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Absorption and emission in the ultraviolet, visible, and infrared spectral range are usually mediated by the electric-field component of light. Only some electronic transitions have significant “magnetic-dipole” character, meaning that they couple to the magnetic field of light. Nanophotonic control over magnetic-dipole emission has recently been demonstrated, and magnetic-dipole transitions have been used to probe the magnetic-field profiles of photonic structures. However, the library of available magnetic-dipole emitters is currently limited to red or infrared emitters and mostly doped solids. Here, we show that NaYF4 nanocrystals doped with Eu3+ have various electric- and magnetic-dipole emission lines throughout the visible spectral range from multiple excited states. At the same time, the colloidal nature of the nanocrystals allows easy handling. We demonstrate the use of these nanocrystals as probes for the radiative electric and magnetic local density of optical states in a planar mirror geometry. A single emission spectrum can reveal enhancement or suppression of the density of optical states at multiple frequencies simultaneously. Such nanocrystals may find application in the characterization of nanophotonic structures or as model emitters for studies into magnetic light–matter interaction at optical frequencies.
A major topic in traditional photonics research has been the control and enhancement of spontaneous emission from electric-dipole (ED) emitters, that is, those with electronic transitions coupling to the electric-field component of light. Other types of electronic transitions, such as higher-multipole transitions that couple to electric-field gradients of light, have recently gained interest.1,2 Moreover, it has been realized that some technologically relevant emitters, such as infrared-emitting Er3+ in telecommunication3,4 and red-emitting Eu3+ in lamp phosphors,5,6 have electronic transitions with significant magnetic-dipole (MD) character, meaning that they are mediated by the magnetic component of light. In the past few years, several theoretical studies have been performed on emission control of MD emitters in various photonic environments.7,8 For example, possible geometries for plasmonic or dielectric antennas have been explored with magnetic hotspots where emission and excitation of MD emitters can be enhanced.4,9−15 Clearly, control over the interaction of light with MD transitions in matter is of fundamental and technological interest. In addition, MD emitters can be used to map the optical magnetic fields of laser beams,16 plasmonic structures,17 antennas, and metamaterials, as an alternative to near-field microscopy tips.14,18,19 If an emitter exhibits ED and MD transitions from the same excited state, the ratio of ED to MD emission intensity is proportional to the ratio of radiative electric local density of states (LDOS) to magnetic LDOS.6,17 The characterization of optical antennas using simultaneous ED and MD emitters17 can thus complement lifetime-based experiments,20,21 which measure the total LDOS including quenching pathways that contribute negatively to the brightness of emitters.22
Typically, the coupling of electronic transitions to the magnetic component of light is much weaker than to the electric component. Magnetic interactions are important only for materials where electronic transitions are ED forbidden to first order, such as intraconfigurational transitions in transition metals (electronic configuration mdn) or lanthanides (4fn). Most experiments until now have studied the competition between the MD and the ED emission from the 5D0 state of Eu3+ at free-space wavelengths of approximately 600 nm.5,6,23−28 In addition, the partial MD contribution has been characterized for the emission lines of several other lanthanides3,4,29 and transition-metal ions,30,31 embedded in a solid host material and emitting in the near-infrared. The development of suitable MD emitters in the visible is desirable for further research in this new field, especially colloidal emitters that can easily be coupled to any photonic or plasmonic structures. Many candidate MD emitters have been identified from quantum-mechanical calculations on the lanthanide ions, which have multiple transitions with strong MD character and with emission wavelengths throughout the near-infrared, visible, and ultraviolet (UV) spectral range.32,33 However, most of these transitions involve highly excited states, which typically decay rapidly through nonradiative pathways such as multiphonon relaxation.34 To make MD emission lines from such states in a lanthanide ion experimentally accessible, the lanthanide must be doped into a host material with a low phonon energy, where multiphonon relaxation processes are relatively slow. NaYF4 is useful for this purpose,35,36 as shown in the context of upconversion luminescence that requires emission from highly excited states upon excitation at low energy.37−39
Here we study various ED and MD emission lines from Eu3+ doped in NaYF4 nanocrystals (NCs). This low-phonon host material allows the observation of ED as well as MD emission lines from three excited states of Eu3+, covering the visible spectral range from the blue (464 nm) to the deep red (690 nm). We place the emitters at a controlled separation from a flat silver mirror to systematically vary the electric and magnetic LDOS6,23 and examine how the decay pathways in NaYF4:Eu3+ NCs are affected. Depending on the electric and magnetic LDOS, excited Eu3+ ions relax primarily via ED or MD transitions. This competition between radiative decay pathways (ED versus MD) determines the relative emission intensities of transitions from the same excited state, while competition from nonradiative loss pathways affects the emission intensities from different excited states.40 To highlight the potential application of nanocrystalline MD emitters as probes for the radiative electric and magnetic LDOS, the spectral characteristics of NaYF4:Eu3+ NCs in a photonic environment (here, on a mirror) are compared to NCs dispersed in a solvent or to bulk NaYF4:Eu3+.
