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Magnetochirality in hierarchical magnetoplasmonic clusters
Solid State Communications 217 (2015) 47–52
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Magnetochirality in hierarchical magnetoplasmonic clusters Vassilios Yannopapas n Department of Physics, National Technical University of Athens, GR-157 80 Athens, Greece
art ic l e i nf o
a b s t r a c t
Article history: Received 17 February 2015 Received in revised form 24 April 2015 Accepted 23 May 2015 Communicated by R. Merlin Available online 2 June 2015
We show theoretically that finite hierarchical assemblies of clusters consisting magnetic (magnetite) and plasmonic (gold) nanoparticles show dramatically increased values of the magnetochiral dichroism compared to those measured in conventional materials exhibiting this phenomenon (liquid molecular systems, anisotropic crystals and chiral ferromagnets). These values are attributed to the strong interaction of the magnetite nanoparticles within the clusters as well as by the excitation of surfaceplasmons in the gold nanoparticles. Along with the magnetochiral dichroism, in the studied hierarchical magnetoplasmonic designs, magneto-optical phenomena such as magnetic dichroism and Faraday rotation are also enhanced relative to the case of purely magnetic nanostructures. & 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Magneto-topics B. Faraday effect C. Plasmonics D. Nanoparticles
1. Introduction The term magnetochirality entails phenomena related with electromagnetic (EM)-wave propagation in chiral substances or structures under the influence of an external magnetic field such as birefringence in EM wave refraction or dichroism [1]. The presence of an external magnetic field within a chiral medium introduces time-reversal as well as space-reversal symmetry breaking simultaneously, and, as a second-order phenomenon, it is very hard to measure experimentally. So far, magnetochirality has been verified in liquid molecular systems, organic compounds, anisotropic crystals and chiral ferromagnets [2–14]. Recently, it has been theoretically proposed that magnetochiral dichroism (MChD) can be promoted in chiral magnetic metamaterials such as helical lattices of magnetic garnet spheres [15]. Moreover, it has been demonstrated experimentally that chiral magnetic nanohelices can exhibit strong MChD in the optical regime [16]. In the present work we present a new design with which MChD can be enhanced by several orders of magnitude in clusters of magnetic (Fe3 O4 – magnetite) nanoparticles (NPs) as well as in assemblies of clusters of magnetite NPs due to the interaction of the magnetite NPs within the clusters. By substituting magnetite NPs with gold NPs in the clusters, the MChD can be even more enhanced by the excitation of surface-plasmon resonances in the surface of the gold NPs. Such clusters are termed as binary magnetoplasmonic clusters since they consist of magnetic (magnetite) and gold (plasmonic) NPs. Below we provide a brief outline of the theory of
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magnetochirality along with a presentation of the basic quantities involved.
2. Magnetochiral dichroism The dielectric tensor of chiral media subject to a magnetic field B, to first order in wavevector k and B is written as [3] L;R L;R ϵL;R 7 ðω; k; BÞ ¼ ϵ0 ðωÞ 7 αNCD ðωÞk 7 β MCD ðωÞB þ γ MChD ðωÞk B
ð1Þ
where the symbol L indicates left-circularly polarized (LCP) and R indicates right-circularly polarized (RCP) light. αL;R NCD k is the contribution of natural circular dichroism (NCD) (in the absence of magnetic field, i.e., B ¼ 0), β MCD ðωÞB is the contribution of magnetic circular dichroism (MCD- Faraday effect), and the third term γ L;R ðωÞk B corresponds to the MChD effect taking place in the MChD presence of a magnetic field acting on a chiral medium. The MChD term depends on the relative orientation of the wavevector k and the magnetic field B, on the sense of handedness of the chiral medium and it is independent of the polarization of incident light (MChD occurs for unpolarized incident light). The above three effects are substantiated via the measurement of absorption circular dichroism (CD) for LCP and RCP incident light, i.e., ARCP ALCP CD ¼ 2 ARCP þ ALCP
ð2Þ
NCD ¼ CDðB ¼ 0Þ
ð3Þ
MCD ¼ CDðBÞ NCD
ð4Þ
MChD ¼ Aðk↑↑BÞ Aðk↑↓BÞ
ð5Þ
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V. Yannopapas / Solid State Communications 217 (2015) 47–52
Fig. 1. (Color online) (a): A spherical cluster of 170 magnetite nanoparticles of 20 nm radius, i.e., the average radius of the cluster is about 160 nm while the average interparticle distance is 0.5 nm. (b): A tetramer of clusters placed at the positions: (320,0,0) nm, (0,480,0) nm, (0, 320,0) nm, and (0,0,480) nm.
where A in the last of the above equations is the absorbance for unpolarized light, i.e., A ¼ ðARCP þ ALCP Þ=2. When the real part of the dielectric tensor of 1 is much larger than its imaginary part, then MChD ðNCDÞ ðMCDÞ verifying the cross-effect nature of MChD [3].
