Communication: X-ray excited optical luminescence from TbCl₃ at the giant resonance of terbium Free

Tb³⁺ ions are used as activators for green phosphors in color TV tubes, in special lasers, and as a dopant in solid-state devices. Luminescence from Tb³⁺ activators shows dominant optical emissions in the green (⁵D₄–⁷F_J) and much weaker emission in the blue (⁵D₃–⁷F_J).^1–3 At low concentrations the rare earth (RE) ions act as luminescence activators for charge carriers to recombine.¹ At higher Tb³⁺ concentration the cross-relaxation between neighboring Tb³⁺ ions becomes very effective and optical emission preferentially originates from ⁵D₄ levels.^2,4 Due to a substantial overlap of the wave functions, the rare earth optical and electronic properties are strongly driven by the interplay of localized 4f electrons and itinerant (more delocalized) 6s, 5d electrons (heavy fermions).⁵ At binding energies as low as 2–8 eV, large Coulomb correlation energies prevent the formation of 4f bands⁶ and the partially filled 4f orbitals are mostly atomic like.⁷ The conversion of absorbed X-rays to optical photons is a complex interplay of primary and secondary processes. The former depends on effective coupling of excitation channel and luminescence chromophore; the latter on X-ray penetration depth, sample thickness, and secondary excitations (thermalization). In the soft X-ray regime the attenuation length of the incident photons and electrons emitted are usually short and secondary processes are confined in the vicinity of the absorbing atom so that the event can be site specific. In TbCl₃, the attenuation length at the Tb N_4,5-edge is ∼20 nm.^7,8 This is a total absorption situation for a powder specimen (typical powder crystallite size is ∼μm). The enhancement of the N_4,5-edge cross section (giant resonance) is due to the coherent resonant 4d–4f and 4f excitation into continuum creating an intermediate 4d-hole state which decays into the same final state by super Coster-Kronig (sCK) transition.⁹ A typical Tb N_4,5-edge displays a set of very sharp pre-edge multiplets (∼0.3 eV) from low lying 4f states, and a very broad and asymmetric peak (∼9 eV) from the coupling of the degenerate states.

The giant resonance has been investigated by several experimental techniques, such as resonant and non-resonant X-ray photoemission spectroscopy (XPS),⁷ X-ray magnetic circular dichroism (XMCD),⁷ resonant X-ray inelastic scattering (RIXS)/X-ray emission (XES),^10,11 as well as optical spectroscopy.^12–16 The correlation of absorption and luminescence in rare earth (Tb,Eu) doped Gd and La phosphors at the N_4,5-edge was first reported by Klaasen et al.¹² The observed decrease in luminescence across the edge was attributed to the number of e-h pairs created.¹² However, neither the penetration depth nor the sCK decay channel was taken into account.

X-ray excited optical luminescence (XEOL) and Time-resolved XEOL (TRXEOL) were performed at the Grasshopper beamline of the Canadian Synchrotron Radiation Facility (CSRF) and the VLS-PGM beamline of the Canadian Light Source (CLS). Optical photons were collected with a lens system then focused on the entrance slit of an optical monochromator (JY 100) using a detector (Hamamatsu R943-02 photomultiplier tube, ∼3 ns anode pulse rise time) with a response that is mostly flat over the entire working range (160–930 nm). TbCl₃ powder deposited on a carbon tape in dry nitrogen was studied at room temperature. TRXEOL was carried out in a pump-probe-like experiment, using a single bunch (∼300 ps pulse, 300 ns repetition rate at SRC).

Figure 1(a) shows the XEOL from TbCl₃ excited at 141.5 eV, just below the Tb N_4,5 pre-edge multiplet. The prominent peaks at 488 nm–696 nm arise from ⁵D₄–⁷F_J (J = 0–6) transitions (green). The weak peaks at 382 nm–464 nm are the radiative footprints of ⁵D₃–⁷F_J (J = 6, 5, 4, 3) transitions (blue). The ⁵D₃–⁷F₃ transition merges with the ⁵D₄–⁷F₆ peak (488 nm) and appears as a shoulder. Features beyond 760 nm are 2nd order from ⁵D₃–⁷F_J transitions. The results are in good agreement with the literature.^12–18 

