regions. As compared to the visible (characteristic of Eu³⁺), micron-sized plasmonic nanostructures are much easier to fabricate than nano-sized ones and their resonances exhibit higher-quality factors due to lower ohmic losses. However, as compared with the ⁴I_13/2 → ⁴I_15/2 Er³⁺ transition at λ ≈ 1.5 μm, emissions at λ < 1100 nm can be observed using standard Si photodetector technology, which simplifies the detection process. Moreover, among MD Ln³⁺ emissions at this wavelength range, those that can be pumped at the NIR will be the better candidates to be used. From the above considerations the ²F_5/2 ↔ ²F_7/2 transitions of Yb³⁺ (typically λ_EXC ≈ 940–980 nm and λ_EMI ≈ 980–1060 nm) in a centrosymmetric crystal site are very interesting options. The simple two-state energy structure of Yb³⁺ means that MD emission can account for a significant contribution to the overall decay. In fact, relatively long Yb³⁺ lifetime (τ) characteristics of MD transitions have been measured for Yb-doped BaF₂ and SrF₂ fluorites (τ = 9.72 ms and 8.20 ms, respectively), as well as for Rb₂NaYF₆ elpasolite (τ = 10.84 ms) crystals, with Yb³⁺ at centrosymmetric sites of cubic eightfold and perfect octahedral coordination,¹³ respectively, in both cases with calculated MD branching ratios of ∼50%.¹²

Cubic garnets A₃M₂N₃O₁₂ with space group Ia3̄d (No. 230) offer simultaneously non centrosymmetric dodecahedral 24c sites (A) and octahedral 16a centrosymmetric sites (M) to host Ln. An illustration of the garnet structure can be seen in the general view given in Fig. 1a. Fig. 1b shows the coordination of dodecahedral AO₈ and octahedral MO₆ garnet sites. Further drawings showing other atomic arrangements can be seen for instance in ref. 14. The Ln³⁺ distribution over 24c and 16a garnet sites is a topic which has been addressed with several purposes and under different approaches.^15–23 The main factor governing the site preference of Ln³⁺ in the garnet structure is the ionic size, in such a way that garnets with any Ln³⁺ cation occupying the dodecahedral 24c site are known,¹⁵ and only the smallest size Ln³⁺ cations, typically Dy³⁺ to Lu³⁺ and also Y³⁺ or Sc³⁺, are able to enter into the octahedral 16a site, even up to its complete filling, but in this case a 24c cation with a considerably large size, for example Ca²⁺ in the germanate series Ca₃Ln₂Ge₃O₁₂,¹⁸ including Ca₃Y₂Ge₃O₁₂,²⁰ is required, thus the relative sizes of 24c and 16a cations also play a role. The presence of Yb³⁺ in both garnet sites would offer the possibility of having the MD probe and ED reference ions in the same tested volume minimizing uncertainties related to excitation and detection processes, but so far the properties of Yb coexisting in both garnet sites have not been properly documented. Either the studies are limited to crystallographic aspects,^16,17,20 or the spectroscopic-based proposals^21,23 are not soundly supported by crystallographic data and/or crystal field (CF) interaction calculations.

Fig. 1 (a) General view of the A₃M₂N₃O₁₂ garnet structure. (b) Oxygen coordinations of the AO₈ 24c dodecahedra and MO₆ 16a octahedra.

In this work we present the first report and characterization of the ²F_5/2(n′) ↔ ²F_7/2(n) MD transitions of Yb³⁺ at the octahedral 16a (centrosymmetric C_3i symmetry) site of the CaNbGa garnet (thereafter CNGG). The host selection is based on the large Ca²⁺ ionic size filling the dodecahedral site, see before, while a large variety of ionic filling (Nb⁵⁺, Ga³⁺ and even vacancies) is found for the octahedral and tetrahedral sites of this garnet composition. The occupancy of the 24c dodecahedral site of the CNGG garnet by Yb³⁺ is well documented from both crystallographic and spectroscopic points of view.^24–27

The emphasis of the present work is the study of Yb³⁺ in the octahedral 16a CNGG garnet site. Through low temperature (6 K) optical absorption (OA) and photoluminescence (PL) spectra followed by the modeling of CF interactions, it has been possible to establish the sequence of 16a Yb³⁺ energy levels as a well-separated set with regards to those of Yb³⁺ at the 24c dodecahedral site. The lifetime associated with the 16a Yb^{3+ 2}F_5/2 → ²F_7/2 MD emissions has been also measured, and the MD branching ratio has been calculated as β_MD = 50%, a value that equals those of previously indicated for Yb³⁺ in centrosymmetric sites of fluoride-based hosts.¹² Furthermore, by using their different kinetics, ED and MD Yb³⁺ PL contributions have been separated even at room temperature (RT), opening the possibility of its application as a sensor for the magnetic field radiation in plasmonic systems.

