Optomagnetic Effect Induced by Magnetized Nanocavity Plasmon

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Optomagnetic Effect Induced by Magnetized Nanocavity Plasmon Sai Duan, Zilvinas Rinkevicius, Guangjun Tian, and Yi Luo J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.9b07817 • Publication Date (Web): 20 Aug 2019 Downloaded from pubs.acs.org on August 20, 2019

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Journal of the American Chemical Society

Optomagnetic Effect Induced by Magnetized Nanocavity Plasmon Sai Duan,†,‡ Zilvinas Rinkevicius,‡,¶,§ Guangjun Tian,∥ and Yi Luo∗,† †Hefei

National Laboratory for Physical Sciences at the Microscale, Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, 230026 Anhui, P. R. China. ‡Department

of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, S-106 91 Stockholm, Sweden. ¶Swedish e-Science Research Centre, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden. §Department of Physics, Kaunas University of Technology, Kaunas LT-51368, Lithuania.  ∥Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, P. R. China

Supporting Information Placeholder ABSTRACT: We propose a new type of optomagnetic

effect induced by a highly confined plasmonic field in a nanocavity. It is shown that a very large dynamic magnetic field can be generated as the result of the inhomogeneity of nanocavity plasmons, which can directly activate spin-forbidden transitions in molecules. The dynamic optomagnetic effects on optical transitions between states of different spin multiplicities are illustrated by first principles calculations for C60. Remarkably, the intensity of spin forbidden singlet-totriplet transitions can even be stronger than that of singlet-to-singlet transitions when the spatial distribution of plasmon is comparable with the molecular size. This approach not only offers a powerful optomagnetic means to rationally fabricate molecular excited states with different multiplicities but also provides a groundbreaking concept of the light-matter interaction that could lead to the observation of new physical phenomena and the development of new techniques.

Electromagnetic (EM) field by name has electric and magnetic components. However, in the optical region, the strength of the magnetic component in EM field from conventional sources is very small, resulting in the negligible effect of the magnetic component when it interacts with substances.1 Although some interesting optomagnetic effects2 were discovered in the past for the condensed gyrotropic materials, our ability to control spin states3 in ordinary materials is very limited. We will demonstrate here that the locality of the plasmonic field could significantly enhance the magnetic component in EM field, providing a unique means for the manipulation of the molecular spin states. Within non-relativistic regime, the light-matter interaction is governed by the minimal coupling

Hamiltonian,4,5 which is adequate even for plasmonic fields.6–10 In this context, the light-matter interaction Hamiltonian, 𝐻′, can be expressed as the summation of the vector potential component 𝐻′𝐴 and magnetic field component 𝐻′𝐵4,6 𝐻′ = 𝐻′𝐴 + 𝐻′𝐵 1

𝐻′𝐴 = 2∑𝑘[𝐩𝑘 ⋅ 𝐀(𝐫𝑘,𝑡) + 𝐀(𝐫𝑘,𝑡) ⋅ 𝐩𝑘]

(1)

1

𝐻′𝐵 = 2∑𝑘𝝈𝑘 ⋅ 𝐁(𝐫𝑘,𝑡) where subscript “k” represents the kth electron, 𝐩 is the momentum operator of the electron, 𝐀 is the vector potential of the light, 𝐫 is the electron position, 𝝈 is the Pauli matrix, and 𝐁 is the magnetic field determined by8,11 𝐁(𝐫𝑘,𝑡) = ∇ × 𝐀(𝐫𝑘,𝑡). Here the high-order 𝐀2 (𝐫𝑘,𝑡) term is neglected.5,11 In general, for a monochromatic EM field, vector potential could be expressed as (Figure 1a) 𝐀(𝐫,𝑡) = 𝐴0𝑔(𝐫)𝑒 ―ı𝜔𝑡𝐧 + c.c. (2) where 𝐴0 is the constant field amplitude, 𝑔(𝐫) is the mode function that represents its spatial distribution, ω is the frequency of the field, 𝐧 is the norm of the vector potential, and 𝐁(𝐫,𝑡) = 𝐴0∇𝑔(𝐫) × 𝐧𝑒 ―ı𝜔𝑡 + c.c. (3) As a consequence, large magnetic field would be expected in highly inhomogeneous EM field. It is known that the vector potential component of EM field governs the spin-independent 𝐻′𝐴 term to determine selection rules between states of the same multiplicity. The magnetic field component controls the spindependent 𝐻′𝐵 term that is responsible for selection rules between states of different multiplicities. For a plane wave EM field, we have 𝑔(𝐫) = 𝑒ı𝐤 ⋅ r, where k is the wave vector. Within the dipole approximation,1 i.e.,

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𝑒ı𝐤 ⋅ r ≈ 1, the transition between the same multiplicity is controlled by the spatial selection rule (the so-called “dipole selection rule”).1,5 Meanwhile, the dipole approximation (𝑔 ≈ 1) gives zero magnetic field (Eq. 3). As a result, the transitions between different multiplicities in optical regions are strictly forbidden, i.e. the so-called “spin selection rule”.13

Figure 1. (a) Schematic of a single C60 in a cavity with the 6-Ring adsorption configuration. (b) Experimental (black line) and theoretical (blue line) absorbance of C60 in vacuum. The experimental data were taken from Coheur et al.12 The theoretical spectrum was convoluted by a Lorentzian function with full width at half-maximum of 0.3 eV. The red and blue bars on the top of xaxis indicate the triplet and singlet transition energies, respectively. The gray zone indicates the dipole and spin forbidden region for the absorption of C60.

