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Controlling Magnetic Dipole Resonance in Raspberry-like Metamolecules Chen Li, Sunghee Lee, Zhaoxia Qian, Connor Woods, So-Jung Park, and Zahra Fakhraai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00439 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 2, 2018

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The Journal of Physical Chemistry

Controlling Magnetic Dipole Resonance in Raspberry-like Metamolecules Chen Li1, Sunghee Lee2, Zhaoxia Qian3, Connor Woods1, So-Jung Park2*, and Zahra Fakhraai1* 1. Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, PA 19104, USA 2. Department of Chemistry and Nanoscience, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul, 120750, Korea 3. Department of Chemistry, University of Washington, 4000 15th Ave NE, 36 Bagley Hall, Seattle, WA 98195, USA ABSTRACT: Raspberry-like metamolecules (RMMs), clusters of closely-packed noble metal nanobeads self-assembled on a dielectric core, exhibit emergent optical properties not available in simple nanoparticles. Examples include broadband far-field extinction and artificial optical magnetism. An important feature of these clusters is that their magnetic plasmon resonance and the breadth of their extinction spectra can be tuned via simple synthetic routes, such as by changing the bead size, core size, or the average interbead distance. However, the effect of each of these variables on the final magnetic resonance frequency and strength has not been studied in-depth. Understanding how to tune the electric and magnetic resonance modes in these clusters can help improve the design of novel metamaterials for various applications. In this article, we combine theoretical analyses using numerical finite-different timedomain (FDTD) modeling and analytical dipole-dipole coupling theory to study the role of these variables in the global electric and global magnetic dipole modes of RMMs. We also demonstrate that these variables can be readily controlled experimentally by using surfactants with varying lengths or changing synthetic conditions, and show that the experimental results are consistent with theoretical predictions. The results provide a guideline for synthesizing plasmonic nanoparticle assemblies when specific resonant frequencies and bandwidths are desired.

1. Introduction

semblies. Despite their relatively large structural disorder compared to precisely patterned metasurfaces, these nanoclusters benefit from a few advantages, such as easily tunable magnetic resonances through variations in synthetic parameters, robust magnetic response originating from an ensemble-average property over the relatively large clusters16, and the potential to support isotropic magnetism independent of the direction of the polarization of the incident light16. Since the magnetic properties of these metamolecules depend on the strong coupling between the building block at the resonance frequency, their artificial magnetism weaken rapidly away from the resonant frequency. As such, it is important to understand the properties of the global cluster-level resonant modes and their dependence on the structural features, such that the resonance frequency can be tuned as needed for the desired application.

With the rapid development in modern nanotechnology, a large variety of optical metamaterial structures have been designed in the past decade.1–10 With subwavelength components featuring special shapes and geometric arrangements, these structures can be designed to manipulate light-matter interactions to produce emergent optical properties not found in nature. Among these properties, the quest for resonant magnetism at optical frequencies using non-magnetic subwavelength structures has raised increasing interest.6,11–19 Achieving far-field magnetic plasmon resonance at optical frequencies may allow the design of materials with negative index of refraction1,20–24 and Fano-resonances8,12,14,25,26,27, and are also often considered potential candidates for hyper lenses28,29 and invisibility cloaks30–35. Magnetic plasmon resonance at optical frequencies was first theoretically proposed in structures composed of circular nanoparticle arrangements, as an analogy to split-ring resonators11,22,36 and was experimentally realized in 201012. While most of the existing structures supporting optical magnetism have been precisely patterned 2D metasurfaces fabricated by top-down lithographic techniques3,31,32,34,35, nanoparticle assemblies produced using more facile and affordable solution processes have also been demonstrated to accommodate strong optical magnetism.11–16,37 Such nanoparticle systems, termed “raspberrylike metamolecules (RMM)16 or core-satellite structures,37 have been fabricated using diverse synthetic or self-assembly methods from electrostatic assembly11–14 to protein-directed15 as-

In single and small-cluster nanoparticles, the effect of the size and shape of the building blocks as well as their interparticle distance on the cluster’s electric dipole resonance has been extensively studied using various analytical and numerical simulation techniques19,41–48. Most of these studies have either been conducted on particles or clusters much smaller than the incident wavelength of light or on periodic arrays of subwavelength structures. For these conditions, the overall plasmon response is typically dominated by the single particle’s electric dipole resonance as well as the dipole-dipole coupling interactions, which can either be sufficiently described with analytical electromagnetic theories6,11,22,36, 49-51 or clearly visulized through direct near-field examination using quasi-static calculations.12 1