3. Description of the magnetoplasmonic clusters Our case study are the material designs depicted in Fig. 1. Fig. 1a shows a cluster of magnetite NPs arranged randomly around the center of the cluster without touching each other. Spherical clusters of magnetite nanoparticles have been formed by self-assembly techniques based on solvophobic interactions [17]. The magnetite NPs have 20 nm radius while the average cluster radius is 160 nm. The average interparticle distance is 0.5 nm. Fig. 1b shows an assembly (tetramer) consisting of the clusters of Fig. 1a wherein the clusters are placed at positions: (320,0,0) nm, (0,480,0) nm, (0, 320,0) nm, and (0,0,480) nm. This tetramer possesses an intrinsic structural chirality which is prerequisite for observing the magnetochiral phenomena. It is worth noting that in the single cluster of magnetite NPs of Fig. 1a, there is also a residual structural chirality stemming from the inequivalent (random) positioning of the magnetite NPs around the center of the cluster. The EM modeling of the designs of Fig. 1 is performed via the Discrete-Dipole Approximation (DDA) technique [18] for magnetooptical (MO) targets (scatterers) [19,20]. In the calculations that follow, the dielectric tensor (diagonal and off-diagonal elements) of the magnetite NPs is taken from experimental measurements of bulk magnetite [21,22]. The dielectric function of the gold NPs is also taken from experiment [23]. The corresponding azimuth and ellipticity rotation angles which quantify the magnitude of the Faraday effect, are calculated as the real and imaginary part, respectively, of the difference in the extinction cross sections between LCP and RCP incident light [20]. Fig. 2. (Color online) (a) Azimuth and ellipticity rotation angle, (b) NCD, (c) MCD and (d) MChD for light incident on the cluster of Fig. 1a.
4. Results and discussion We begin by studying the single cluster of magnetite NPs shown in Fig. 1a. Namely, in Fig. 2, we show the azimuth and ellipticity rotation angles (a), CD (b), MCD (c) and MChD (d) for the cluster of Fig. 1a. Light is incident along the z-axis (k ¼ kz z^ ) while an external magnetic field B ¼ 0:5 T is applied either parallel or antiparallel to the incident wavevector k. From Fig. 2a, we observe that both rotation angles are of the order of a hundreds of millidegrees which are values at least one of order of magnitude
larger than for isolated magnetite NPs [19]. This is an expected result since the interaction of magnetic NPs enhances the MO effects such as the rotation angles of incident light and MCD – see Fig. 2c [24]. The NCD spectrum depicted in Fig. 2b does not depend on the application of the external field and is a result of the structural chirality of the assembly. However, since the cluster of Fig. 1a consists of NPs which are randomly positioned in space and not in a chiral fashion, the values of NCD are much lower than genuinely chiral designs of NPs [25–29].
V. Yannopapas / Solid State Communications 217 (2015) 47–52
Fig. 3. (Color online) (a) Azimuth and ellipticity rotation angle, (b) NCD, (c) MCD and (d) MChD for light incident on a spherical cluster of 170 magnetite nanoparticles of 20 nm radius, i.e., the average radius of the cluster is about 240 nm. The average interparticle distance is 0.75 nm.
The MChD spectrum, however, shows an opposite trend compared to the NCD and MCD spectra as it becomes weaker (smaller absolute values) with increasing wavelength. This is a demonstration of the so-called pure MChD being distinct from the cascaded MChD associated with the product ðNCDÞ ðMCDÞ [3]. A pure MChD effect has been recently demonstrated experimentally in chiral nanomagnets [16]. Namely, MChD is a cross effect and takes
49
Fig. 4. (Color online) (a) Azimuth and ellipticity rotation angle, (b) NCD, (c) MCD and (d) MChD for light incident along the positive z-axis at the tetramer of Fig. 1b.
place in systems containing both natural circular dichroism (NCD) and magnetic circular dichroism (MCD). Therefore, to a first approximation, an enhancement of both NCD and MCD leads to an increase of the magnitude of MChD (cascade effect). However, the conditions for explaining the resulting MChD as a cascade effect of NCD and MCD is that the real part of the dielectric tensor elements be much larger than the corresponding imaginary parts.
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V. Yannopapas / Solid State Communications 217 (2015) 47–52
Fig. 5. (Color online) (a) Azimuth and (b) ellipticity rotation angles for light incident along the positive z-axis at the tetramer of Fig. 1b, for various binary mixtures of 20 nm magnetite (Fe3 O4 ) and gold NPs.