The selection rules can be well demonstrated by the optical absorption of C60 with very high Ih symmetry. Under the dipole approximation, only transitions to 1T1u excited states are optically allowed.15 The first absorption band (the C band) in the experimental spectrum12 is thus resulted from 11T1u and 21T1u states. The energy region lower than 2.5 eV consists of many forbidden states in Figure 1b. Although the inclusion of the Herzberg-Teller (for singlet-to-singlet) and spinorbit coupling (for singlet-to-triplet) could soften both selection rules, it only makes very small contribution to the low energy transitions as illustrated in previous experiments (black line in Figure 1b).12 Without considering both vibronic and spin-orbit couplings, our computational method works very well for the low-lying excited states that are relevant to the plasmonic effects as shown in Figure 1b. In the inhomogeneous EM field, the function 𝑔(𝐫) becomes a part of the transition operator. As a result, the

spatial selection rule relies on the symmetry of the whole interactive system that includes the molecule and plasmonic field.16 Meanwhile, a large field gradient leads to an enhanced magnetic field (Eq. 3), making the transitions between different multiplicities possible. In this context, the spatially confined plasmon generated either by optical excitation or electron current has offered perfect choices.

Figure 2. Electric (left) and magnetic (right) field distribution in cavity with different sizes of the confined sharp plasmonic mode (Γ from 20 to 5.27 Å). The incident power density, wavelength, and the maximum enhancement factor for electric field are set to 100 W/cm2 (electric field amplitude of 1.9×104 V/m), 632.8 nm, and 100, respectively. The open circles represent the electric field distribution adopted from Figure 1E of Ref. 14 and the size of the broad plasmonic mode is the same for all situations (see Supporting Information for details).

In recent years, the size of the plasmonic cavity has been constantly decreased,14,19–21 while many exciting new properties of the plasmonic field have also been discovered, including the nonlocality of dielectric response, quantum tunneling, and strong coupling between the plasmon and the molecular layer.22–25 It was found both theoretically and experimentally that the spatial distribution of the plasmon could be confined within a size of 2 nm in a cavity,21,26 which was responsible for sub-nm resolution Raman images of a porphyrin derivative.20 A recent study has shown that the plasmon could be further confined in a picocavity under the cryogenic temperatures.14 As shown in Figure 2, the electric field in picocavity consists of two confined plasmonic modes.14 The size of the broad and sharp plasmonic mode is around 15 nm and 5.27 Å, respectively, which can generate a magnetic field up to 1.3 Tesla. Hence, even with vanished spin-orbit coupling, the spin selection rule can be completely removed under such a circumstance, resulting in a complete new phenomenon, namely plasmon induced spin transition (PIST). It is certainly very useful for studying organic systems, as they often possess with negligible spin-orbit coupling strength.


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Journal of the American Chemical Society

To verify the actual magnitude of PISTs, the absorbance of a highly symmetric C60 under different confined plasmons was calculated (full details can be found in the Supporting Information). The interaction between physisorbed C60 and substrate is reduced by introducing a spacer, as widely employed in scanning probe microscopy experiments.27–29 In the calculations, different sizes of the sharp plasmonic mode (Γ hereafter) were considered, while the size of the broad plasmonic mode was fixed to 15 nm as the “background” of the cavity14 (see Supporting Information for details). It was suggested by our field simulations of the adsorbate-gap combined system (Figure S1) and previous studies30,31 that the actual magnitude of Γ could be strongly related to the molecular size. Therefore, the smallest Γ in this study is set to the size of C60 (7 Å),32 for which the maximum magnetic field is around 0.75 Tesla (Figure 2). In the calculations, the plasmon intensities were taken from Refs. 17 and 18 (Figure 3a), which could produce the required plasmon around 2 and 3 eV, respectively. The mostly observed 6-Ring configuration of C60 on a spaced substrate33,34 (Figure 1a) was considered.