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sis, an aqueous solution containing polystyrene (PS) cores decorated with small silver seed particles was mixed with a growth solution containing aromatic surfactants (benzyldimethyldodecyl ammonium chloride (BDDAC), Benzyldimethyltetradecyl ammonium chloride (BDTAC), Benzyldimethylhexadecyl ammonium chloride (BDAC), and Benzyldimethylsteary ammonium chloride monohydrate (BDSAC) denoted as R-12, R-14, R-16, and R-18 according to the number of carbon atoms in the chain, with chemical structures shown in Figure S1), HAuCl4, AgNO3, and ascorbic acid. Syntheses using all four surfactants generated similar RMM structures (Figure S2 and S3) composed of PS core and gold nanobeads separated by the surfactant (Figure 1). The same synthetic procedure was used for R-12, R-14, and R-16. The reaction conditions (i.e., temperature and the amount of reagents) were slightly modified for R-18 because of the stronger tendency of BDSAC to crystallize. More detailed synthetic procedures are provided in the SI. The synthesized nanoparticles were characterized by transmission electron microscopy (TEM) and scanning electron microscopy (SEM). Structural parameters of the synthesized RMMs obtained from the microscope images are presented in Table S2.

Nanoparticle assemblies with complicated local structures or sizes comparable to the incident wavelength of light can host higher order resonance modes, such as electric quadrupole and magnetic dipole resonances, and thus have more interesting, but rarely-observed plasmonic properties.6,15,16,52,53 However, the role of structural variations on the spectral shape and frequency of these higher order resonance modes have not been extensively studied.38,54,55 Furthermore, the disorder in particle size and packing in large clusters can also add significant challenges to systematic studies of their plasmonic resonance modes. As the sizes of the clusters are increased with increasingly complicated local structures and interparticle interactions, common analytical approaches become insufficient due to disorder-induced spectral damping and complex coupling between different resonance modes. In comparison, rigorous full wave numerical simulations are much more flexible. As computing resources become increasingly more accessible, numerical methods, or a combination of analytical and numerical methods become more practical in predicting optical properties of large clusters.16,52,56 Specifically, for artificial magnetism, theoretical analyses have been mostly performed by constructing dipole-dipole interaction functions,36,57,58 while the magnetic properties of clusters mimicking experimental structures have been commonly investigated using numerical simulations to calculate either the near electric field and polarization currents formed in single clusters12 or effective magnetic permeability functions retrieved from far-field scattering matrices for periodic structures1,50 or single clusters with crystalline packings58. Although these analytical methods combined with simple visualizations provide important physical insights in the formation of artificial magnetism, they do not work as well on large disordered nanoparticle assemblies as discussed above and thus need assistance from full wave numerical modeling and analyses. We have recently employed full wave numerical modeling to study the optical properties of RMMs and have demonstrated that this method works well in demonstrating the existence of strong magnetic resonances, which contributes to broadband extinction spectrum in RMMs 16

Figure 1. Schematic description for the synthesis and structure of RMM. 2.2 FDTD Modeling and Multimode Analysis Structures representing experimental RMMs were produced using a molecular dynamics simulation procedure described in our previous publications16,39 and the supporting info (SI). The structure were then imported into the Lumerical FDTD Solutions package (V8.16) to calculate the far-field scattering and the extinction cross-section spectra. Snapshots of RMM models, the meshing schemes and source properties can be seen in Figure S4. Both the total far-field scattering cross section and the electric near-field at each position around the modeled RMMs were recorded as a function of the incident wavelength. Figure 2 shows examples of such calculations on a typical RMM model (supplemental simulated spectra can be found in Figure S5). The details of the model are shown in Table S1 row 3. In Figure 2A, the calculated extinction spectrum from FDTD simulations is compared with the experimental measurements for a similarly sized RMM, as shown in Table S2, row 7, to verify the robustness of the model. As shown in this figure peak positions and the spectral shape generally agree with the experimental UV-Visible extinction measurements. Two spectral peaks can be observed in the calculated optical extinction (Figures 2A, black) and scattering (Figures 2C, dashed) of the modeled RMM, which can be attributed to the electric plasmon scattering (broad, centered around 600-800 nm) and the magnetic plasmon scattering (sharp centered around 910 nm), respectively. It is worth noting that the simulation typically generates

In this article, we use a combination of numerical finite-difference time-domain (FDTD) modeling and analytical dynamic theory of dipole-dipole interactions to explore the dependence of the global electric dipole (GED) and global magnetic dipole (GMD) modes on the structural parameters of modeled RMMs and compare the predictions with the optical extinction of RMM structures synthesized using a seed-mediated growth method. Experimentally, two critical structure parameters, the inter-particle distance and bead size were controlled by using surfactants of varying lengths and the relative amount of precursors, respectively, to investigate the effect of these variables on GMD. The combinations of these methods allow us to both understand the origins of experimental observations of artificial magnetic resonances and provide physical insights that can guide the synthesis of RMM with desired properties. 2. Methods 2.1 Synthesis and characterization RMMs were synthesized by the templated surfactant-assisted seed growth method following our previously published procedure, as schematically shown in Figure 1.16 In a typical synthe2