2. Methods

2.1 Crystal growth

The crystal precursor polycrystalline material with a nominal cationic composition Ca_2.991Yb_0.009Nb_1.6875Ga_3.1875 (0.3 at%Yb:CNGG) was prepared by mixing CaCO₃ (Alfa Aesar 99.5%), Yb₂O₃ (99.99%, acquired through Shangai Zimei International Co., Ltd), Nb₂O₅ (Aldrich 99.9%) and Ga₂O₃ (Aldrich 99.99%) in a 36.33 : 0.21 : 27.21 : 36.25 weight% ratio. This off-stoichiometry formula is within the composition range with congruent melting that allows garnet crystal growth from the melt.²⁸ The mixture was heated in air to 1648–1673 K for several hours with intermediate regrinding. The garnet phase purity of the synthesized crystal precursor material was checked at RT using powder X-ray diffraction using a Bruker AXS D-8 Advance diffractometer with Cu K_α radiation. From this polycrystalline powder the single crystal was grown in air by the Czochralski technique. For this purpose we used a Cyberstar crystal growth equipment incorporating a radiofrequency (RF) coil fed by a Huttinger TruHeat MF 3020 power supply operated at 9.2 kHz. The crucible (40 mm in diameter and height) was made of platinum, and a platinum wire was used as the seed, which was rotated and pulled simultaneously. Samples for optical purposes were obtained by crystal cutting and polishing using conventional methods.

2.2 Structural and compositional analyses

Due to the low Yb³⁺ doping (nominally 0.3 at% with regard to the dodecahedral site occupancy) of the currently studied 0.3 at%Yb:CNGG crystal, its structure should be very similar to that described for the undoped CNGG single crystal in one of our previous studies.¹⁴ So, we shall adopt the crystal formula previously determined by the refinement of single crystal X-ray diffraction (XRD) data, i.e. {Ca_0.985□_D}₃[Nb_0.625Ga_0.372□_O]₂(Ga_0.821Nb_0.102□_T)₃O₁₂, □ stating for vacancies at 24c dodecahedral (curly brackets), 16a octahedral (square brackets) and 24d tetrahedral (parentheses) sites.

The low concentration of Yb in the studied garnet prevents their compositional determination using XRD or X-ray fluorescence methods. However, these methods were successfully used for heavily (>10 at%) Yb-doped crystals. Thus, the actual Yb content of the used 0.3 at%Yb:CNGG crystal was determined by comparison of the integrated RT OA in this and in heavily Yb-doped crystals. This methodology provides a 0.08 at%Yb content for the grown crystal with regards to the dodecahedral occupancy.

2.3 Spectroscopic techniques

OA in the visible and NIR region was determined by using a Varian spectrophotometer, model Cary 5E, with a limiting spectral resolution of 0.04 nm at λ ≈ 1000 nm. An extensive 6 K OA study in the whole visible region using a thick (≈5.1 mm) 0.3 at%Yb:CNGG sample discarded the contamination with any Ln different to the studied Yb³⁺. PL was excited either in a continuous wave (cw) with a tunable Ti-sapphire laser or pulsed (10 Hz) with a tunable Quanta-Ray MOPO-HF system providing ns laser pulses. PL light was dispersed in a SPEX (f = 34 cm) spectrometer and detected using a 77 K cooled Ge photodiode in cw experiments, or with a Hamamatsu InP/InGaAs phototube (model H10330A-75) in lifetime measurements and time-resolved spectroscopy. In cw PL experiments the laser beam was chopped at ≈200 Hz and the PL signal recovered with a lock-in amplifier. Yb³⁺ lifetime measurements were carried out using a thin crystal plate (60 μm) in order to minimize emission reabsorption. Time-resolved spectroscopy was discriminated by a Stanford Research SR400 photon counter. For 6 K optical spectroscopic measurements a He close-cycle cryostat connected to a suitable temperature controller was used.

3. Results

The OA and PL spectra of Yb³⁺ in the CNGG host originate from electronic transitions between ground ²F_7/2 and excited ²F_5/2 Yb³⁺ multiplets. Both, the D₂ and C_3i local symmetries of the dodecahedral 24c and octahedral 16a garnet sites, respectively, split these multiplets into four ²F_7/2 (n = 0, 1, 2, 3) and three ²F_5/2 (n′ = 0′, 1′, 2′) Kramers doublets.