By inspecting the elements of the dielectric tensor of magnetite (see Figs. S1 and S2 of the supplemental material) it is evident that such a condition is not satisfied. In Fig. 3 we consider a more dilute cluster of magnetite NPs, i.e., a cluster consisting, again, of 170 magnetite nanoparticles of 20 nm radius, but with larger average radius, i.e., 240 nm. This means that the average interparticle distance now is 0.75 nm (instead of 0.5 nm in Fig. 2). We observe that the range of values for the NCD is more or less the same as for the denser cluster of Figs. 1a and 2. For the MO effects we observe opposite trends. While both rotations angles are significantly reduced (see Fig. 3a), MCD (Fig. 3c) is enhanced by 2 orders of magnitude, on the average. The fact that a more close-packed arrangement of NPs does not necessarily favor MO phenomena has already been previously reported [24]. However, MChD, which is the main focus of our study here, has been reduced by one order of magnitude (the absolute value of), on the average. We, therefore, continue with the dense cluster of Figs. 1a and 2 in an effort to enhance the phenomenon of magnetochirality. Next, in Fig. 4 we study the case of the chiral assembly (tetramer) of magnetoplasmonic-nanoparticle clusters as shown in Fig. 1b. Evidently, all related quantities, i.e., rotation angles, NCD, MCD and MChD are enhanced due to the chiral positioning of the clusters (the tetramer lacks of mirror symmetry). The azimuth and ellipticity rotation angles are increased by more than the order of magnitude thanks to the chiral arrangement to the clusters but, primarily, thanks to the increase in the mass of magneto-optical material (more magnetite NPs). In the same trend, all the three dichroism spectra (NCD, MCD, MChD) are also enhanced by about one order of magnitude. The local maxima observed in the MCD, MChD spectra correspond to a local maximum of the off-diagonal (magneto-optical) elements of the dielectric tensor of magnetite (see Fig. S2 of the supplemental material) which is more or less
Fig. 6. (Color online) (a) NCD, (b) MCD and (c) MChD for light incident along the positive z-axis at the tetramer of Fig. 1b, for various binary mixtures of 20 nm magnetite (Fe3 O4 ) and gold NPs.
expected as the influence of an externally applied magnetic field is more evident when the corresponding MO tensor elements are maximized. In hope of enhancing ever further the MChD effect, we substitute some of the magnetite NPs in the clusters by gold ones. Gold NPs support surface-plasmon (SP) resonances, i.e., plasma oscillations occurring at the surface of the gold NP. The strong confinement of light in subwavelength volumes such as the surface of gold NP results in huge values of the local field, boosting the impact of a plethora of phenomena and properties such as Raman scattering, nonlinearities, light-matter interactions, to name a few. Among these phenomena which are promoted by SP excitations are the MO phenomena such as the Kerr/Faraday effects and MCD which take place in nanostructures combining magnetic and plasmonic functionalities [30–39]. In Fig. 5 we show the azimuth and rotation angles corresponding to the Faraday effect, for the tetramer of Fig. 1b where a fraction (see inset) of the 20 nm magnetite NPs have been substituted by gold NPs of the same size. We observe that the MO Faraday effect is enhanced around and above the SP resonance of gold NP (around 530 nm) as
V. Yannopapas / Solid State Communications 217 (2015) 47–52
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dramatically the MO effect among the magnetite NPs and outweighs the contribution of the chiral arrangement of the clusters in space. The latter, again, suggests that the MO effect dominates all other sources of chirality and implies that the observed MChD is not necessarily a cascaded phenomenon of magneto-optical and natural dichroism (see the discussion above).
5. Conclusion We have shown theoretically that the magneto-optical and magnetochiral effects are dramatically enhanced in spherical clusters of magnetic (magnetite) nanoparticles as well as in chiral assemblies of such, thanks to their mutual interaction within the same or neighboring clusters. The phenomenon is maximized with the substitution of some magnetite nanoparticles with gold ones which boost the magneto-optical effect within the magnetite nanoparticles and subsequently the magnetochiral dichroism which is an especially weak phenomenon in nature. Spherical clusters of magnetite nanoparticles have already been realized in the laboratory via bottom-up self-assembly methods [17] while chiral assemblies of such clusters can be realized in the same manner, via, e.g., DNA-assisted self-assembly [40–42].
Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.ssc.2015.05.016. References
Fig. 7. (Color online) (a) NCD, (b) MCD and (c) MChD for light incident along the positive z-axis at a single cluster (Fig. 1a), for various binary mixtures of 20 nm magnetite (Fe3 O4 ) and gold NPs.