The decay curve of the ⁵D₃–⁷F₆ (blue) and ⁵D₄–⁷F₅ (green) transitions (hν = 143.9 eV) are shown in Fig. 1(b). Compared to compounds with similar Tb concentration,¹⁹ the blue emission decays considerably faster and is clearly not single-exponential, indicating that the recombination is governed by non-radiative cross-relaxation. In general, the energy transfer between Tb³⁺ ions depends critically on the ion concentration and becomes important for concentrations higher than 0.1 mol%. Below 0.1 mol% the decay can be described by a single exponential and lifetimes for both, ⁵D₃ and ⁵D₄ transitions, are on the order of milliseconds.^19–22 Optical via non-radiative cross relaxation is described by the Inokuti-Hirayama (IH) equation¹⁹ 

where τ₀ is the intrinsic lifetime of the activated Tb³⁺ ion in absence of Tb-Tb interactions, α = c/c₀Γ(1–3/s), and c is the nominal Tb concentration. At the critical transfer concentration c₀ the energy transfer rate is equal to the radiative recombination rate. The critical distance between two Tb ions (R₀) is given by c₀ = 3/(4πR₀³). The Euler function Γ is 1.77 in the case of dipole-dipole interaction (s = 6), 1.43 for dipole-quadrupole (s = 8), and 1.3 for quadrupole-quadrupole (s = 10). For very short times (t ≪ τ₀) cross-relaxation dominates, whereas at longer times (t ≈ τ₀) the decay is driven by the intrinsic lifetime τ₀, showing single exponential behavior.

Within the time window of 300 ns we are clearly in a t ≪ τ₀ situation (t/τ₀∼0.03%, τ₀ ∼ 1 ms). With a ∼80% drop off within 300 ns the 382 nm transition decays much faster. The 544 nm transition appears as a flat line, suggesting that the decay is too slow to show significant changes over the 300 ns time window which is in fact the case if the decay is mainly driven by the intrinsic lifetime τ₀ of the ⁵D₄ state. Note that the ⁵D₃ decay rate is determined by the ⁵D₃–⁵D₄ cross-relaxation which depopulates the ⁵D₃ state.²³ 

The characteristic time of the cross-relaxation can be estimated using an average value, we consider the 1/e-lifetime or the mean duration τ_m of luminescence²⁴ defined by

where I(t) is the luminescence yield.²⁰ Except for a purely exponential decay the 1/e-lifetime and the mean duration are in general different.²⁰ By taking the steepest and shallowest slope of the decay we obtained a decay time in the range of 150–360 ns, respectively, with an expected value of 215 ns that characterizes the cross-relaxation. Using the IH equation we find a characteristic time of 266 ns and an S value of 4.4. The exponent S was obtained by plotting the data on a t^α scale for different values of α until we obtain a straight line. To estimate the characteristic time we used a simplified IH equation, assuming that the radiative decay probability within the observed time window (300 ns) is nearly a constant. The rate constant for the cross relaxation is

where the k₀ is the rate constant for a given Tb ion in the absence of other Tb ions and r is the distance between them. R₀ is the critical distance and S is the exponent of the IH equation.² This means that the decay with S = 4.4 is slightly non-exponential, but not as much as one would expect for dipole-dipole cross-relaxation (s = 6).

Figure 2(a) shows the XANES of the Tb-N_4,5 edge from total electron yield (TEY) and partial photoluminescence yield (PLY) at 544 nm in which several sharp lines mark the low energy states of the Tb 4d⁹4f⁹ multiplet, spreading over some 10 eV by strong 4d–4f Coulomb correlation. At the giant resonance the line widths are much broader, reflecting the much shorter 4d-hole lifetime (∼10⁻¹⁷ s) compared to the pre-edge (∼10⁻¹⁵ s), which corresponds to an intrinsic width of 2Γ ≈ 0.4 eV.⁷ In the limit of vanishing 4d spin–orbit coupling, the Tb absorption spectrum would simply contain ⁷D, ⁷F, and ⁷G states, which are reached via dipole transition from the 4f⁸ (⁷F₆) ground state, following LS-coupling selection rules.⁷ The spectrum has mostly LS character and is only partially weakened²⁵ by 4d spin–orbit coupling, giving rise to ⁵H or ⁷H pre-edge states which in intermediate coupling can be reached by higher order transitions.^2,11

The 544 nm partial PLY shows signal inversion at resonance which is not uncommon in soft X-ray XEOL from optically thick specimens. The optical yield reaches a maximum prior to the first peaks of the Tb 4d⁹4f⁹ multiplet, and then abruptly decreases at the first peak (∼141.6 eV), showing a series of sharp multiplets which finds their correspondence in the TEY spectrum, and reaches a minimum at 152 eV. It is apparent that the optical yield gives a much enhanced footprint of the otherwise rather weak Tb 4d⁹4f⁹ multiplet in TEY.