Synthesis procedures for NaYF4 NCs are well developed, mostly because they are a popular host material for upconversion.35,39,41,42 Because Y3+ ions are chemically similar to lanthanide ions, NaYF4 NCs can be doped with different types and combinations of lanthanide ions by simply using a mixture of Y3+ precursors and dopant precursors during their synthesis.43 Our synthesis method for NaYF4 NCs doped with 5% Eu3+ is based on existing procedures41,44 and described in the Supporting Information (see also Figure S1). Transmission electron microscopy (Figure Figure11a) shows that the NCs are approximately 15 nm in diameter. A nominal 5% doping concentration then corresponds to 1300 Eu3+ ions per NC that each act as an individual color center (Figure Figure11b). The localized electronic states of lanthanide dopant ions are not influenced by the size or shape of the (nano)crystal host, which is in contrast to the delocalized conduction- and valence-band states of semiconductor nanocrystals. Organic ligands on the NC surface provide colloidal stability so that the NCs make clear dispersions in many common organic solvents, such as hexane, toluene, or chloroform. In principle, this allows the NCs to be placed on or near a (nano)photonic structure by spin-coating, lithographic positioning,45,46 or electro-hydrodynamic printing.47 Independent of how the NCs were processed, the crystalline host material ensures that the electronic structure of the Eu3+ dopants is protected and constant.
Figure Figure11c shows the energy-level diagram of Eu3+ and the excited-state decay pathways relevant to our experiments. The strongest excitation line is at 395 nm (Supporting Information, Figure S2), corresponding to the transition from the 7F0 ground state to the 5L6 excited state (blue arrow in Figure Figure11c). Following excitation, a Eu3+ ion can decay down the ladder of energy levels by nonradiative relaxation pathways. The rate of nonradiative multiphonon relaxation depends exponentially on the phonon energy of the host material.34 NaYF4 has a relatively low phonon energy (300–400 cm–1)36 and hence relatively low losses from multiphonon relaxation.37 As a result, radiative decay can compete with nonradiative channels in NaYF4:Eu3+ not only from the lowest 5D0 (red arrows in Figure Figure11c) excited state but also from the higher 5D1 (yellow arrows) and 5D2 (green arrows) excited states48 that are quenched in other host materials.5,6 Nevertheless, nonradiative decay pathways make the photoluminescence decay rate of the higher excited state 5D1 considerably faster (yellow data points in Figure Figure11d) than that of the lowest excited state 5D0 (red data points). From any of the excited states, the ion can decay radiatively to one of the seven spin–orbit split states of the 7FJ ground state (splitting of 500–1000 cm–1 between states), some of which are further split into crystal-field components (splitting up to 100 cm–1). The many possible emission pathways, from three excited states to a multitude of ground states, results in a complex emission spectrum with many different lines (Figure Figure11d,e). Some of these transitions have a predominant MD character,33,49 as indicated in Figure Figure11c,e,f.
We fabricated a series of samples with the NCs at a controlled distance of up to 240 nm from a flat Ag mirror (Figure Figure22a; see also Supporting Information, Figure S3) to systematically vary the electric and magnetic LDOS experienced by the Eu3+ ions. Optically thick flat Ag mirrors were thermally evaporated and template-stripped.50 Such films typically exhibit root-mean-square roughness values of less than 1 nm.50 Al2O3 spacer layers of different thicknesses were deposited on the Ag by reactive sputtering of Al in an O2/Ar plasma. The NCs were then spin-coated from a dispersion in hexane, resulting in a submonolayer coverage (Figure Figure22b). See Supporting Information for fabrication details. This geometry ensures that the Eu3+ ions in a sample are located at the same distance to the Ag mirror to within 15 nm (the average diameter of the NCs; Figures Figures11a and and2a)2a) so that each emitter experiences the same LDOS.