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The Journal of Physical Chemistry magnetic dipole induced by excitation from a linearly polarized incident field are orthogonal to each other. Thus, scattering power collected in a specific direction, as indicated by the square-shaped dots in the inset, is dominated by only one of the two modes. This technique has been experimentally used to separate the GED and GMD scattering signatures15,16. As can be seen from the schematic setup shown in Figure 2D, this experiment can also be numerically simulated by simply calculating the Poynting vector in two orthogonal directions in the field plane. For an incident wave polarized in the y direction and propagating in the x direction, modal scattering can be identified by calculating the scattered Poynting vectors in the z (Sz for GED) and y (Sy for GMD) directions. Figure 2D shows the calculated Poynting vectors Sz and Sy dominated by GED and GMD scattering, respectively. Though not a rigorous multimode analysis when compared to the one shown in Figure 2C, the directional scattering simulation provides reasonable reliability in separating resonant dipole scattering modes but requires much fewer computing resources, as only scattered power at one location needs to be calculated. In this work, general trends of the structural dependence of the GED and GMD resonance properties were studied using the directional scattering technique, unless otherwise stated.

spectral features much sharper than in experiments because of the structural inhomogeneity within each synthesized RMM as well as in the ensemble of clusters, which are missing in the simulated spectra. The assignment of the resonance modes in Figures 2A (extinction) and 2C (scattering) were performed using multi-mode analysis. One method to calculate the electric and magnetic dipole, quadrupole, and higher order modes is direct calculation of the moments using the electromagnetic near-field distributions (such as the example map shown in Figure 2B) and their resulting polarization currents.14,16,44,52,56,59,60 In a large nanocluster such as an RMM, the existence of large number of nanometer-scale gaps between metallic interfaces generates strong electromagnetic near-field hotspots. In a numerical simulation, the accuracy of the value of the field in such hot-spots can strongly depend on the choices of the mesh size and the accuracy of the simulated curvatures, which makes direct calculations based on the near-field values impractical due to the increasing need for computing power for such large structures. As such, in this study we chose an alternative T-matrix based method described in our previous publications16,56. In this approach, the scattered far-field at a distance away from the cluster is decomposed through expansion into a basis of vector spherical wave functions (VSWFs). The resulting coefficients are used to calculate the far-field optical response.56,60,61 Compared with the more commonly used near-field expansion technique14,52, this method is more accurate because only scattered field away from the RMM’s internal hotspots is used for calculation, which lowers the requirement for fine mesh settings. The details of the mesh settings used for these calculations are described in SI. More details about the calculation of different modes can be found in Section V-I of SI and our previous publications.16,56

We note that in the calculated GED in Figure 2D (red), there is a slight spectral perturbation at ~900 where the GMD resonant scattering (blue) is positioned. This is likely due to the Fanolike modal interference between the GMD and GED modes, similar to what has previously been observed in spiky nanoshells between dipole and quadrupole resonance modes.56 We have previously demonstrated that such modal interference is due to the spectral overlap of the modes as well as the inherent disorder of the structure that results in random coupling between the modes through hotspots56. Full T-Matrix calculations, including non-diagonal terms, of the scattered power and direct experimental scattering measurements on single particles are required to verify this hypothesis.

Figure 2C demonstrates an example of the multimode calculations on the modeled RMM particle shown in Figure 2A using such T-matrix formalism. As mentioned above, specific structural parameters are listed in Table S1, row 3. The total scattered electric field, and thus the scattered power, can be decomposed into contributions from the GED and GMD modes, respectively. Figure 2C shows that the combined scattering cross-section from these two modes (dashed green line) accounts for most of the total scattering cross-section (dotted black line). As such, scattering from higher order modes, such as the quadrupole modes, are insignificant in this particular RMM structure, and can thus be neglected. This observation holds for all other RMMs studied in this manuscript. This is both due to the small overall size of the RMMs in this study compared to our previous work16, which reduces the effect of higher order modes, as well as the isotropic shape of these particles, which leads to negligible modal interference that could otherwise be potentially broadcasted by the dipole modes.56

2.4 Dipole-dipole Interaction and Dipole Moment Calculations All nanoparticle clusters in this study are composed of nanobead building blocks much smaller than the incident wavelength of light (maximum bead size of 60 nm). As such, the electric field of the uncoupled nanobeads can be adequately described by the bead electric dipole (BED) moment and the GED and GMD modes are results of the coupling between all the induced BED moments. The interactions between these bead dipoles can be described by the dyadic Green’s function under dipole approximation22,36, where optical scattering from each nanobead is treated as radiation from a point dipole. It is worth noting that by treating the optically excited beads as point dipoles with zero volume, inaccuracy in optical coupling is introduced. Specifically, under the dipole approximation, higher ordered terms are neglected in the multipole expansion, but do contribute to the near electric field around the nanobead surfaces, and thus, their mutual interactions.