Due to the large and abrupt increase of the cross-section, the attenuation length at the N_4,5 edge for incident X-rays, and thus the probing depth, decreases abruptly (∼5 nm).²⁵ Below the edge, X-ray penetrates at least an order of magnitude deeper into the sample. In the present experiment the samples were optically thick. Therefore, the luminescence yield across the edge per photon absorbed is reduced.²⁶ 

We can explain the inversion by considering the following: (1) Just below the edge, no 4d holes are created, and the absorbed X-ray energy is transferred to 5s, 5p, 4f photoelectrons (Tb) and Cl valence electrons. In the case of 4f photoelectrons, the kinetic energy is ∼140 eV. Inside the sample, these electrons thermalize via inelastic scattering, creating secondary electrons and holes. (2) At the absorption edge, 4d–4f resonant excitation dominates, and electrons from subsequent sCK emission, and direct 4d photoemission are in the same (degenerate) final state with nearly the same kinetic energy. The difference is sampling depth, and that energetic electrons near the surface are more likely to escape the sample without contributing to the secondary processes (thermalization path is truncated). Therefore, if the secondary process is the important contribution to luminescence, as it often is, the PLY will drop across the edge. As seen in Fig. 2(a), the partial luminescence yield (PLY) follows the characteristics of absorption albeit inverted. In particular, the pre-edge peaks, which are very weak in TEY, appear in the optical yield much amplified.

Figure 2(b) shows the relative intensity of the optical bands with excitation energy. As one can see, there is a relative intensity increase in the ⁵D₃ transitions over ⁵D₄ from the pre-edge region (147.1 eV) to the giant resonance (151.5 eV). The ⁵D₃ enhancement is either related to an increase of the ⁵D₃ state population or a decrease in the ⁵D₃–⁵D₄ cross-relaxation probability due to the switch on of the new channel.

The intensity ratio of ⁵D₃–⁷F₆ (382 nm) to ⁵D₄–⁷F₅ transition (544 nm) over a broader range of excitation energies (382 nm and 544 nm PLY in the inset) shows that the ⁵D₃–⁷F₆ transition yield gains over that of the ⁵D₄–⁷F₅ with increasing excitation energy (Fig. 3). The shape of the ratio resembles that of the TEY, but has a pronounced minimum in the pre-peak region, and a steeper decrease on the high-energy side of the peak (the ratio should be a flat line across the energy range if both yields were proportional linearly to absorption). When the ⁵D₃ population increases, the ⁵D₄ population should increase in a similar way, and the ratio should not be affected if the cross-relaxation is independent of the ⁵D₃ population. However, the ratio will change if the cross-relaxation rate changes, i.e., with decreasing cross-relaxation time the ratio will increase and vice-versa. Since total luminescence is suppressed at resonance, the ⁵D₃–⁷F₆ over ⁵D₄–⁷F₅ enhancement can come from a decrease in cross-relaxation time as well as an increase in ⁵D₃ population. Apparently, resonance affects the relative magnitude of the ⁵D₃–⁵D₄ transitions in a similar way like sparse Tb doping where the intensity of ⁵D₃–⁷F_J transitions increases by default of little cross-relaxation. As the excitation rate is at least a couple of orders of magnitude higher than the (observed) characteristic cross-relaxation time, quenching of the cross-relaxation is probably just a natural consequence of the ⁷F_J level depopulation by sCK excitation, and thus a lack of available ⁷F₆–⁷F₀ up-conversions to compensate the ⁵D₃–⁵D₄ relaxation. Note that the ratio decreases when the resonant 4d–4f excitation starts to populate directly into the ⁷F₆ level (cf. Fig. 2(b)).

In conclusion, we have reported the optical properties of Tb by monitoring the optical emission as the Tb sites in TbCl₃ were excited with the photon energy ramped across the 4d–4f giant resonance. In comparison to similar experiments in the literature, we have provided more detailed insight into the correlation of luminescence and absorption. We have shown that the total luminescence yield exhibits a dramatic drop at the edge, which is a consequence of the interplay of the different excitation and recombination channels, change in sampling depth and hole distribution. We have estimated the time scale of the non-radiative ⁵D₃–⁵D₄ cross-relaxation for TbCl₃ which turns out to be very fast (150–360 ns) compared to the normally expected intrinsic Tb^{3+ 5}D₃-lifetime of ∼1 ms. The results show the importance of element and excitation channel selective time-resolved optical studies for improved understanding of correlated phenomena in light emitting materials.²⁷ 

Research at the CSRF is supported by NSERC and NRC (Canada). SRC was supported the National Science Foundation under Award No. DMR-0537588. The Canadian Light Source is supported by NSERC, NRC, CIHR, and the University of Saskatchewan. Research at UWO is supported by NSERC, CFI, OIT, and CRC.