Analytical expressions can be derived for the rate of radiative decay of MD and ED emitters in a planar geometry.6,51 We consider a three-layer geometry (Figure Figure22a) with a semi-infinite layer of air on top (dielectric constant ϵ0 = 1), a layer of Al2O3 (ϵ1 = 2.82) with thickness d in the center and a semi-infinite layer of Ag on the bottom (with frequency-dependent ϵ2; ref. (53)). The Eu3+ ions are modeled as isotropic point dipoles52 at h = 7.5 nm (half of an NC diameter) above the Al2O3 layer, while the effect of the refractive-index contrast between NC and air is taken into account using a local-field factor χ.54 We explicitly distinguish the radiative decay rate γdet into photon modes that can be collected by the objective of our microscope with numerical aperture NA = 0.9, and the total radiative decay rate γtot including energy transfer to the metal, plasmon emission, and emission of photons under large angles from the surface normal. See the Supporting Information for details of the calculations. There, we also show the theoretical difference between the parameters γdet and γtot for the various geometries considered in this work (Figure S4).
For a particular excited state in Eu3+, the total rate of decay is given by the sum over the total radiative decay rates for each of the transitions (colored arrows in Figure Figure11c) plus intrinsic nonradiative pathways (black arrows). For example, for the 5D1 excited state the total decay rate is
where the subscripts 1 → J denote the radiative transitions from excited state 5D1 to ground state 7FJ, and γnonrad is the nonradiative decay rate. The branching ratios of the Eu3+ emission lines as measured in an emission spectrum depend only on the part of the radiative decay that enters the microscope objective. For example, the branching ratio of the 5D1 → 7F0 emission line is
where IJ→J′ denotes the collected emission intensity of the transition 5DJ → 7FJ′. The photoluminescence lifetime of an emitter is the inverse of the total decay rate (eq 1), τ = 1/Γ. Hence, lifetime-based characterization of plasmonic nanostructures or antennas using a probe emitter20,21,55 is sensitive to the total decay rate, including intrinsic nonradiative decay γnonrad and possible metal-induced quenching contained in γtot. Characterization based on the relative intensities of ED and MD emission lines from the same excited state of a probe emitter can provide useful complementary information. It probes plasmonic enhancement of the detectable part of the radiative decay and therefore, by reciprocity, about enhancement of absorption.
Figure Figure22c,d shows the theoretical radiative LDOS of our planar Ag mirror structure, that is, the enhancement of the (detectable) radiative decay rate γdet, for an ED emitter (panel c) or a MD emitter (panel d). The radiative LDOS depends on the separation between emitter and mirror with a first maximum at a spacer thickness of 40–80 nm (depending on emission wavelength) for an ED emitter and at 120–180 nm for a MD emitter. These regions of high electric LDOS (Figure Figure22c) and high magnetic LDOS (Figure Figure22d) are also directly evident in the series of experimental emission spectra of Figure Figure22e from the intensities of ED and MD emission lines. Strong ED emission is observed at a spacer thickness of 40–80 nm (highlighted in blue), while strong MD emission is observed for spacers of 120–180 nm. In this way, interesting locations of high radiative electric or magnetic LDOS for wavelengths throughout the visible spectral range are readily identified using Eu3+-doped NaYF4 NCs.
For a more quantitative analysis of the competition between ED and MD emission, we focus on the branching ratios of the various emission lines originating from the same excited state. As discussed above (eq 2), the branching ratios are determined by the rate γdet of radiative decay into photon modes collected by the spectrometer. It is important to realize that they do not depend on anything else. Any intrinsic nonradiative decay pathways or quenching induced by a plasmonic structure would deplete the excited state. However, because this reduces the recorded intensity of all excited states by the same factor, the branching ratios would be unaffected. We can therefore analyze the branching ratios of the different excited states using eq 2 (Figure Figure33) despite significant nonradiative decay of the higher excited states 5D1 and 5D2 (see Figure Figure11d). Furthermore, note that as different emission lines come from the same excited state, the branching ratios provide information about the LDOS ratio at different frequencies and not the absolute LDOS. In other words, if both electric and magnetic LDOS in the visible are enhanced by the same factor the branching ratios in the Eu3+ emission spectrum remain the same.