2.3 Directional Scattering Calculations Since the far-field spectrum of the RMMs used in this study can be adequately described by their global dipole modes, an alternative approach can be used for their multimode analysis that is computationally much cheaper to perform. This approach utilizes the directional scattering property of a point electric dipole and a point magnetic dipole under the same excitation used for the FDTD simulations. As can be seen from the inset of Figure 2D, the maximum scattering directions from an electric and a

Thus, this method can only provide qualitative trends observed in GED and GMD resonances when structural parameters are varied, and does not quantitatively match the experimental data. However, these calculations are helpful in providing insight into the origins of such trends, as has been demonstrated by Kim, et al., where effective permittivity and permeability functions were calculated using similar methods from nanoparticle 3



clusters with a crystalline packing58. The details of these calculations are provided in Section V-II of the SI.

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ious carbon chain lengths, as shown in Figure S1, with corresponding SEM images shown in Figures S2 and S3. Statistics on the number of beads and the bead sizes in a typical RMM structure were obtained through analysis of the electron microscope images after the functionalization with thiolated polyethylene glycol (PEG), as described in more details in SI and our previous publication.16 The synthesized RMMs and their corresponding simulation models are denoted as R-12, R-14, R-16, and R-18 respectively, according to the total number of carbon atoms in the alkyl chain of the surfactant molecules (Figure S1). Table S2 in SI shows the average cluster size (Z), bead diameter (D), number of beads (N), and the core diameter for these RMMs. The measured structures shown in Figure 3A and Figure 5 are chosen such that Z is conserved unless otherwise noted. As seen in Table S2 for RMMs R-12, R-14, and R-16, at a specific overall size (rows 1,4,7, rows 2,5, 8, and rows 3,6,9, respectively), three surfactant molecules produce structures with similar number of beads and bead sizes. The UV-visible extinction spectra of these structures are shown in Figure 3A. It is observed in this figure that all three spectra for three RMMs share similar overall shapes and features, with two broad peaks positioned around ~680 nm and ~900 nm, respectively. As the length of the linker, thus the inter-bead distance, is decreased by four carbons (about 0.5 nm in terms of chain length) from BDAC (R-16) to BDDAC (R-12), a slight but noticeable red-shift is observed for the second peak. The same trend is consistently observed for a series of other assemblies with different overall sizes (Figure S6). Corresponding full-wave FDTD simulated far-field extinction spectra are shown in Figure 3B. In these calculations, the average interbead distances were adjusted by increasing the thickness of the polystyrene coating on each bead, to imitate the increasing carbon chain length, as described in the SI, and shown in Figure S7. The interparticle distance-dependence can be seen by comparing the carbon chain lengths in the surfactant molecules (Figure S1) and the modeled interparticle distances in Figure S7. Due to the random packing of the beads, the average inter-bead distance (d) is larger than the thickness of the dielectric coating. However, a similar degree of redshift is observed in the simulated spectra as the average inter-bead distance (d) is increased by the corresponding amount. Due to the sub-nanometer changes in the interparticle distances used in the model, convergence tests using various mesh sizes were performed to ensure that the simulations converged and that the observed trends of the spectral shift were not caused by numerical inaccuracy (Figure S10). A more detailed description of the mesh settings can be found in the SI. As discussed earlier, similar to the assignment of peaks in Figure 2A, the two resonances at ~680 nm and ~900 nm can be attributed to the GED and the GMD modes, respectively. Comparison between the shape of the spectra and resonance values for the two modes shows that the GMD resonance is much more sensitive to the inter-bead separations compared with the GED mode. This is due to the strong sensitivity of GMD resonance to the localized electric field in the interbead region, which modulates the strength of the rotating polarization currents that generate the GMD, as will be discussed in more details in the next section.