The Yb³⁺ spectra of heavily doped (>1 at%Yb) CNGG crystals have been previously studied in detail.^14,24–27 So far, the crystallographic and spectroscopic studies only provided evidence for Yb incorporation in the dodecahedral 24c site. The 6 K OA and PL spectra consist in inhomogeneously and thermally broadened bands which hamper the accurate determination of some Yb³⁺ energy levels. Fig. 2 and 3 show selected examples of the optical contributions of dodecahedral Yb in CNGG, while a more extensive dodecahedral Yb spectroscopic review is provided in the ESI.†

Fig. 2 (a) 6 K optical absorption spectrum of the 0.3 at%Yb:CNGG crystal (red line), and its comparison with that of the 8 at%Yb:CNGG crystal (black line) for (b) ²F_7/2(0) → ²F_5/2(2′) and (c) ²F_7/2(0) → ²F_5/2(0′) Yb³⁺ transitions.

Fig. 3 Comparison of the 6 K photoluminescence spectra assigned to the octahedral 16a (λ_EXC = 896.5, 960.3 or 968.5 nm) and dodecahedral 24c (λ_EXC = 970.9 and 971.6 nm) Yb³⁺ in the 0.3 at%Yb:CNGG single crystal.

The only well resolved band in the 6 K spectra of 8 at%Yb:CNGG crystals is ²F_7/2(0) ↔ ²F_5/2(0′) (shortly, 0 ↔ 0′) at λ = 970.9 nm (see Fig. 2c). Even this band is largely broadened by the different crystalline environments coexisting around the dodecahedral 24c site of Yb³⁺, since the spectral position of this 0 ↔ 0′ transition is mainly related to the electric charge of cations/vacancies occupying the two edge-sharing tetrahedra at the shortest distance (∼3.12 Å) from the central 24c Yb³⁺.²⁴ In fact, the small OA band at λ = 973 nm corresponds to a dodecahedral Yb³⁺ center linked to a vacant edge-sharing tetrahedron.²⁴

The 6 K OA (Fig. 2) and PL (Fig. 3) spectra of the 0.3 at%Yb:CNGG crystal show bands not observable in the corresponding spectra for heavily doped >1 at%Yb:CNGG crystals. The new well-resolved OA bands peak at 968.7 nm (10 323 cm⁻¹), 960.3 nm (10 413 cm⁻¹) and 896 nm (11 161 cm⁻¹), while characteristic PL emissions at 968.7 nm, 996.7 nm, 1008.7 nm and 1080.6 nm are observed when exciting any of the three above listed OA bands (see Fig. 3). The absorption intensity of this new band set reaches 40% when the 968.7 nm new OA is compared with that of the dodecahedral Yb 0 ↔ 0′ transition at λ = 970.9 nm, see Fig. 2c. These new OA and PL band sets indicate the actual presence of a second type of Yb center coexisting in the garnet structure with the main dodecahedral Yb³⁺ center but with a much lower solubility limit, and thus, although present with low density, its contribution is not observable in the spectrum of the heavily doped Yb:CNGG crystals. In the following we show that this new center is compatible with the assumption of Yb³⁺ located at the octahedral 16a garnet site, and hereafter we shall refer to it as octahedral Yb.

Therefore, from the OA and PL bands experimentally determined for the octahedral Yb³⁺ center in CNGG, the complete set of Yb³⁺ energy levels can be established as 0, 290, 410 and 1069 cm⁻¹ for the ground ²F_7/2 (0, 1, 2, 3), and 10 323, 10 413 and 11 161 cm⁻¹ for the excited ²F_5/2 (0′, 1′, 2′) multiplets.

In a further attempt to correlate these energy levels with the octahedral C_3i (≡S₆) symmetry of the 16a garnet site, a parametrization of CF effects in this site has been carried out. Since the large number of CF parameters accounting for the C_3i symmetry makes it unrealistic for any CF modeling to reproduce the sequence of Yb³⁺ energy levels, the often followed “descent of symmetry” procedure has considered the tetragonal bypiramidal D_4h symmetry as the better approach, i.e. the higher symmetry polyhedron with coordination number CN = 6 that can be regarded as a distortion of an octahedron O_h whose fourfold rotation axis is chosen as the main axis. For the D_4h symmetry the CF potential is described by B²₀, B⁴₀, B⁴₄, B⁶₀ and B⁶₄ CF parameters, preliminary O_h, B⁴₀ and B⁶₀ being the only independent parameters whose values were initially obtained by using the semi-empirical Simple Overlap Model.²⁹ Details of the procedure for the CF parametrization of 16a Yb³⁺ energy levels in CNGG are given in the ESI.† The energy levels of 16a Yb³⁺ in CNGG were adequately reproduced by using the set of free ion and D_4h CF parameters included in Table 1.