a result of the excitation of this resonance by incident light. Namely, the MO effect is proportional to the local electric field which is, however, greatly enhanced within the magnetite NPs due to the spill over of the electric field in the neighboring gold NPs [37]. This is much more evident in the MCD of Fig. 6b where the enhancement relative to the case of purely magnetic clusters is more than 3 orders of magnitude. MChD (Fig. 6c) is also enhanced by 2 orders of magnitude on the average relative to the case of clusters with magnetite NPs only. The range of values of the NCD (Fig. 6a) is also increased but less than MCD and MChD as the dramatic increase in the MO effect does not affect directly the NCD. Lastly, in Fig. 7 we show the all three dichroism spectra (NCD, MCD and MChD) for a single cluster consisting of mixtures of 20 nm magnetite and gold NPs. Evidently, we observe that all three types of dichroism assume more or less the same values for the single cluster (Fig. 7) as well as for the tetramer of clusters (Fig. 6) of mixtures of magnetite and gold NPs. This in contrast to the case of pure magnetite clusters wherein the chiral positioning of the magnetite clusters enhances all CD spectra by one order magnitude. It seems that the presence of the gold NPs enhances
[1] L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Oxford, 1984. [2] G.L.J.A. Rikken, E. Raupach, Nature (London) 390 (1997) 493. [3] G.L.J.A. Rikken, E. Raupach, Phys. Rev. E 58 (1998) 5081. [4] P. Kleindienst, G.H. Wagnière, Chem. Phys. Lett. 288 (1998) 89. [5] N.G. Kalugin, P. Kleindinst, G.H. Wagnière, Chem. Phys. 248 (1999) 105. [6] G.L.J.A. Rikken, E. Raupach, Nature (London) 405 (2000) 932. [7] M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.Y. Thépot, Phys. Rev. Lett. 87 (2001) 183003. [8] M. Saito, K. Ishikawa, K. Taniguchi, T. Arima, Phys. Rev. Lett. 101 (2008) 117402. [9] C. Train, R. Gheorghe, V. Krstic, L.M. Chamoreau, N.S. Ovanesyan, G.L.J. A. Rikken, Nat. Mater. 7 (2008) 729. [10] Y. Kitagawa, H. Segawa, K. Ishii, Angew. Chem. Int. Ed. 50 (2011) 9133. [11] S. Miyahara, N. Furukawa, J. Phys. Soc. Jpn. 81 (2012) 023712. [12] S. Kibayashi, Y. Takahashi, S. Seki, Y. Tokura, Nat. Commun. 5 (2014) 4583. [13] S. Harroti, K. Ishii, Opt. Mater Express 4 (2014) 2423. [14] R. Sessoli, M.E. Boulon, A. Caneshchi, M. Mannini, L. Poggini, F. Wilhelm, A. Rogalev, Nat. Phys. 11 (2015) 69. [15] A. Christofi, N. Stefanou, Opt. Lett. 38 (2013) 4629. [16] S. Eslami, J.G. Gibbs, Y. Rechkemmer, J. van Slageren, M. Alarcón-Correa, T.C. Lee, A.G. Mark, G.L.J.A. Rikken, P. Fischer, ACS Photon. 1 (2014) 1231. [17] J. Zhuang, H. Wu, Y. Yang, Y.C. Cao, J. Am. Chem. Soc. 129 (2007) 14166. [18] B.T. Draine, Astrophys. J. 333 (1988) 848. [19] D.A. Smith, Y.A. Barnakov, B.L. Scott, S.A. White, K.L. Stokes, J. Appl. Phys. 97 (2005) 10504. [20] D.A. Smith, K.L. Stokes, Opt. Express 14 (2006) 5746. [21] A. Schlegel, S.F. Alvarado, P. Wachter, J. Phys. C: Solid State Phys. 12 (1979) 1157. [22] X. Zhang, J. Schoenes, P. Wachter, Solid State Commun. 39 (1981) 189. [23] R.B. Johnson, R.W. Christy, Phys. Rev. B 6 (1972) 4370. [24] A. Christofi, N. Stefanou, N. Papanikolaou, Phys. Rev. B 89 (2014) 214410. [25] V. Yannopapas, J. Phys. Condens. Matter. 18 (2006) 6883. [26] Z. Fan, A.O. Govorov, Nano Lett. 10 (2010) 2580. [27] Z. Fan, A.O. Govorov, J. Phys. Chem. C 115 (2011) 13254. [28] A. Guerrero-Martínez, J.L. Alonso-Gómez, B. Auguié, M.M. Cid, L.M. LizMarzán, Nano Today 6 (2011) 381. [29] S. Droulias, V. Yannopapas, J. Phys. Chem. C 117 (2013) 1130. [30] Y. Li, Q. Zhang, A.V. Nurmikko, S. Sun, Nano Lett. 5 (2005) 1689. [31] J.B. González-Díaz, A. García-Martín, J.M. García-Martín, J.M.A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, M. Käll, Small 4 (2008) 202. [32] G. Armelles, J.B. González-Díaz, A. García-Martín, J.M. García-Martín, A. Cebollada, M.U. González, A. Srdjan, J. Cesario, R. Quidant, G. Badenes, Opt. Express 16 (2008) 16104. [33] F.E. Moolekamp, K.L. Stokes, IEEE Trans. Magn. 45 (2009) 4888.
52
V. Yannopapas / Solid State Communications 217 (2015) 47–52
[34] P.K. Jain, Y. Xiao, R. Walsworth, A.E. Cohen, Nano Lett. 9 (2009) 1644. [35] J.B. González-Díaz, B. Sepúlveda, B.A. García-Martín, G. Armelles, Appl. Phys. Lett. 97 (2010) 043114. [36] G.X. Du, T. Mori, M. Suzuki, S. Saito, H. Fukuda, M. Takahashi, Appl. Phys. Lett. 96 (2010) 081915. [37] G. Armelles, A. Cebollada, A. García-Martín, M.U. González, Adv. Opt. Mater. 1 (2013) 10.