Figure 2. Far-field optical analysis and simulation results for RMMs: (A) Colloidal UV-Visible extinction spectrum (solid blue) and the corresponding FDTD-calculated far-field extinction spectrum (solid black). Relevant structural parameters of the modeled and measured RMMs are shown in Tables S1 row 3 and S2 row 7, respectively. The inset shows the structure of the modeled RMM. (B) FDTD-calculated near electric field intensity distribution around the GED (786 nm) and GMD (912 nm) resonances in a cross-sectional plane across the center of the modeled RMM structure for an incident field of Ei=1 V2/m2. (C) Scattering cross-section of the same RMM (black dotted line) along with the calculated global electric dipole (GED, red solid line), calculated global magnetic dipole (GMD, blue solid line) and the sum of the two cross-sections (dashed green line), using the T-matrix formalism as described in Section V-I of SI. (D) The results of directional scattering simulations showing the Poynting vector value in the directions representing the electric dipole scattering power (red, Sz) and magnetic dipole scattering power (blue, Sy), respectively. The inset shows a schematic plot of the setup for the calculation to separate the electric dipole scattering power (blue, calculated at the location shown by the blue square) and the magnetic dipole scattering power (red, calculated at the location shown by the red square) under a plane wave excitation propagating in the direction normal to the page. 3. Results and Discussions Optical response from an RMM structure at a specific overall cluster size (Z) depends on both the bead sizes and the interbead separations. To study these two factors in greater details, different sets of RMM particles were synthesized, each with the same overall cluster size, within experimental error, but with either variable bead sizes (D), or inter-bead separations (d). Simulated spectra were performed using experimentally relevant values. 3.1 The Effect of Inter-bead Distance

As can be seen in Figure 2C, due to the broad nature of the GED mode, the two modes significantly overlap around the GMD resonance wavelength. To better study the properties of the GMD, the directional scattering corresponding to GMD (Sy as detailed in Figure 2D) was calculated for each spectrum to be

The effect of inter-bead separation was experimentally studied using far-field UV-visible extinction measurements of a set of RMMs synthesized using surfactant linker molecules with var4


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Figure 3. (A) Extinction spectra of raspberry-MMs synthesized using different length surfactants with a fixed the overall size of Z=191 nm. The inset shows an SEM image of the R-16 clusters. (B) Simulated far-field extinction spectra of modeled RMMs by FDTD with average inter-bead separation set to mimic different linkers used in synthesis. For modeled RMMs, standard deviations of interparticle distance are on the order of ~0.05 nm. Detailed model parameters are shown in Table S1, rows 1-3 and Figure S7. The inset shows the structure of the R-16 model. (C) Calculated scattering power from the magnetic dipole mode by the modeled RMMs used in (B), represented by the scattered Poynting vector in the Sy direction. Inset schematically shows the power broadcasted by the induced GMD spectra also show a relative intensity change between the two main spectral features, which suggests that the magnetic dipole resonance becomes stronger compared to the electric dipole resonance, with increasing D. There is a notable exception to this observation. Figure 5D shows that the far-field spectra for RMMs denoted R-18, synthesized with surfactant BDSAC, the longest surfactant in the series, have a significantly different spectral shape compared to the other sets of measurements. GMD resonances are either barely visible or not visible for these RMMs, despite sharing a similar synthesis and bead packing scheme with the other sets with shorter alkyl chains. It appears that in these clusters, the GMD resonances is weak and blue-shifted, compared to the other cluster sets (Figures 5 A-C) such that it is almost masked by the broad GED mode. Since BDSAC (R-18) molecules are only slightly longer than the other molecules (by 0.2-0.6 nm compared to R-12 – R16), the inter-particle distance alone does not explain the spectral difference observed here. Indeed, structure analyses showed that BDSAC produces clusters with much smaller average beadsizes (24-29 nm in Figure 5D as opposed to 27-39 nm for the other three sets in Figure 5 A-C) at a similar overall RMM size (Table S2, Figure S3). The small size bead in R-18 is attributed to the stronger tendency of longer BDSAC to crystallize, which can potentially impede the growth of gold nanobeads. The smaller bead size together with the longer inter-particle distance explains the significant blue-shifting observed in R-18 compared to the other sets.

separated from the GED contribution, as shown in Figure 3C (The corresponding GED spectra are shown in Figure S11). These data demonstrate that the GMD indeed redshifts from 900 nm to 914 nm and then to 948 nm as d is decreased by only 0.4 nm during each step. Furthermore, as the inter-bead distance is decreased the intensity at the magnetic resonance also increases, as can be observed from Figure 3C. The difference between the black and the red curves in Figure 3C is larger than that observed between the red and the blue curve, indicating the GMD becomes progressively more sensitive to the inter-bead separation at smaller inter-bead values. To better illustrate the effect of inter-bead separation, full-wave FDTD calculations (Figure 4A) were performed in FDTD for a broader range of inter-bead distances, and the contributions of the GED (Figure 4B) and GMD (Figure 4C) moments were calculated using the directional scattering method. Figure 4 shows a series of directional scattering simulation data for a range of inter-bead distances varying from 3.8 nm to 19.6 nm. Detailed structural parameters used for the simulation are given in Table S1, rows 4-8. The resonance wavelengths, as well as the magnitude of the scattered power at the resonance frequency are plotted as a function of inter-bead distance d in Figures 4D and 4E, respectively, which clearly show that both the magnitude and wavelength of the GMD resonance exhibit a stronger d-dependence as compared with the GED resonance. This indicates that the magnetic dipole resonance is more sensitive to the optical coupling between nano-beads compared to the electric dipole resonance. A similar trend can also be observed with sets of RMM models of different bead sizes and numbers, as shown in Figure S12.

