Circular Magnetoplasmonic Modes in Gold Nanoparticles - Nano

Sep 19, 2013 - The quest for efficient ways of modulating localized surface plasmon resonance is one of the frontiers in current research in plasmonic...
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Letter pubs.acs.org/NanoLett

Circular Magnetoplasmonic Modes in Gold Nanoparticles Francesco Pineider,*,†,‡ Giulio Campo,† Valentina Bonanni,§ César de Julián Fernández,†,∥ Giovanni Mattei,*,⊥ Andrea Caneschi,† Dante Gatteschi,† and Claudio Sangregorio†,§ †

Department of Chemistry, University of Florence & INSTM, 50019 Florence, Italy CNR-ISTM Padova, 35131 Padova, Italy § CNR-ISTM & INSTM Milan, 20133 Milan Italy ∥ CNR-IMEM, 43124 Parma Italy ⊥ Department of Physics, University of Padova, 35131 Padova, Italy ‡

S Supporting Information *

ABSTRACT: The quest for efficient ways of modulating localized surface plasmon resonance is one of the frontiers in current research in plasmonics; the use of a magnetic field as a source of modulation is among the most promising candidates for active plasmonics. Here we report the observation of magnetoplasmonic modes on colloidal gold nanoparticles detected by means of magnetic circular dichroism (MCD) spectroscopy and provide a model that is able to rationalize and reproduce the experiment with unprecedented qualitative and quantitative accuracy. We believe that the steep slope observed at the plasmon resonance in the MCD spectrum can be very efficient in detecting changes in the refractive index of the surrounding medium, and we give a simple proof of principle of its possible implementation for magnetoplasmonic refractometric sensing. KEYWORDS: Active plasmonics, magnetoplasmonics, magneto optics, gold nanoparticles, sensing

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detection of small static changes in LSPR, which are crucial in refractometric sensing. In addition to describing the effect and its tight relation to the optical features of the plasmonic system, we compare the experiment with an analytical model describing the effect of the magnetic field on circular plasmonic modes and find a very good qualitative and quantitative agreement. Such uniformity does not haveto the best of our knowledgea match in current literature. The plasmonic systems we chose as a model sample set are colloidal gold nanospheres capped with oleylamine dispersed in organic solvent. All three samples, differing in mean particle size (3.4, 12.8, and 17.7 nm), were prepared using slightly modified literature procedures (see SI for details), involving the reduction of tetrachloroauric acid in the presence of the capping molecules; the reduction is carried out by an external reducing agent13 (3.4 nm particles) or by the capping agent itself14 (12.8 and 17.7 nm particles). All samples were carefully inspected by means of transmission electron microscopy to ensure they had a spherical shape and a narrow size distribution. The 12.8 nm particles (Figure 1a) exhibit a sharp plasmon resonance around 520 nm, as shown in the optical extinction spectrum in Figure 1b (red trace). The MCD spectrum was recorded applying a magnetic field of 1.3 T (Figure 1b black trace, see SI for details on the acquisition

he strong dependence of localized surface plasmon resonance (LSPR) on the dielectric function of the surrounding medium makes them invaluable local probes of the microscopic landscape, leading to a tremendous growth in the interest for localized plasmon-based sensing.1,2 What is indeed even more fascinating is the possibility to actively induce changes in the resonance conditions using an external agent, in order to effectively stir the electronic and optical properties of the plasmonic system in a controlled and reversible manner.3−5 Among the routes that have been proposed so far to achieve active plasmonics, the use of a magnetic field seems a very promising one; the possibility of modulating the optical response by means of an external magnetic field can open the way to dramatic innovations in refractometric sensing, as well as in light-guiding and optoelectronics. Several studies have appeared recently on enhanced magneto-optical response6,7 and on active plasmonics,8 based on coupled ferromagnetic/ noble metal heterostructures to observe magnetoplasmonic effects. Seminal work by Temnov et al.8 elegantly demonstrated that it is possible to induce small modifications in the wave propagation vector of plasmon polaritons in tailored magnetic− plasmonic films. The careful design that is required in both the substrates and in the experiment to observe magnetic tuning of plasmonic modes is somewhat the agony and ecstasy of the current approach toward magneto-plasmonics.9−12 Here we show that by using MCD spectroscopy it is possible to measure field-driven modifications of LSPR in simple, unoptimized colloidal gold nanospheres. We also point out experimentally how the field-induced modulation of the LSPR can benefit the © 2013 American Chemical Society

Received: June 30, 2013 Revised: September 11, 2013 Published: September 19, 2013 4785