[38] [39] [40] [41]
A. Christofi, N. Stefanou, Phys. Rev. B 87 (2013) 115125. A. Christofi, N. Stefanou, Phys. Rev. B 88 (2013) 125133. A. Mastroianni, S.A. Claridge, A.P. Alivisatos, J. Am. Chem. Soc. 131 (2009) 8455. J. Sharma, R. Chhabra, A. Cheng, J. Brownell, J.Y. Liu, H. Yan, Science 323 (2009) 112. [42] S.J. Tan, M.J. Campolongo, D. Luo, W. Cheng, Nat. Nanotechnol. 6 (2011) 268.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Magnetochirality in hierarchical magnetoplasmonic clusters Vassilios Yannopapas n Department of Physics, National Technical University of Athens, GR-157 80 Athens, Greece
art ic l e i nf o
a b s t r a c t
Article history: Received 17 February 2015 Received in revised form 24 April 2015 Accepted 23 May 2015 Communicated by R. Merlin Available online 2 June 2015
We show theoretically that finite hierarchical assemblies of clusters consisting magnetic (magnetite) and plasmonic (gold) nanoparticles show dramatically increased values of the magnetochiral dichroism compared to those measured in conventional materials exhibiting this phenomenon (liquid molecular systems, anisotropic crystals and chiral ferromagnets). These values are attributed to the strong interaction of the magnetite nanoparticles within the clusters as well as by the excitation of surfaceplasmons in the gold nanoparticles. Along with the magnetochiral dichroism, in the studied hierarchical magnetoplasmonic designs, magneto-optical phenomena such as magnetic dichroism and Faraday rotation are also enhanced relative to the case of purely magnetic nanostructures. & 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Magneto-topics B. Faraday effect C. Plasmonics D. Nanoparticles
1. Introduction The term magnetochirality entails phenomena related with electromagnetic (EM)-wave propagation in chiral substances or structures under the influence of an external magnetic field such as birefringence in EM wave refraction or dichroism [1]. The presence of an external magnetic field within a chiral medium introduces time-reversal as well as space-reversal symmetry breaking simultaneously, and, as a second-order phenomenon, it is very hard to measure experimentally. So far, magnetochirality has been verified in liquid molecular systems, organic compounds, anisotropic crystals and chiral ferromagnets [2–14]. Recently, it has been theoretically proposed that magnetochiral dichroism (MChD) can be promoted in chiral magnetic metamaterials such as helical lattices of magnetic garnet spheres [15]. Moreover, it has been demonstrated experimentally that chiral magnetic nanohelices can exhibit strong MChD in the optical regime [16]. In the present work we present a new design with which MChD can be enhanced by several orders of magnitude in clusters of magnetic (Fe3 O4 – magnetite) nanoparticles (NPs) as well as in assemblies of clusters of magnetite NPs due to the interaction of the magnetite NPs within the clusters. By substituting magnetite NPs with gold NPs in the clusters, the MChD can be even more enhanced by the excitation of surface-plasmon resonances in the surface of the gold NPs. Such clusters are termed as binary magnetoplasmonic clusters since they consist of magnetic (magnetite) and gold (plasmonic) NPs. Below we provide a brief outline of the theory of
n
Tel.: þ 30 211 7721481. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.ssc.2015.05.016 0038-1098/& 2015 Elsevier Ltd. All rights reserved.
magnetochirality along with a presentation of the basic quantities involved.
2. Magnetochiral dichroism The dielectric tensor of chiral media subject to a magnetic field B, to first order in wavevector k and B is written as [3] L;R L;R ϵL;R 7 ðω; k; BÞ ¼ ϵ0 ðωÞ 7 αNCD ðωÞk 7 β MCD ðωÞB þ γ MChD ðωÞk B
ð1Þ
where the symbol L indicates left-circularly polarized (LCP) and R indicates right-circularly polarized (RCP) light. αL;R NCD k is the contribution of natural circular dichroism (NCD) (in the absence of magnetic field, i.e., B ¼ 0), β MCD ðωÞB is the contribution of magnetic circular dichroism (MCD- Faraday effect), and the third term γ L;R ðωÞk B corresponds to the MChD effect taking place in the MChD presence of a magnetic field acting on a chiral medium. The MChD term depends on the relative orientation of the wavevector k and the magnetic field B, on the sense of handedness of the chiral medium and it is independent of the polarization of incident light (MChD occurs for unpolarized incident light). The above three effects are substantiated via the measurement of absorption circular dichroism (CD) for LCP and RCP incident light, i.e., ARCP ALCP CD ¼ 2 ARCP þ ALCP
ð2Þ
NCD ¼ CDðB ¼ 0Þ
ð3Þ
MCD ¼ CDðBÞ NCD
ð4Þ
MChD ¼ Aðk↑↑BÞ Aðk↑↓BÞ
ð5Þ
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Fig. 1. (Color online) (a): A spherical cluster of 170 magnetite nanoparticles of 20 nm radius, i.e., the average radius of the cluster is about 160 nm while the average interparticle distance is 0.5 nm. (b): A tetramer of clusters placed at the positions: (320,0,0) nm, (0,480,0) nm, (0, 320,0) nm, and (0,0,480) nm.
where A in the last of the above equations is the absorbance for unpolarized light, i.e., A ¼ ðARCP þ ALCP Þ=2. When the real part of the dielectric tensor of 1 is much larger than its imaginary part, then MChD ðNCDÞ ðMCDÞ verifying the cross-effect nature of MChD [3].