To better understand the effect of the bead size, D, on both global dipole resonance modes, we investigated the scattering response from the two modes, as shown in Figure 6. Under a similar inter-bead distance and its distribution, numbers of beads are adjusted according to bead sizes to maintain a constant overall RMM cluster size, Z. Figure 6A shows total farfield scattering spectra using various D values. Figures 6B and 6C show the corresponding GED and the GMD scattering power and Figures 6D and 6E show the change of the wavelength and magnitude of each mode at resonance as a function of D. Figure 6B-E show that in general, RMMs with larger beads exhibit stronger and more red-shifted GED and GMD resonances, similar to the effect observed by decreasing d. However, due to the increasing spectral coupling between GED and GMD resonances with larger beads, the two modes become less separable, leading to a less obvious trend shown in Figures 6D

3.2 The Effect of Bead Size Using a similar approach, the effect of bead size on the magnetic dipole resonance with respect to the electric dipole resonance was investigated using a combination of experimental measurements and numerical simulations, as shown in Figures 5 and 6. Figures 5 A-D show that at a constant inter-bead separation by using the same type of surfactants, RMMs with larger nano-beads, D, (and thus a larger overall size, Z) exhibit broader far-field spectra. The broader spectrum is mostly due to a combination of the red-shifting of the magnetic resonance with the relatively unaffected electric resonance in these clusters. The 5



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In this section, a simplified ring-shaped model is used to study the physical nature and structure dependence of the GED and GMD resonances formed in RMMs. As described in Figure 7, either the bead size or the inter-bead distance were varied while the size of the ring was kept constant (analogous to the overall size of the RMM particle).

and 6E compared with Figure 4. This coupling is the most evident for the largest bead size, blue curve in Figure 6B, where a strong dip in the spectrum is observed in the GED mode, at the same wavelength as the GMD resonance around ~900 nm (blue line in Figure 6C). This coupling is likely due to Fano-like modal interference between GMD and GED modes caused by the spectral overlap of the modes as well as the disorder in the structure similar to those observed in spiky nanoshells between the dipole and quadrupole resonance modes56. The coupling strength between the two modes can be calculated using T-matrix analyses as described in our previous publication and needs to be experimentally verified using single particle scattering measurements.56 However, this is beyond the scope of this study and will be studied in our future work.

Unlike in numerical simulations, specially designed excitation configurations are used in order to create pure electric or pure magnetic resonances. Both the GED and the GMD modes result from optical coupling between induced BEDs of closely packed nanobeads. As such, these effective optical properties depend on both the strength of the induced bead electric dipoles (BEDs) within individual nanobeads (determined by the size and of the nanobeads) as well as the strength of the dipole-dipole coupling (determined by both the bead sizes and the separation between them), as detailed in Section V-II of the SI. To quantitatively relate the properties of the two global dipole modes with the structure of the RMMs, the dipole moments for both the global electric dipole and the magnetic dipole resonances are analyzed with the dynamic theory of dipole-dipole interaction using the dyadic Green’s function analysis explained in section V-II of the SI and in reference 36.

Using simplified models, we can spectrally construct pure GED and GMD modes under different excitations to avoid mode coupling, and to further gain physical insight into the effect of the bead size and the inter-bead distance on GMD resonance properties, which will be shown in the next section. Nonetheless, the results presented in Figure 6 clearly show that the size of nanobeads is an efficient parameter to tune to manipulate the GMD mode.

Figure 5. (A-C) Extinction spectra of RMMs (R-12, R-14, and R-16) constructed with various bead sizes, D. The three sets of samples were synthesized with three different surfactants (BDDAC (A), BDTAC (B), and BDAC (C)). (D) Extinction spectra of RMMs synthesized using BDSAC (R-18). The bead size in the R-18 samples are smaller than those found in RMMs synthesized with other surfactants. The overall size of RMMs was kept constant for each set of data for all RMMs, (dotted lines: Z~155 nm, dashed lines: Z~179 nm, solid lines: Z~191 nm), as can be found in Table S2. The labels show the average bead size, D, for each cluster.