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Figure 1. (a) TEM micrograph of colloidal gold nanoparticles; the scale bar is 40 nm. The average particle size is 12.8 ± 0.7 nm. (b) Optical absorption spectrum (red ○) and magnetic circular dichroism (black ○) of the gold nanoparticles. Optical absorption (A) is given in normalized units at peak maximum (A/AMax); dichroism (ΔA) is scaled in accordance (ΔA/AMax) and for B = 1 T along light propagation direction.

larger normalized MCD response with respect to the 12.8 nm particles. The comparison is clear in Figure S4. The question is on how such shift is originated in a LSPR peak: while this theoretical framework is well-established for electronic transitions between orbitals or bands,15,16 no rationalization has been presented so far for the case of collective oscillations of free electrons as in the case of surface plasmons. Circularly polarized light excites circular plasmonic modes in geometries that exhibit rotational symmetry in at least one direction;17 in the case of spherical nanoparticles such a condition is met for all relative orientations between particles and the propagation vector of light. The two circular plasmonic modes are degenerate at zero field; however if an external magnetic field is applied along the light propagation direction, the degeneration is lifted. The resulting force acting on the electrons that collectively oscillate in circular orbits includes an additional term due to Lorentz force and reads: F = −eE − ev × B. Consequently, the collective circular charge motion will be more or less confined according to the helicity of the circular plasmonic mode, and a shift in the resonance frequency will be observed (see Figure 2). We can express the motion equation in terms of the Drude model with a term that takes into account the effect of the magnetic field:

method). As can be seen, the line shape of the plasmonic MCD signal is a derivative-like peak crossing zero in correspondence of the maximum of the plasmon resonance; the positive lobe lies at higher energy with respect to the absorption peak and the negative at lower energy. The origin of such a line shape can be understood considering that MCD spectroscopy does in fact measure the difference between two absorption spectra acquired using light with opposite helicity in the presence of an external magnetic field parallel to the incident light direction. If the absorption spectra corresponding to left and right circularly polarized light (LCP and RCP) are shifted in energy, their difference results in a derivative-like shape (see Figure 2). From

m

dv + γmv = −e E − e v × B dt

(1)

where e and m are the charge and effective mass of the electron, v its velocity, γ the damping constant, E the electric field of the incident light, and B the external magnetic induction. For experimentally accessible fields, the field-dependent term −ev × B is small compared to the light-induced polarization, so the equation of motion (1) can be solved perturbatively as described by Gu et al.18 Given the size of the spheres, we can work within the quasi-static approximation;19 based on the morphological and optical characterization we can also consider particles to be spherical and with negligible size dispersion, as well as being fully dispersed in the solvent matrix. Solving the Laplace equation inside and outside the nanoparticles and applying the boundary conditions for circularly polarized incoming electric field of the form E = E0e±iωt = E0 cos(ωt) ± iE0 sin(ωt) = Ex ± iEy we obtain a generalized expression for the field- and helicity-dependent polarizability:

Figure 2. Scheme of the process leading to the diamagnetic line shape in the magnetic circular dichroism (orange) resulting from the difference between the left (blue) and right (red) circular plasmonic modes. The insets show the effect of LCP and RCP light and of the magnetic induction B (perpendicular to the orbital plane) in terms of the electric (FE) and magnetic (FB) components (both radial in direction) of the Lorentz force acting on the electrons.

this consideration it is clear that the line shape of the absorption spectrum is directly involved in the spectral features of the MCD spectrum; for instance, the distance between the positive and negative lobes (i.e., the magnitude of the signal) depends linearly on the LSPR shift of the magnetoplasmonic modes, thus on the magnitude of the applied magnetic field (see also Figure S1). In addition, the width of the LSPR influences shape and amplitude of the MCD signal: therefore smaller nanoparticles, whose LSPR is broader due to electronic surface scattering (3.4 nm particles, Figure S2) show a smaller normalized MCD signal, while larger particles, with a slightly sharper LSPR (17.7 nm particles, Figure S3), exhibit a slightly

αB(ω) = − 4786

πD3 (ε(ω) − εm) + (f (ω) − fm )B 2 (ε(ω) + 2εm) + (f (ω) − fm )B

(2)