3. Description of the magnetoplasmonic clusters Our case study are the material designs depicted in Fig. 1. Fig. 1a shows a cluster of magnetite NPs arranged randomly around the center of the cluster without touching each other. Spherical clusters of magnetite nanoparticles have been formed by self-assembly techniques based on solvophobic interactions [17]. The magnetite NPs have 20 nm radius while the average cluster radius is 160 nm. The average interparticle distance is 0.5 nm. Fig. 1b shows an assembly (tetramer) consisting of the clusters of Fig. 1a wherein the clusters are placed at positions: (320,0,0) nm, (0,480,0) nm, (0, 320,0) nm, and (0,0,480) nm. This tetramer possesses an intrinsic structural chirality which is prerequisite for observing the magnetochiral phenomena. It is worth noting that in the single cluster of magnetite NPs of Fig. 1a, there is also a residual structural chirality stemming from the inequivalent (random) positioning of the magnetite NPs around the center of the cluster. The EM modeling of the designs of Fig. 1 is performed via the Discrete-Dipole Approximation (DDA) technique [18] for magnetooptical (MO) targets (scatterers) [19,20]. In the calculations that follow, the dielectric tensor (diagonal and off-diagonal elements) of the magnetite NPs is taken from experimental measurements of bulk magnetite [21,22]. The dielectric function of the gold NPs is also taken from experiment [23]. The corresponding azimuth and ellipticity rotation angles which quantify the magnitude of the Faraday effect, are calculated as the real and imaginary part, respectively, of the difference in the extinction cross sections between LCP and RCP incident light [20]. Fig. 2. (Color online) (a) Azimuth and ellipticity rotation angle, (b) NCD, (c) MCD and (d) MChD for light incident on the cluster of Fig. 1a.
4. Results and discussion We begin by studying the single cluster of magnetite NPs shown in Fig. 1a. Namely, in Fig. 2, we show the azimuth and ellipticity rotation angles (a), CD (b), MCD (c) and MChD (d) for the cluster of Fig. 1a. Light is incident along the z-axis (k ¼ kz z^ ) while an external magnetic field B ¼ 0:5 T is applied either parallel or antiparallel to the incident wavevector k. From Fig. 2a, we observe that both rotation angles are of the order of a hundreds of millidegrees which are values at least one of order of magnitude
larger than for isolated magnetite NPs [19]. This is an expected result since the interaction of magnetic NPs enhances the MO effects such as the rotation angles of incident light and MCD – see Fig. 2c [24]. The NCD spectrum depicted in Fig. 2b does not depend on the application of the external field and is a result of the structural chirality of the assembly. However, since the cluster of Fig. 1a consists of NPs which are randomly positioned in space and not in a chiral fashion, the values of NCD are much lower than genuinely chiral designs of NPs [25–29].
V. Yannopapas / Solid State Communications 217 (2015) 47–52
Fig. 3. (Color online) (a) Azimuth and ellipticity rotation angle, (b) NCD, (c) MCD and (d) MChD for light incident on a spherical cluster of 170 magnetite nanoparticles of 20 nm radius, i.e., the average radius of the cluster is about 240 nm. The average interparticle distance is 0.75 nm.
The MChD spectrum, however, shows an opposite trend compared to the NCD and MCD spectra as it becomes weaker (smaller absolute values) with increasing wavelength. This is a demonstration of the so-called pure MChD being distinct from the cascaded MChD associated with the product ðNCDÞ ðMCDÞ [3]. A pure MChD effect has been recently demonstrated experimentally in chiral nanomagnets [16]. Namely, MChD is a cross effect and takes
49
Fig. 4. (Color online) (a) Azimuth and ellipticity rotation angle, (b) NCD, (c) MCD and (d) MChD for light incident along the positive z-axis at the tetramer of Fig. 1b.
place in systems containing both natural circular dichroism (NCD) and magnetic circular dichroism (MCD). Therefore, to a first approximation, an enhancement of both NCD and MCD leads to an increase of the magnitude of MChD (cascade effect). However, the conditions for explaining the resulting MChD as a cascade effect of NCD and MCD is that the real part of the dielectric tensor elements be much larger than the corresponding imaginary parts.
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Fig. 5. (Color online) (a) Azimuth and (b) ellipticity rotation angles for light incident along the positive z-axis at the tetramer of Fig. 1b, for various binary mixtures of 20 nm magnetite (Fe3 O4 ) and gold NPs.