Figure 4. The GED and GMD resonance values as calculated based on far-field scattering spectrum for an RMM with cluster size of Z=350, D=20 nm beads at different inter-bead separations, d. Detailed model parameters and inter-bead distance distributions are shown in Table S1, rows 4-8, and Figure S8, respectively. (A) Total scattering cross section of modelled RMMs with various inter-bead distances. (B) Scattered power calculated 800 nm away from the RMM in the direction with maximum GED scattering (Sz). (C) Scattered power calculated 800 nm away from the RMM in the direction with maximum GMD scattering (Sy). (D) Dependence of the dipolar resonance wavelength (resonance) on inter-bead distance (d) for the GED and GMD modes. (E) Dependence of maximum power of the dipolar resonant scattering power on the inter-bead distance for the GED and GMD modes. Fitted trendlines in D and E were plotted to guide the eye only.

These global dipole modes are the results of the coupling between the polarization currents from the near electric field distributions around individual beads, forming either a net dipole (as shown in Figure S13) or a current loop (net magnetic dipole, Figure S14), respectively. In contrast, as demonstrated in the rest of this manuscript, the global magnetic dipole resonance is an emergent property of the cluster as a whole. As a result of the broad GED mode, there is significant spectral overlap between the two modes around the GMD resonance in the nearIR spectral region.

3.3 Dipole-coupling calculations

3.3.1 Effect of Inter-bead Distance 6


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The Journal of Physical Chemistry global dipole due to their rotation, making the resonance frequency and intensity less sensitive to the gap.

Figure 7. Calculation setup for the global electric dipole resonance (a) and magnetic dipole resonance (b), with incident field configuration.

Figure 6. The electric dipole and magnetic dipole resonance in the calculated far-field scattering spectrum for an RMM with various bead sizes and numbers, a constant average inter-bead separation around d=7.8 nm, and an overall size of Z~240 nm. Detailed model parameters and inter-bead distance distributions are shown in Table S1, rows 9-13 and Figure S9, respectively. (A) Total scattering cross section of a modelled RMM. (B) Scattered Poynting vector calculated 800 nm away from the RMM in the direction with maximum GED scattering as schematically shown on the inset. (C) Scattered Poynting vector calculated 800 nm away from the RMM in the direction with maximum GMD scattering, as schematically shown on the inset. (D) Dependence of dipolar resonance wavelength on the bead size, D. (E) Dependence of the maximum dipolar resonant scattering power on D. Trendlines are shown as linear fit to guide the eye.

Figure 8. (A) GED, and (B) GMD calculations for the core-satteline model with various inter-bead separations (d) using the dyadic Green’s function calculations. The model is schematically shown in the inset of B. (C) The amplitude of the GED (red) and GMD (blue) modes at resonance, normalized to the maximum, and (D) The resonance wavelength of GED (red) and GMD (blue) modes, as a function of the inter-bead separation, d.

GED and GMD dipole moments as a function of inter-bead separation for the simplified clusters were calculated using the dyadic Green’s function, based on a ring model of 12 gold spheres with a diameter of 30 nm. At d=1 nm, the overall size of the ring, Z was ~120 nm, slightly increasing with increasing d. Figures 8A and 8B show the dispersion profiles of the calculated global dipole moments. The evolution of both the amplitude and the resonance wavelength are shown in Figures 8C and 8D. While both dipole resonances are results of coupling of the BED dipoles on a global scale, the global electric dipole resonance mode shows a much smaller sensitivity to the inter-bead separation compared with the global magnetic dipole resonance mode, especially at smaller separations (d< 5 nm). This is consistent with the numerical modeling using FDTD on full RMM models discussed above (Figure 4). The strong red-shift in the magnetic dipole resonance is likely due to the fact that the formation of the GMD resonance strongly relies on the couplinginduced local electric field in the gap between the beads, that is normal to the surface of the beads at the gap, thus bending the polarization direction of the light and forming a closed loop at the resonance frequency (the magnetic response in proportional to the curl of the electric field). As such, the closer the gap distance (d) is, the stronger the magnetic resonance is and the lower the energy is to rotate the polarization currents. In contrast, for the GED resonance as shown in Figure S13 the oriented dipoles contribute by a smaller component to the overall

3.3.2 Effect of the Bead Size As demonstrated in Figure 5D, R-18 RMMs have significantly weaker GMD resonances due to their smaller bead diameters. This data demonstrates that the bead diameter D can play a stronger role in tuning the GMD resonance compared to the inter-bead distance d. This interpretation is also consistent with the experimental observations reported from similar structures synthesized using other synthetic methods.54 Compared with the inter-bead distance effect, the bead size effect is where the analytical methods can provide clearer physical insights than the numerical modeling. Figures 9A and 9B present the effect of D on the GED and GMD modes. For the ease of comparison, the overall ring size of the cluster and the inter-bead distances were kept constant at Z = 120 nm and d = 1 nm respectively. As such, the number of beads was increased as the bead size was decreased to keep d and Z constant. Consistent with the experimental data shown in Figure 5 and the calculations shown in Figures 6, the GMD for the ring structure varies much more strongly with the core size, and its strength at resonance has a 7