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where D is the particle diameter, ε(ω) = ε1(ω) − iε2(ω) the complex dielectric function of the metal, εm the dielectric constant of the medium surrounding the particle, and f(ω) = f1(ω) + if 2(ω) and f m are the coupling functions describing the interaction with the magnetic field B of the metal and the surrounding medium, respectively (see ref 18 and SI for details). Equation 2 is the basic relation to quantitatively describe the effect of an external magnetic field on the resonance condition for a small metallic particle excited by circularly polarized light. By considering the symmetry of the problem, it is clear that a change in helicity is topologically equivalent to an inversion of the applied field direction, that is, to a change in the algebraic sign of B in eq 2. Thus, in the following, we will associate LCP or RCP excitation to a magnetic field with magnitude B or −B, respectively. Moreover for B = 0 we obtain the standard polarizability expression for small particles; by imposing for its denominator ε(ω0) + 2εm = 0 we define the standard Fröhlich condition for the LSPR resonance ω0. Writing Δf(ω) ≡ f(ω) − f m = Δf1(ω) + iΔf 2(ω) and equating to zero the denominator of eq 2, we can now derive a generalized Fröhlich condition for analytically evaluating the LSPR frequencies of the magnetoplasmonic modes ωB as a function of the magnetic field and light helicity by expanding to first order in ω the dielectric and the coupling functions around the LSPR frequency ω0 as: ωB = ω0 −

Figure 3. Calculation of the effect of an applied magnetic field on the shift of LSPR taking into account the full dielectric function of gold (black line) and the free-electron contribution only (red line).

BΔf1 (ω0) (∂ε1/∂ω)|ω0 + B(∂Δf1 /∂ω)|ω0

(3)

where B (−B) describes LCP (RCP) polarization. In the denominator of eq 3, the field-dependent term is largely negligible with respect to the dielectric function slope (it is about 4 orders of magnitude smaller at 1 T and would be relevant only at unphysically large magnetic fields, ∼103/104 T (see Figure S5). Therefore the LSPR shift can be accurately calculated in a linearized form as: ωB = ω0 −

BΔf1 (ω0) (∂ε1/∂ω)|ω0

= ω0 − g (ω0)B

Figure 4. Comparison between the experimental MCD spectrum (black ○) and the simulated MCD spectrum (red line); all spectra are shown in normalized units.

modulation induced by the magnetic field on the LSPR of the gold particles we studied: Δω = |ωB − ω0| = g(ω0)B ≅ 6.95 × 1010 rad/s for B = 1 T, corresponding to a shift in the LSPR wavelength of about 0.01 nm per applied tesla. It is worth mentioning that, even if the shift is relatively small, MCD spectroscopy allows easy detection of the related dichroic signal. As can be seen in Figure 4, the asymmetry in the derivativelike line shape is reproduced as well; the origin of such asymmetry stems from the fact that, unlike electronic transitions between orbitals or bands, for which the rigid shift approximation holds in the weak field regime,15,16 in this case the shape and intensity of the resonance depend strongly on the value taken by ε2 at resonance. For small gold spheres, LSPR falls in a spectral region in which ε2 varies quickly due to the onset of interband transitions; thus peak intensity changes significantly for small shifts. The remarkable agreement between the experiment and the theory describing magnetoplasmonic modes is one of the key points of this investigation; in fact, previous observations of similar phenomena limited their theoretical analysis to a qualitative modeling20 or to a combination of magneto optical terms21 in the MCD framework for molecular compounds. Moreover, in addition to presenting a fully rational theoretical approach, which is strictly based on the analytical description of the phenomenon, we are able to match the experimental measurements both in line shape and magnitude. This bridges the recurring gap between poorly understood experiments and unconfirmed

(4)

It is important to point out that, if we restrict our description of the optical properties of the metal to a simple Drude model and not consider the full dielectric function (including interband transitions), we obtain g(ω0) = −e/2m (see the SI). Thus, introducing the cyclotron frequency ωC ≡ eB/m, it turns out that eq 4 is in fact a generalized form of the familiar expression ωB = ω0 ± ωC/2, commonly associated with the effect of a magnetic field on free charge carriers.9−12 The generalized formula reported here allows quantifying accurately the effect of a magnetic field on LSPR in real metals: as can be seen in Figure 3, considering the Drude-like free electron contribution only (red curve) or the full dielectric function (black curve) leads to a significant difference in the estimation of the shift. The experimental curve of MCD (Figure 4, black trace) can be compared to a simulated MCD spectrum (red trace). The latter is calculated by subtracting two absorption spectra with opposite helicity under an applied field of 1 T derived from the polarizability expression of eq 2: the model accurately reproduces the line shape and magnitude of the experimental data. The good agreement of the calculated spectrum with the experiment confirms the importance of using the full dielectric function of gold in eq 2. We can use eq 4 to assess the 4787