Table 1 Free ion (E⁰ and ζ) and D_4h (B²₀, B⁴₀, B⁴₄, B⁶₀ and B⁶₄) crystal field parameters (in cm⁻¹) used to reproduce the sequence of ²F_7/2 and ²F_5/2 energy levels of 16a Yb³⁺ in the CNGG crystal

Parameter		Yb^3+ energy levels
		Label	Observed (cm^−1)	Calculated (cm^−1)
E ^0	4809.4	^2F7/2(0)	0	−3.4
ζ	2905.3	^2F7/2(1)	290	288
B ^20	−64	^2F7/2(2)	410	409
B ^40	2375	^2F7/2(3)	1069	1076
B ^44	1844	^2F5/2(0′)	10 323	10 328
B ^60	−210	^2F5/2(1′)	10 413	10 416
B ^64	251	^2F5/2(2′)	11 161	11 153

---

The ²F_5/2 Yb³⁺ PL intensity decay kinetics has been also studied as a further signature of the different symmetry of the two (octahedral and dodecahedral) Yb³⁺ centers observed in the 0.3 at%Yb:CNGG crystal. The ²F_5/2 Yb³⁺ PL time constant (τ) after 970–973 nm excitation through the ²F_7/2(0) → ²F_5/2(0′) Yb³⁺ transition in the dodecahedral centers was shown to vary in the τ = 800–450 μs range depending on the selected excitation/emission wavelength, i.e. the inhomogenously modified dodecahedral center selected.²⁴ The increase of the Yb concentration further reduces this time constant. An example of the PL kinetics is shown in Fig. 4a.

Fig. 4 Comparison of the ²F_5/2 photoluminescence intensity decay of the (a) dodecahedral 24c Yb³⁺ center, λ_EXC = 970.9 nm and λ_EMI = 1022 nm, and (b) octahedral 16a Yb³⁺ center, λ_EXC = 960.3 nm and λ_EMI = 1080.6 nm, of the 0.3 at%Yb:CNGG crystal. The points are the experimental results measured at 6 K (black points) and 300 K (red points). The lines are the fits of the long component of the corresponding decay.

The octahedral Yb center of the 0.3 at%Yb:CNGG crystal exhibits completely different PL intensity decay kinetics, see Fig. 4b. Its time extent widely covers the 10 ms range, it is more sensitive to the sample heating from 6 K to RT than in the dodecahedral case and most often a non-single exponential behavior is observed. The PL decay kinetics excited at λ_EXC = 960.3 nm are basically independent of the monitored wavelength (λ_EMI = 968.7 nm, 996.7 nm, 1008.7 nm or 1080.6 nm), see the ESI† (Fig. S4). They most typical show a fast decay for t < 2 ms and later a rather slow decay for the rest of the monitored time. This is understood as the overlapped contributions of the dodecahedral (short-lived) and octahedral (long-lived) Yb³⁺ centers. The long time tail of the decay can be fit to a single exponential law with a time constant τ ≈ 6–7 ms at 6 K and τ ≈ 4 ms at 300 K, i.e. the PL lifetime of the octahedral Yb³⁺ center is nearly one order of magnitude larger than that of the dodecahedral Yb one in the same crystal. This strong difference is consistent with the expected ED or MD Yb³⁺ PL contributions of these centers. For the non-centrosymmetric 24c D₂ dodecahedral site the contribution of ED transitions is expected to dominate the PL emission; thus the obtained ²F_5/2 Yb³⁺ lifetime is in the range observed for crystals hosting Yb³⁺ in similar non-centrosymmetric sites, like YAG, τ ≈ 950 μs,³⁰ NaLn(WO₄)₂τ ≈ 300–500 μs,³¹ or LnVO₄τ ≈ 250–350 μs.³² However, as stated in the Introduction, the presence of a center of symmetry forbids ED transitions, thus MD ones are observed with similar or even larger intensities than for the ED contributions. Such MD transitions are characterized by long PL lifetimes, thus the much larger lifetime obtained for the so-called Yb octahedral center may be regarded as the ultimate probe of the occupancy by Yb³⁺ in the centrosymmetric 16a crystal site of the CNGG host.