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RMMs (Figures 4A and 6A), and likely in the experimental spectra if single particle measurements are performed. In these systems, the coupling strengths are random, generating even more disorder in the features observed in GED, analogous to Debye modes in a disordered solid. The comparison between the red and the blue curves in Figure 9C shows that the GED resonance strength does not increase as rapidly as the GMD resonance with increasing D.

cubic power dependence on D, as shown in the inset of Figure 9. To understand the origins of the strong power-law dependence of GMD we investigated the coupling mechanism i.e. the dyadic Green’s function, as detailed in section V-II of the SI. For isolated gold beads much smaller than the wavelength of incident light (typically < 100 nm) where high order modes can be ignored, Taylor expansion of the leading term in the Mie scattering coefficient (proportional to the excited dipole moment) reveals a cubic-power-dependence on the particle size48 As such, the induced BED also has a cubic-dependence on D. Following a similar mathematical analysis described in reference 36, a crude derivation (section V-III of the SI) can be used to show that the GMD follows with the similar cubic dependence on D. This is consistent with data shown in Figure 9C where the normalized bead size dependence functions of GMD and of BED overlap strongly, indicating that GMD is proportional to BED.

4. Summary In summary, we used both analytical and numerical electrodynamic theory analyses to investigate the effect of structural parameter such as bead size and inter-bead distance on the magnetic dipole resonance of chemically-synthesized raspberry-like gold metamolecule structures and compared with the respective electric dipole mode. In these structures, the magnetic dipole resonance shows a sharp resonance and is red-shifted compared to the broad and disordered electric dipole mode. The results showed that the strength of both the global electric and the global magnetic modes increased with decreasing the interparticle distance and increasing the bead size, consistent with previous reports. The dependence on both parameters was greater for the magnetic mode than the electric mode. These results also showed that the bead size has an especially strong effect on the magnetic dipole resonance, with the dipole moment proportional to the cubic power. As such, the visibility of the magnetic dipole resonance and thus the tunability in the overall far-field spectral shape necessitates the metamolecules to have sufficiently large building blocks (beads). We also demonstrated experimentally that these variables can be easily tuned in raspberry-like metamolecules. The inter-bead distance can be tuned by varying the length of the alkyl chain in surfactant molecules, and the bead size can be tuned by adjusting several synthetic conditions such as relative amounts of precursors. The experimental results agree well with the theoretical predication and shows the important role of the bead size in the strength and red-shifting of the magnetic dipole resonance. This study can be used as a guideline to design nanoparticle assemblies with tunable magnetic resonance in accordance with the desired applications.

Figure 9. Global electric dipole moment (A) and magnetic dipole moment (B) calculation with different bead sizes using dyadic Green’s function on a gold sphere ring model. The resonant amplitude (C, normalized to the maximum) and wavelength (D) dependence on inter-bead separation from ring models were recorded. The inset of (C) plots the same results in log-log scale, showing the cubic power dependence on bead sizes for isolated electric dipole moment and magnetic dipole moment, with a reference line (dashed black) of slope 3 for comparison.

Glossary

In contrast, the GED does not have such a closed-form solution and thus can only be evaluated directly using the constructed Dyadic Green’s Functions. This is because there is no natural pathway for charges to couple and oscillate across an RMM construct as a whole. The GED cross-section is primarily due to the random coupling of BED dipolar resonances. For N number of coupled dipolar oscillator there are 3N normal modes that are slightly separated from each other across the spectrum and depend on the orientation of the polarization of the incident light. The strength weakens as the length scale increases, and the loss dominates, thus resembling a resonance for an intermediate number of coupled oscillators. When excited normal to the ring, the GED is primarily composted of the single bead dipoles. This is analogous to the Debye modes in a solid. The broad GED observed in the ring structure becomes spectrally even broader in RMMs and its shape becomes more rugged in the simulated

d

Nearest-neighbor inter-bead separation

N

Number of beads in an RMM

D

Bead size in an RMM

Z

Overall RMM size

GED

Global electric dipole

GMD

Global magnetic dipole

BED

Uncoupled bead electric dipole

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ASSOCIATED CONTENT

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Supporting Information. Detailed experimental procedure and parameters, modeling setup and parameters and additional figures are included in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author * Email: [email protected] * Email: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors thank Nader Engheta for helpful discussions and insight in theoretical analysis. Zahra Fakhraai acknowledges the support from the NSF career award (DMR-1350044) and the Sloan Research Fellowship. So-Jung Park acknowledges support from the National Research Foundation of Korea grant funded by the Korea government (MSIT) (NRF-2015R1A2A2A01003528) and the support from the Science Research Center (NRF2017R1A5A1015365).

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