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plasmonic architectures, such as particles with different shapes2 or dielectric layer-covered structures22 show a very high RI sensitivity. Such plasmonic substrates, in conjunction with magnetoplasmonic detection can be devised to prepare ultrahigh sensitivity refractometric sensing platforms. In conclusion, in this work we measured the circular magnetoplasmonic modes of solvent-dispersed gold nanoparticles using magnetic circular dichroism spectroscopy. We rationalized the effect as to be originating from the coupling of the circular plasmonic modes with an external magnetic field, and formulated a generalized set of equations taking into account the full dielectric function of the metal. Comparing such model with the experimental measurements, we found them in full agreement. Finally, we proposed a novel fixed wavelength LSPR detection scheme based on MCD and supported it with a proof of concept experiment on gold nanoparticles dispersed in different solvents. The magnetic modulation of the MCD response in gold nanoparticles brings a new impulse to the field of active plasmonics, since magnetic field is a fast, reversible, and convenient external stimulus: using light or magnetic field modulation and phase-sensitive recovery techniques, LSPR position can be associated to a steep slope, thus dramatically increasing the potential for the detection of very small shifts in the resonance in label-free refractometric sensing.

theoretical models and provides the community with a simple yet powerful instrument for the understanding and for the rational design of optimized magnetoplasmonic structures. To give a proof of concept of how the detection of circular magnetoplasmons with MCD can represent a significant push to the field of LSPR refractometric sensing, we performed a series of measurements in which the same batch of 12.8 nm gold nanoparticles was dispersed in solvents with different refractive indexes (RI), namely, chloroform (RI = 1.446) and toluene (RI = 1.497), in addition to hexane (RI = 1.375). As can be seen in Figure 5, the zero crossing moves toward lower

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Figure 5. MCD spectra of 12.8 nm gold nanoparticles dissolved in hexane (black ○, RI = 1.375), in chloroform (red ○, RI = 1.446), and in toluene (blue ○, RI = 1.497). The vertical line at 520 nm highlights the significant changes in MCD signal magnitude as the RI of the medium is changed.

ASSOCIATED CONTENT

S Supporting Information *

Methods: nanoparticle synthesis, MCD setup and measurement, details on the theoretical model. Optical absorption and MCD spectra of AuNPs with different size and in different solvents. Experimental and simulated magnetic field scans. Comparison between experimental and simulated optical absorption spectra. This material is available free of charge via the Internet at http://pubs.acs.org.

energy as the RI of the medium increases, coherently with what is observed at the absorption peak (Figure S6). Instead of considering the position of the zero crossing though, we can focus our attention on a more interesting quantity: the magnitude of the MCD signal at a fixed wavelength. This approach is similar to the high sensitivity, fixed angle reflectivity measurement used in commercial SPR platforms: as the resonance condition of the particles is shifted due to a change in the RI, the magnitude of the MCD signal around the resonance wavelength varies drastically, since its slope is very high. Thus, a RI change of 0.071 units (from hexane to chloroform) yields a change of about 11% of the magnitude of the signal and in the case of toluene (RI change of 0.122) the magnitude change reaches an amazing 35% in simple gold nanospheres. It is important to remark that this experiment is a demonstration of the potential lying in magnetoplasmonic sensing: the small field-induced LSPR shift detected by means of MCD acts here as a small modulation around the bigger, static shift due to the RI changes of the medium. As a consequence, this approach can be considered as a promising alternative in the detection compartment of refractometric sensing. As can be seen in Figure 5, the changes in signal magnitude are in the 10−4 range for RI changes of the order of 0.1; if we consider that a well-tuned MCD setup can detect dichroic signals down to 10−6−10−7,16 RI changes down to 10−3 could be traced using simple gold spheres. From this starting point, the choice and design of the plasmonic substrate can dramatically boost both MCD response and RI sensitivity: for instance, a sharper LSPR peak will give a greater MCD magnitude, as it is clear from Figure S4, and consequently a more strongly sloping signal; on the other hand, advanced

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: francesco.pineider@unifi.it (F.P.). *E-mail: [email protected] (G.M). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge Mauro Perfetti for the preparation of the 3.4 nm gold nanoparticle sample and thank Prof. Roberta Sessoli, Prof. Paolo Ghigna, and Dr. Marı ́a Ujué González for the helpful scientific discussion. We acknowledge the financial support of the EC through FP7-214107-2 NANOMAGMA, the Italian MIUR through FIRB projects RBPR05JH2P Rete ItalNanoNet, RBFR10OAI0 Nanoplasmag, and Fondazione Cariplo through project “Chemical synthesis and characterization of magneto-plasmonic nano-heterostructures”.

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