Once the origin of the described OA and PL features of the 0.3 at%Yb:CNGG crystal has been clarified thanks to 6 K spectroscopy, its application as a probe of plasmonic induced radiation fields requires operation at RT. Fig. 5 shows a comparison of the OA spectra corresponding to 0.3 at% and 11.6 at%Yb:CNGG crystals, the spectroscopy of the latter being purely dominated by the dodecahedral Yb³⁺ contributions. It is obvious that excitation of the octahedral Yb³⁺ center at RT through its 0 → 0′ transition at λ = 968.7 nm is not possible because with increasing temperature the relative intensity of this band decreases and overlaps with the 0 → 0′ (at λ = 972.3 nm) band tail corresponding to the dodecahedral Yb³⁺ center. However, the comparison of the spectra at both Yb doping concentrations shows that the octahedral Yb³⁺ 0 → 1′ transition at λ = 960.3 nm is clearly resolved from the background dodecahedral Yb contribution, the latter amounts to about 50% at this wavelength. Although the standard (integrated over time) cw PL spectra show little difference for excitation at the octahedral Yb³⁺ (λ = 960.3 nm) or in the side bands corresponding to the dodecahedral Yb³⁺ centers (see Fig. S3, ESI†), taking advantage of the different PL kinetics of both Yb³⁺ garnet centers, time-resolved spectroscopy can disclose the separate contributions of these two Yb³⁺ garnet centers.

Fig. 5 Comparison of the 300 K OA spectra of 0.3 at%Yb:CNGG (red continuous line) and 11.6 at%Yb:CNGG (black dashed line) crystals. The spectral intensity of the latter crystal is divided by a factor of 170 to equal the intensity of the dodecahedral Yb³⁺ bands (920–944 nm) in both crystals.

Fig. 6 shows the RT time-resolved PL emission obtained for different delays and gate widths after the laser pulse (<5 ns of duration, tuned at λ = 960.3 nm) excitation. For short times (5 μs of delay and 250 μs of gate width) the PL is dominated by the short-lived ED contributions of the dodecahedral Yb³⁺ center. Correspondingly, the emission spectrum shows a broad peak at 1022 nm characteristic of the PL observed in highly doped Yb:CNGG,^24,26 which is also shown in Fig. 3 (λ_EXC = 971.6 nm). However, over a long time (2.5 ms of delay and 8 ms of gate width) the spectrum is quite different, and matches the emission of the octahedral Yb³⁺ shown in Fig. 3. Although the contribution of the λ = 1022 nm band is still present, this PL spectrum contains four well resolved emissions at λ = 998, 1011, 1068 and 1080 nm, with intensities 2.80, 2.56, 2.94 and 3.76 times those corresponding to the dodecahedral Yb³⁺ contributions at the same wavelengths, respectively. The origin of the 1068 nm RT emission is related to the thermal redistribution of the ²F_5/2 electronic population, and corresponds to the ²F_5/2(1′) → ²F_7/2(3) transition of the octahedral Yb³⁺ center.

Fig. 6 300 K time-resolved photoluminescence emission of the 0.3 at%Yb:CNGG crystal after excitation at λ = 960.3 nm for different delay and gate times. Gate width of 250 μs delay 5 μs after laser pulse excitation (representative of the dodecahedral Yb³⁺ contribution, black dashed line) and gate width of 8 ms delay 2.5 ms (representative of the octahedral Yb³⁺ center, red continuous line).

4. Discussion

From 6 K OA and the excitation/emission PL spectra shown in Fig. 2 and 3, it has been disclosed that along the predominant dodecahedral Yb³⁺ optical center associated with 24c D₂ symmetry in YAG-like garnets, another minority Yb³⁺ center with very different spectroscopic characteristics coexists in the 0.3 at%Yb:CNGG crystal.

Several CF considerations support the above conclusion. On one side, the experimental energies determined for the m_J levels of the so called 16a octahedral Yb³⁺ center are well reproduced by using a CF parameter set describing a centrosymmetric center, see Table 1. On the other side, the absolute CF splittings of 1069 cm⁻¹ and 838 cm⁻¹ for ground ²F_7/2 and excited ²F_5/2 Yb³⁺ multiplets and their corresponding barycenters, lying at 442 cm⁻¹ and 10 632 cm⁻¹ energies, respectively, are consistent with those found in other 6-fold oxygen coordinated Yb ionic oxides: in Yb-doped sexquioxides the ²F_7/2 splitting ranges from 1193 cm⁻¹ in Lu₂O₃,³³ to 1076 cm⁻¹ in Sc₂O₃.³⁴ ΔE(²F_7/2) = 1023 cm⁻¹ is found for Ca₄YO(BO₃)₃ (with 6O-Yb-2B coordination),³⁵ 964 cm⁻¹ in Y₂SiO₅,³⁴ and 900 cm⁻¹ in Ba₃Lu(BO₃)₃.³⁴ Smaller ΔE(²F_7/2) values in 6-fold oxygen coordinated Yb compounds are also found, for instance 788 cm⁻¹ in LiNbO₃,³⁶ or even below 600 cm⁻¹ in Yb metalorganic complexes,³⁷ indicating a reduction of the CF strength on Yb³⁺. In the latter case, a reduction of the effective Yb charge due to covalent bonds of oxygen to the neighboring organic ligands may contribute to the observed CF reduction, while in ionic crystals such CF strength reductions are partially ascribed to larger Yb³⁺ bond distances.