By inspecting the elements of the dielectric tensor of magnetite (see Figs. S1 and S2 of the supplemental material) it is evident that such a condition is not satisfied. In Fig. 3 we consider a more dilute cluster of magnetite NPs, i.e., a cluster consisting, again, of 170 magnetite nanoparticles of 20 nm radius, but with larger average radius, i.e., 240 nm. This means that the average interparticle distance now is 0.75 nm (instead of 0.5 nm in Fig. 2). We observe that the range of values for the NCD is more or less the same as for the denser cluster of Figs. 1a and 2. For the MO effects we observe opposite trends. While both rotations angles are significantly reduced (see Fig. 3a), MCD (Fig. 3c) is enhanced by 2 orders of magnitude, on the average. The fact that a more close-packed arrangement of NPs does not necessarily favor MO phenomena has already been previously reported [24]. However, MChD, which is the main focus of our study here, has been reduced by one order of magnitude (the absolute value of), on the average. We, therefore, continue with the dense cluster of Figs. 1a and 2 in an effort to enhance the phenomenon of magnetochirality. Next, in Fig. 4 we study the case of the chiral assembly (tetramer) of magnetoplasmonic-nanoparticle clusters as shown in Fig. 1b. Evidently, all related quantities, i.e., rotation angles, NCD, MCD and MChD are enhanced due to the chiral positioning of the clusters (the tetramer lacks of mirror symmetry). The azimuth and ellipticity rotation angles are increased by more than the order of magnitude thanks to the chiral arrangement to the clusters but, primarily, thanks to the increase in the mass of magneto-optical material (more magnetite NPs). In the same trend, all the three dichroism spectra (NCD, MCD, MChD) are also enhanced by about one order of magnitude. The local maxima observed in the MCD, MChD spectra correspond to a local maximum of the off-diagonal (magneto-optical) elements of the dielectric tensor of magnetite (see Fig. S2 of the supplemental material) which is more or less
Fig. 6. (Color online) (a) NCD, (b) MCD and (c) MChD for light incident along the positive z-axis at the tetramer of Fig. 1b, for various binary mixtures of 20 nm magnetite (Fe3 O4 ) and gold NPs.
expected as the influence of an externally applied magnetic field is more evident when the corresponding MO tensor elements are maximized. In hope of enhancing ever further the MChD effect, we substitute some of the magnetite NPs in the clusters by gold ones. Gold NPs support surface-plasmon (SP) resonances, i.e., plasma oscillations occurring at the surface of the gold NP. The strong confinement of light in subwavelength volumes such as the surface of gold NP results in huge values of the local field, boosting the impact of a plethora of phenomena and properties such as Raman scattering, nonlinearities, light-matter interactions, to name a few. Among these phenomena which are promoted by SP excitations are the MO phenomena such as the Kerr/Faraday effects and MCD which take place in nanostructures combining magnetic and plasmonic functionalities [30–39]. In Fig. 5 we show the azimuth and rotation angles corresponding to the Faraday effect, for the tetramer of Fig. 1b where a fraction (see inset) of the 20 nm magnetite NPs have been substituted by gold NPs of the same size. We observe that the MO Faraday effect is enhanced around and above the SP resonance of gold NP (around 530 nm) as
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dramatically the MO effect among the magnetite NPs and outweighs the contribution of the chiral arrangement of the clusters in space. The latter, again, suggests that the MO effect dominates all other sources of chirality and implies that the observed MChD is not necessarily a cascaded phenomenon of magneto-optical and natural dichroism (see the discussion above).
5. Conclusion We have shown theoretically that the magneto-optical and magnetochiral effects are dramatically enhanced in spherical clusters of magnetic (magnetite) nanoparticles as well as in chiral assemblies of such, thanks to their mutual interaction within the same or neighboring clusters. The phenomenon is maximized with the substitution of some magnetite nanoparticles with gold ones which boost the magneto-optical effect within the magnetite nanoparticles and subsequently the magnetochiral dichroism which is an especially weak phenomenon in nature. Spherical clusters of magnetite nanoparticles have already been realized in the laboratory via bottom-up self-assembly methods [17] while chiral assemblies of such clusters can be realized in the same manner, via, e.g., DNA-assisted self-assembly [40–42].
Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.ssc.2015.05.016. References
Fig. 7. (Color online) (a) NCD, (b) MCD and (c) MChD for light incident along the positive z-axis at a single cluster (Fig. 1a), for various binary mixtures of 20 nm magnetite (Fe3 O4 ) and gold NPs.