The data points in Figure Figure33 are the experimental branching ratios (from the emission spectra in Figure Figure22e) for emission lines from the 5D2 high-energy excited state (Figure Figure33a), the 5D1 high-energy excited state (Figure Figure33b), and the 5D0 lowest excited state (Figure Figure33c). The different transitions are labeled with the J value of the ground state 7FJ. For each excited state, the experimental data are fitted to eq 2 with as fit parameters the radiative decay rates γEDbulk and γMDbulk of the different transitions in homogeneous bulk NaYF4 (see Supporting Information). If we allow for transitions with mixed ED and MD character in the fits,29−31,49 we obtain ratios of ED/MD character (or vice versa) of 90% or greater. To reduce the number of fit parameters, we therefore approximate that each transition has pure ED or pure MD character. The match between data and fit is good for the 5D1 (Figure Figure33b) and the 5D0 emission lines (Figure Figure33c). The model performs less well for the 5D2 state (Figure Figure33a) where integration of the emission lines is complicated by relatively strong background emission, presumably from the Al2O3 spacer itself.
The transitions with MD character are labeled with an asterisk in Figure Figure33. They clearly stand out as those with a maximum in branching ratio around 150 nm spacer thickness. Table 1 summarizes the estimated values of γbulk for each of the transitions, obtained from the fits to the branching ratios (Figure Figure33) and the theoretical MD transition rates.33 The values add up to a total radiative decay rate of the lowest 5D0 excited state in bulk NaYF4 of Γ0 = γ0→1bulk + γ0→2bulk + γ0→4bulk = 161 s–1. This would translate into a radiative lifetime of 5.7 ms for NCs dispersed in an organic solvent (e.g., tetradecane, see below and Supporting Information), matching well with the experimental decay time of 6.3 ms for the 5D0 luminescence (Figure Figure11d). However, we should be careful not to make a quantitative comparison, because the experimental “apparent” lifetime for the 5D0 state is affected by the slow relaxation from higher excited states and potentially by nonradiative quenching.
The last data points in each of the panels of Figure Figure33 are the measured branching ratios for NCs dispersed in a homogeneous photonic environment, tetradecane. (This nonvolatile solvent was chosen because a droplet containing the NCs could be placed on the inverted microscope without evaporating during the measurement.) The horizontal lines in Figure Figure33 are the theoretical values based on the fit results. The branching ratios on top of a mirror oscillate between values that are higher and lower than those in tetradecane, both in experiment and in theory. This shows that characterizing a batch of Eu3+-doped NCs in a homogeneous environment provides a useful reference measurement. Subsequently, it is immediately clear from the emission spectrum of the NCs on a photonic structure (here, a mirror) whether the ratio of radiative electric over magnetic LDOS (via eq 2) is enhanced or reduced by the structure.
Finally, in Figure Figure44 we compare the emission intensities from the different emissive excited states of Eu3+. Figure Figure44a shows the fraction of the total emission that comes from the 5D1 state (yellow) and from the 5D2 state (green), as a function of separation from the Ag mirror. For both excited states, the intensity has a minimum at a spacer thickness of 100 nm, and a maximum at a spacer of 160 nm. While the relative intensities of the emission lines from the same excited states can be modeled relatively easily considering competition between radiative decay pathways (Figure Figure33; eq 2), understanding the relative emission intensities from different excited states is more complex because many more decay processes can play a role. However, with some simple assumptions we can extract an estimate for the relative intensities of different excited states in terms of rate constants for the individual transitions. First, most of the emission (~90%; see Figure Figure11e) originates from the lowest excited state 5D0, so the total measured emission intensity can be approximated as Itot ≈ ∑J′I0→J′, where ∑J′ denotes summation over ground states 7FJ′. Second, we neglect that the population of the 5D0 state is slightly affected by the relaxation pathway of the highly excited states 5D1,2, which, if nonradiative, can feed into the 5D0 state. Finally, we assume that nonradiative relaxation from the 5D0 state is negligible, because the gap to the closest ground state 7F6 is many phonon energies.54 The 5D0 intensity is then simply proportional to the collection efficiency: ∑J′I0→J′ ∑J′ γ0→J′det/∑J′ γ0→J′tot. The intensity from the higher excited states is determined by competition between “detectable” radiative decay and all other decay pathways: ∑J′IJ→J′ ∑J′ γJ→J′det/ΓJ. The relative intensity from a high-energy excited state (5D2 or 5D1) compared to the total emission intensity can then be written as
where J labels the excited state 5D1 or 5D2.