Even when the same Yb³⁺ coordination occurs in a given material the site symmetry influences the ^2S+1L_J multiplet splitting. Sesquioxides sharing 6-fold oxygen coordinated Yb³⁺ with and without a center of symmetry are a case similar to the present 0.3 at%Yb:CNGG that can guide us for the spectroscopic assignments. While efforts have been made in the assignment of usually experimentally incomplete Yb³⁺ energy level sets both for C₂ and C_3i Yb centers of cubic sesquioxides,^38,39 mainly through the application of the barycenter plot law,³⁴ only CF analyses of 24c dodecahedral Yb³⁺ energy levels have been attempted for garnet hosts.^40,41 These previously known data for cubic sesquioxides indicate that CF splittings of ²F_7/2 and ²F_5/2 are always wider and their corresponding barycenters are located at higher energies for centrosymmetric C_3i Yb³⁺ centers than for the C₂ ones, see Table 2 in ref. 38 and the ESI† (Table S1). The above indicated splittings for the C_3i 16a Yb³⁺ center in the 0.3 at%Yb:CNGG crystal are considerably larger than those of Yb³⁺ in the noncentrosymetric D₂ 24c site in other garnet hosts, for instance, 766 cm⁻¹ and 352 cm⁻¹ for ²F_7/2 and ²F_5/2, respectively, in YbAG, or 624 cm⁻¹ and 434 cm⁻¹ for YbGG, see Table S2 (ESI†). It could be assumed that larger CF splitting amplitudes for the centrosymmetric C_3i 16a Yb³⁺ center are associated with the cooperative effect of considerably smaller bond distances for 16a Yb³⁺ than for Yb³⁺ in the dodecahedral environment as well as with an increase of the symmetry in the 16a center with regard to the 24c one.

The solubility limit for Yb³⁺ incorporation at 16a positions in the CNGG crystal is rather low, obviously below 0.3 at% of the dodecahedral site. From the facts that the background optical absorption at λ = 960.3 nm of dodecahedral Yb³⁺ centers in the 0.3 at%Yb:CNGG crystal is about 50% of the total, see Fig. 5, and that the total Yb content was estimated from OA comparison as 0.08 at% of the dodecahedral site, the Yb density in the octahedral 16a garnet site can be roughly estimated to be ≈5 × 10¹⁸ cm⁻³. Such a low limit is in fact expected due to the large Yb³⁺ ionic radii (0.868 Å for VI coordination) compared to those of Nb⁵⁺ and Ga³⁺ (0.64 Å and 0.62 Å, respectively, also for VI coordination). Due to the low solubility limit for Yb incorporation in the octahedral garnet site, direct evidence of corresponding MD transitions in the OA spectrum will diminish with the increase of Yb content in the crystal, and in fact the same OA bands from 16a Yb³⁺ can be also perceived with very low intensity in the 77 K OA spectrum of the 2 at%Yb:CNGG crystal reported by Voronko et al.,²⁵ while they are no longer observed in the OA spectrum of the 8 at%Yb:CNGG crystal, see Fig. 2b, since for these latter crystals ED transitions of Yb³⁺ in the dodecahedral garnet site have intensities several orders of magnitude stronger than those of the MD of Yb³⁺ in the octahedral garnet site.

Given that forced ED intraconfigurational f–f Ln³⁺ transitions from the centrosymmetric sites are strictly forbidden, the ²F_5/2 → ²F_7/2 emission from 16a Yb³⁺ has a predominant MD character. Consequently, Yb:CNGG is able to provide simultaneously well-differentiated sets of Yb^{3+ 2}F_7/2 ↔ ²F_5/2 ED and MD transitions, arising from 24c and 16a garnet sites, respectively.

The evaluation of the MD contribution of the 16a Yb^{3+ 2}F_5/2(0′) → ²F_7/2(1, 2, 3) (λ_EMI = 996.7, 1008.7 and 1080.6 nm) transitions can be performed by comparing the total decay rate derived from the measured lifetime value, Γ_total = 1/τ, with the MD spontaneous emission rate, A_MD = A′_MD × n_r³, where the vacuum value A′_MD is predicted in ref. 12 and n_r = 1.96 is the measured refractive index for CNGG at λ ≈ 1000 nm.¹⁴ The MD branching ratio, defined as β_MD = A_MD/Γ_total, results in β_MD ≈ 50% for 16a Yb³⁺ in CNGG if the room temperature center lifetime is taken as τ ≈ 4 ms, see Fig. 4b. This value is similar to previous β_MD values indicated for the ²F_5/2(0′) → ²F_7/2(0) Yb³⁺ emission in crystals hosting Yb³⁺ in lattice sites with a center of symmetry, such as SrF₂, Rb₂NaYF₆ or ScBO₃.¹² Such crystals are difficult to grow and are not easily available with specific Yb doping, while unfortunately the MD branching ratio of Yb³⁺ in standard YAG is only 10.8%.¹² Therefore, even though the 16a Yb³⁺ center is present in the CNGG garnet with a low density, the strong MD character of its transitions makes them observable, which highlights the interest of the 0.3 at%Yb:CNGG crystal to be used for probing local magnetic fields in plasmonic resonances and metamaterials.