a result of the excitation of this resonance by incident light. Namely, the MO effect is proportional to the local electric field which is, however, greatly enhanced within the magnetite NPs due to the spill over of the electric field in the neighboring gold NPs [37]. This is much more evident in the MCD of Fig. 6b where the enhancement relative to the case of purely magnetic clusters is more than 3 orders of magnitude. MChD (Fig. 6c) is also enhanced by 2 orders of magnitude on the average relative to the case of clusters with magnetite NPs only. The range of values of the NCD (Fig. 6a) is also increased but less than MCD and MChD as the dramatic increase in the MO effect does not affect directly the NCD. Lastly, in Fig. 7 we show the all three dichroism spectra (NCD, MCD and MChD) for a single cluster consisting of mixtures of 20 nm magnetite and gold NPs. Evidently, we observe that all three types of dichroism assume more or less the same values for the single cluster (Fig. 7) as well as for the tetramer of clusters (Fig. 6) of mixtures of magnetite and gold NPs. This in contrast to the case of pure magnetite clusters wherein the chiral positioning of the magnetite clusters enhances all CD spectra by one order magnitude. It seems that the presence of the gold NPs enhances
[1] L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon, Oxford, 1984. [2] G.L.J.A. Rikken, E. Raupach, Nature (London) 390 (1997) 493. [3] G.L.J.A. Rikken, E. Raupach, Phys. Rev. E 58 (1998) 5081. [4] P. Kleindienst, G.H. Wagnière, Chem. Phys. Lett. 288 (1998) 89. [5] N.G. Kalugin, P. Kleindinst, G.H. Wagnière, Chem. Phys. 248 (1999) 105. [6] G.L.J.A. Rikken, E. Raupach, Nature (London) 405 (2000) 932. [7] M. Vallet, R. Ghosh, A. Le Floch, T. Ruchon, F. Bretenaker, J.Y. Thépot, Phys. Rev. Lett. 87 (2001) 183003. [8] M. Saito, K. Ishikawa, K. Taniguchi, T. Arima, Phys. Rev. Lett. 101 (2008) 117402. [9] C. Train, R. Gheorghe, V. Krstic, L.M. Chamoreau, N.S. Ovanesyan, G.L.J. A. Rikken, Nat. Mater. 7 (2008) 729. [10] Y. Kitagawa, H. Segawa, K. Ishii, Angew. Chem. Int. Ed. 50 (2011) 9133. [11] S. Miyahara, N. Furukawa, J. Phys. Soc. Jpn. 81 (2012) 023712. [12] S. Kibayashi, Y. Takahashi, S. Seki, Y. Tokura, Nat. Commun. 5 (2014) 4583. [13] S. Harroti, K. Ishii, Opt. Mater Express 4 (2014) 2423. [14] R. Sessoli, M.E. Boulon, A. Caneshchi, M. Mannini, L. Poggini, F. Wilhelm, A. Rogalev, Nat. Phys. 11 (2015) 69. [15] A. Christofi, N. Stefanou, Opt. Lett. 38 (2013) 4629. [16] S. Eslami, J.G. Gibbs, Y. Rechkemmer, J. van Slageren, M. Alarcón-Correa, T.C. Lee, A.G. Mark, G.L.J.A. Rikken, P. Fischer, ACS Photon. 1 (2014) 1231. [17] J. Zhuang, H. Wu, Y. Yang, Y.C. Cao, J. Am. Chem. Soc. 129 (2007) 14166. [18] B.T. Draine, Astrophys. J. 333 (1988) 848. [19] D.A. Smith, Y.A. Barnakov, B.L. Scott, S.A. White, K.L. Stokes, J. Appl. Phys. 97 (2005) 10504. [20] D.A. Smith, K.L. Stokes, Opt. Express 14 (2006) 5746. [21] A. Schlegel, S.F. Alvarado, P. Wachter, J. Phys. C: Solid State Phys. 12 (1979) 1157. [22] X. Zhang, J. Schoenes, P. Wachter, Solid State Commun. 39 (1981) 189. [23] R.B. Johnson, R.W. Christy, Phys. Rev. B 6 (1972) 4370. [24] A. Christofi, N. Stefanou, N. Papanikolaou, Phys. Rev. B 89 (2014) 214410. [25] V. Yannopapas, J. Phys. Condens. Matter. 18 (2006) 6883. [26] Z. Fan, A.O. Govorov, Nano Lett. 10 (2010) 2580. [27] Z. Fan, A.O. Govorov, J. Phys. Chem. C 115 (2011) 13254. [28] A. Guerrero-Martínez, J.L. Alonso-Gómez, B. Auguié, M.M. Cid, L.M. LizMarzán, Nano Today 6 (2011) 381. [29] S. Droulias, V. Yannopapas, J. Phys. Chem. C 117 (2013) 1130. [30] Y. Li, Q. Zhang, A.V. Nurmikko, S. Sun, Nano Lett. 5 (2005) 1689. [31] J.B. González-Díaz, A. García-Martín, J.M. García-Martín, J.M.A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, M. Käll, Small 4 (2008) 202. [32] G. Armelles, J.B. González-Díaz, A. García-Martín, J.M. García-Martín, A. Cebollada, M.U. González, A. Srdjan, J. Cesario, R. Quidant, G. Badenes, Opt. Express 16 (2008) 16104. [33] F.E. Moolekamp, K.L. Stokes, IEEE Trans. Magn. 45 (2009) 4888.
52
V. Yannopapas / Solid State Communications 217 (2015) 47–52
[34] P.K. Jain, Y. Xiao, R. Walsworth, A.E. Cohen, Nano Lett. 9 (2009) 1644. [35] J.B. González-Díaz, B. Sepúlveda, B.A. García-Martín, G. Armelles, Appl. Phys. Lett. 97 (2010) 043114. [36] G.X. Du, T. Mori, M. Suzuki, S. Saito, H. Fukuda, M. Takahashi, Appl. Phys. Lett. 96 (2010) 081915. [37] G. Armelles, A. Cebollada, A. García-Martín, M.U. González, Adv. Opt. Mater. 1 (2013) 10.
[38] [39] [40] [41]
A. Christofi, N. Stefanou, Phys. Rev. B 87 (2013) 115125. A. Christofi, N. Stefanou, Phys. Rev. B 88 (2013) 125133. A. Mastroianni, S.A. Claridge, A.P. Alivisatos, J. Am. Chem. Soc. 131 (2009) 8455. J. Sharma, R. Chhabra, A. Cheng, J. Brownell, J.Y. Liu, H. Yan, Science 323 (2009) 112. [42] S.J. Tan, M.J. Campolongo, D. Luo, W. Cheng, Nat. Nanotechnol. 6 (2011) 268.