Figure Figure44b shows how the different factors of eq 3 depend on the spacer thickness in our experimental mirror geometry. The factor ∑J′ γ0→J′tot/∑J′ γ0→J′det is the inverse collection efficiency for emission from the lowest-energy excited state 5D0, which is plotted in red. The total radiative decay rate into collectable photon modes ∑J′ γJ→J′det is plotted in yellow for the 5D1 state and in green for the 5D2 state. We see that the dependence of these three factors on the spacer thickness is relatively weak (±50%) and the maxima do not match the maximum of the high-energy excited-state intensity in the experiment (Figure Figure44a). These three factors alone can therefore not explain the experimental observations.
We argue that the dependence of excited-state intensity on spacer thickness arises mostly from variations in the total decay rate ΓJ of the excited states. The spacer thickness affects this rate indirectly, not via changes in emission rates but in excitation rates. The situation is schematically depicted in Figure Figure44c. At low excitation rates (left), an important mechanism of nonradiative decay from high-energy excited states of the Eu3+ ion to lower-energy states is cross-relaxation,48 that is, the transfer of part of the excited-state energy to a neighboring ion in the ground state. At higher excitation rates (right), the ground-state population decreases, so that cross-relaxation should become less likely.56 This results in less nonradiative relaxation and more emission from high-energy states (see Supporting Information, Figure S5). Indeed, our experimental conditions correspond to an estimated excitation rate of approximately 0.1 ms–1 (see Supporting Information), sufficiently high to lead to depletion of the Eu3+ ground-state population. The blue line in Figure Figure44b is the excitation rate of the Eu3+ ions, which by reciprocity is equal to γdet for the excitation transition 7F0 → 5L6 (an ED transition at 395 nm). This factor has a strong dependence on spacer thickness with a minimum at 100 nm and a maximum at 160 nm coinciding with the experimental extremes in high-energy excited-state intensity (Figure Figure44a). This indicates that the photonic effect on ΓJ via the excitation rate strongly affects the relative intensities from different excited states.
Figure Figure44d,e summarizes how strongly the excited-state decay pathways of Eu3+ in NaYF4 NCs are affected simply by the presence of a mirror, by considering emitter–mirror separations of 100 nm (Figure Figure44d) and 160 nm (Figure Figure44e). At 100 nm separation, 24% of the emission comes through MD transitions (red) and 76% through ED transitions (blue), whereas at 160 nm separation these numbers are 65% and 35%, respectively. These differences come mainly from competition between different radiative pathways from the same excited state (Figure Figure33; eq 2) and provide information about the radiative electric and magnetic LDOS. In addition, the different spacer thicknesses show different relative amounts of high-energy excited-state emission (dark shading): 6% at 100 nm spacer versus 13% at 160 nm spacer. As discussed above, multiple radiative and nonradiative processes determine the relative emission intensities from different excited states (Figure Figure44b), where under our experimental conditions the most prominent effect is due to the photonic enhancement of the excitation rate.
As we showed in Figures Figures22f and and3,3, the various ED and MD emission lines from Eu3+-doped NaYF4 NCs can be used to probe the radiative electric and magnetic LDOS near a photonic or plasmonic structure. Many more MD transitions in the visible and infrared spectral range from lanthanide-doped colloidal NC emitters are accessible experimentally33 if one uses (A) the right host material of low phonon energy to avoid multiphonon relaxation36 and (B) low doping concentration38,48 or high excitation power38,56 to avoid cross-relaxation. As a few examples, the 5D3 excited state of Tb3+,48 the 2H11/2 excited state of Er3+,35,36 the 4G1 excited state of Tm3+,38 and the 2F5/2 excited state of Yb3+ have emission lines with (partial) MD character.33 Some of these may be useful as probes for the electric and magnetic LDOS of plasmonic antennas and metamaterials. More generally, our work highlights how strongly even a relatively simple photonic environment affects the competition between ED and MD transition rates (Figure Figure44d,e). This is of importance for the photonic or plasmonic enhancement of lanthanide and transition metal luminescence, for example, for optical communication4 or upconversion.57,58
F.T.R. acknowledges support from The Netherlands Organisation for Scientific Research (NWO; Rubicon Grant 680-50-1509). This work used equipment and resources funded by the European Research Council under the European Union’s Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement Nr. 339905 (QuaDoPS Advanced Grant).
The authors declare no competing financial interest.