5. Conclusions

A new centrosymmetric octahedral Yb³⁺ center has been identified in the disordered CaNbGa garnet crystal with spectroscopic properties clearly different, both at 6 K and 300 K, from the usual dodecahedral Yb³⁺ center found in this and similar garnets. This new center, which shows favorable properties to be used as a probe for the intensity of magnetic fields radiated by plasmonic structures, operates around λ = 1 μm which is a good compromise for lithographic fabrication and optical detection techniques. It is characterized by ²F_7/2(0–3) = 0, 290, 410, 1069 cm⁻¹ and ²F_5/2(0′–2′) = 10 323, 10 413, 11 161 cm⁻¹ Yb³⁺ m_J energy levels, which are consistent with the large CF splittings and barycenter energies expected for centrosymetric Yb³⁺ centers in ionic compounds, their individual positions being well reproduced by a CF simulation assuming a lower, but still with inversion center, D_4h symmetry.

The probe center can be operated at room temperature by excitation at λ = 960.3 nm and with best sensitivity detection near λ = 1080 nm, although other additional detection channels are found at λ = 998, 1011 and 1068 nm. The coexistence of dodecahedral and octahedral Yb³⁺ centers in the same crystal with roughly similar densities allows the detection of reference ED and signal MD PL contributions corresponding to the above centers, respectively. Separation of both contributions has been conveniently made by using time-resolved spectroscopy, since ED Yb³⁺ PL is short-lived (τ < 0.8 ms) and the MD one is long-lived (τ ≈ 4 ms). The measured MD branching ratio in the studied garnet, β ≈ 50%, is equivalent to those previously reported in other centrosymmetric hosts, but the easy growth in air of the present CaNbGa garnet with congruent melting at ≈1470 °C will facilitate the fabrication of the required plasmonic or metamaterial structures in comparison for instance with Y₂O₃ whose crystal availability is very limited due to its high melting point of ≈2490 °C.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work has been supported by the Spanish Ministry of Economy and Competitiveness and by the European Regional Development Fund through project RTI2018-094859-B-I00. CSIC support for Open Access publication and advice of Prof. Rafael Valiente on time-resolved spectroscopic measurements are acknowledged.

References

1. W. T. Carnall, P. R. Fields and K. Rajnak, J. Chem. Phys., 1968, 49, 4424.
2. Q. Thommen and P. Mandel, Opt. Lett., 2006, 31, 1803.
3. N. Noginova, G. Zhu, M. Mavy and M. A. Noginov, J. Appl. Phys., 2008, 103, 07E901.
4. N. Noginova, Y. Barnakov, H. Li and M. A. Noginov, Opt. Express, 2009, 17, 10767.
5. N. Yang, Y. Tang and A. E. Cohen, Nano Today, 2009, 4, 269.
6. X. Ni, G. V. Naik, A. V. Kildishev, Y. Barnakov, A. Boltasseva and V. M. Shalaev, Appl. Phys. B: Photophys. Laser Chem., 2011, 103, 553.
7. T. H. Taminiau, S. Karaveli, N. F. van Hulst and R. Zia, Nat. Commun., 2012, 3, 979.
8. S. Karaveli and R. Zia, Opt. Lett., 2010, 35, 3318.
9. S. Karaveli and R. Zia, Phys. Rev. Lett., 2011, 106, 193004.
10. M. Kasperczyk, S. Person, D. Ananias, L. D. Carlos and L. Novotny, Phys. Rev. Lett., 2015, 114, 163903.
11. C. M. Dodson, J. A. Kurvits, D. Li, M. Jiang and R. Zia, Opt. Mater. Express, 2014, 4, 2441.
12. C. M. Dodson and R. Zia, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 86, 125102.
13. L. DeLoach, S. Payne, L. Chase, L. Smith and W. Kway, IEEE J. Quantum Electron., 1993, 29, 1179.
14. E. Castellano-Hernández, M. D. Serrano, R. J. Jiménez-Riobóo, C. Cascales, C. Zaldo, A. Jezowski and P. A. Loiko, Cryst. Growth Des., 2016, 16, 1480.
15. S. Geller, Z. Kristallogr., 1967, 125, S1 (and refs. therein).
16. L. Suchow, M. Kokta and V. J. Flynn, J. Solid State Chem., 1970, 2, 137.
17. L. Suchow and R. Mondegarian, J. Solid State Chem., 1973, 6, 553.
18. B. V. Mill’, Sov. Phys. Crystallogr., 1975, 19, 653.
19. M. Asano and J. A. Koningstein, Chem. Phys., 1979, 42, 369.
20. D. Lévy and J. Barbier, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1999, 55, 1611.
21. M. O. Ramírez, L. E. Bausá, E. Cavalli and E. Bovero, J. Appl. Phys., 2006, 99, 013507.
22. H. G. Liu, W. C. Zheng and W. L. Feng, Philos. Mag., 2008, 88, 3075.
23. A. Kaminska, M. G. Brik, G. Boulon, M. Karbowiak and A. Suchocki, J. Phys.: Condens. Matter, 2010, 22, 255501.
24. M. D. Serrano, J. O. Álvarez, C. Zaldo, J. Sanz, I. Sobrados, J. A. Alonso, C. Cascales, M. T. Fernández-Díaz and A. Jezowski, J. Mater. Chem. C, 2017, 5, 11481.
25. Y. K. Voronko, A. V. Popov, A. A. Sobol and S. N. Ushakov, Inorg. Mater., 2006, 42, 1133.
26. V. E. Shukshin, Phys. Wave Phenom., 2009, 17, 165.
27. V. Lupei, A. Lupei, C. Gheorghe, L. Gheorghe, A. Achim and A. Ikesue, J. Appl. Phys., 2012, 112, 063110.
28. K. Shimamura, M. Timoshechkin, T. Sasaki, K. Hoshikawa and T. Fukuda, J. Cryst. Growth, 1993, 128, 1021.
29. P. Porcher, M. C. dos Santos and O. Malta, Phys. Chem. Chem. Phys., 1999, 1, 397.
30. D. S. Sumida and T. Y. Fan, Opt. Lett., 1994, 19, 1343.
31. E. V. Zharikov, C. Zaldo and F. Díaz, MRS Bull., 2009, 34, 271 (and refs. therein).
32. J. Liu, X. Mateos, H. Zhang, J. Wang, M. Jiang, U. Griebner and V. Petrov, Opt. Lett., 2005, 30, 3162.
33. D. C. Brown, Z. Fleischman, L. D. Merkle, L. D. Sanjeewa, C. D. McMillen and J. W. Kolis, Appl. Phys. B: Photophys. Laser Chem., 2020, 126, 62.
34. P. Haumesser, R. Gaumé, B. Viana, E. Antic-Fidancev and D. Vivien, J. Phys.: Condens. Matter, 2001, 13, 5427.
35. A. Lupei, G. Aka, E. Antic-Fidancev, B. Viana, D. Vivien and P. Aschehoug, J. Phys.: Condens. Matter, 2002, 14, 1107.
36. E. Montoya, J. A. Sanz-García, J. Capmany, L. E. Bausá, A. Diening, T. Kellner and G. Huber, J. Appl. Phys., 2000, 87, 4056.
37. J. Wang, J. J. Zakrzewski, M. Heczko, M. Zychowicz, K. Nakagawa, K. Nakabayashi, B. Sieklucka, S. Chorazy and S. Ohkoshi, J. Am. Chem. Soc., 2020, 142, 3970 (and ref. 78 and 79 therein).
38. Y. Guyot, M. Guzik, G. Alombert-Goget, J. Pejchal, A. Yoshikawa, A. Ito, T. Goto and G. Boulon, J. Lumin., 2016, 170, 513.
39. E. Antic-Fidancev, J. Holsa and M. Lastusaari, J. Phys.: Condens. Matter, 2003, 15, 863.
40. L. Hong-Gang, Z. Wen-Chen and F. Wen-Lin, J. Lumin., 2010, 130, 103.
41. L. Hong-Gang, G. Paweł and R. Czesław, J. Lumin., 2011, 131, 2690.

---

Footnote

† Electronic supplementary information (ESI) available: (i) Detailed comparative optical spectroscopy of dodecahedral and octahedral Yb³⁺ centers in CNGG crystals. (ii) Detailed procedures of crystal field analyses applied to octahedral Yb³⁺ centers in 0.3 at%Yb:CNGG crystals. (iii) Crystal field splitting of ²F_J Yb³⁺ levels and the barycenter law. See DOI: 10.1039/d0tc01608j

---