Figure 3. (a) Energy profile of plasmons around 2.0 and 3.0 eV. Adapted from Figure 3a (Tip 5) and Box 2 of Refs. 17 and 18, respectively. (b) Calculated absorbance of a single C60 with the 6Ring configuration in forbidden (left) and allowed (right) region under the different sizes of the confined sharp plasmonic mode (Γ from 20 to 7 Å). The plasmons are placed on around 2 Å above the center of the central six-member ring. The red and blue areas in absorption spectra represent the contributions from triplet and singlet excited states, respectively. The calculated spectra were convoluted by a Lorentzian function with full width at halfmaximum of 0.05 eV. (c) Schematic illustration of magnetic field (red) for uniform and highly localized electromagnetic field. (d) Schematic illustration of point group changes from isolated molecule to the whole interactive system (including C60 and plasmon) in picocavity. The color surface plot represents the amplitude distribution of the electric field.

Calculated absorption spectra with plasmon localized on the top of the center of the six-member ring were depicted in Figure 3b. It is found that for Γ of 20 Å, which is about 3 times of the molecular size, there are no

significant PISTs due to the negligible magnetic field around the adsorbate (Figure 2). However, the appearance of 11Hg around 2.15 eV in the forbidden region indicates that the spatial selection rule is already broken with a large Γ. The calculated oscillator strength (OS) of 11Hg is 4.26, which is significantly larger than that of allowed 21T1u under uniform EM field (all OSs were listed in Table S1), attributed to the considerable enhancement (around 45) of electric field with Γ of 20 Å (Figure 2). Consequently, the OSs of 11T1u and 21T1u are also enhanced to 6.45 and 169.06, respectively. It is noted that the 11T1u band becomes the most intense one in the allowed region as shown in Figure 3b. This should be contributed by the energy distribution of the plasmon around 400 nm (Figure 3a), which significantly suppresses the intensity of 21T1u. When Γ approaches the molecular size, for example 10 Å, the PIST of 13Hg around 1.9 eV emerges in the forbidden region, highlighting the breakdown of the spin selection rule in highly localized EM field (Figure 3c). The enhanced magnetic field originated from the field gradient (Figure 2) plays the decisive role here. We also noted that, with such a highly localized plasmonic field, the symmetry of the whole interactive system, i.e., the entire system that combines the adsorbate (C60) and the plasmonic field, has reduced from Ih to C3v as shown in Figure 3d. As a result, only 1T1g, 1T2g, 1Au, 1Hu as well as 3A and 3A states remain forbidden, while all other g u states become allowed (Table S2). Specifically, the calculated OSs of 13Hg and 11Hg are 2.99 and 7.36, respectively. Owing to the similar plasmonic intensity at the excitation energy of 13Hg and 11Hg (Figure 3a), the 11Hg transition is still the most intense band in the forbidden region. Although the OS of 21T1u is increased to 277.94 (also see the calculated quantum yields given in Figure S2), the PIST of 13T1u that has OS of 25.46 contributes the most intense band around 2.9 eV in the allowed region. This is again attributed to the significant suppression of 21T1u by the inefficient excitation of plasmon around 3.8 eV (Figure 3a). It is noted that the transition of 11T1u and PIST of 23T1u (around 3.2 eV) are also observable in the allowed region. For a smaller cavity, stronger PISTs are expected to occur. The calculated OS of 13Hg with Γ of 7 Å is 16.99, which is more than five times larger than that with 10 Å. On the other hand, the OS of 11Hg only slightly increases from 7.36 to 9.17. Hence, PIST of 13Hg becomes the most intense band in the forbidden region. It is noted that a new PIST of 13T2u with OS of 8.02 also contributes 7% to the most intense band around 2.9 eV. Strikingly, with Γ of 7 Å, the OS of 13T1u is more than 400 times larger than that of optically allowed 21T1u (the C band in gas phase), highlighting the effect of spatially highly inhomogeneous magnetic field in picocavity plasmons. It should be noted that the x and y components of magnetic field in the sharp plasmonic



mode determine the PISTs in the present modeling. Thus, the observation of PISTs under an even larger gap is feasible (Figure S3). Definitely, we would expect further enhanced PISTs for smaller molecules, as they could generate even smaller picocavity.14 It is noted that PISTs would be position dependent, as the symmetry could be further reduced to C1 symmetry as shown in Figure 3d. The position dependent absorbance and images can be found in Figures S4-6. In summary, we theoretically demonstrate a new optomagnetic effect generated from highly confined plasmonic field that can break the strict spin selection rule in optical spectroscopies. Our findings open up an entirely new optical channel for molecular dark states and can be naturally extended to other linear and nonlinear optical processes, which could have strong impact on applications in plasmon based single molecular spectroscopies, sensors and catalysis.

(6) Rivera, N.; Kaminer, I.; Zhen, B.; Joannopoulos, J. D.; Soljačić, M. Shrinking Light to Allow Forbidden Transitions on the Atomic Scale. Science 2016, 353, 263–269. (7) Altewischer, E.; van Exter, M. P.; Woerdman, J. P. Plasmon-Assisted Transmission of Entangled Photons. Nature 2002, 418, 304–306. (8) Archambault, A.; Marquier, F.; Greffet, J.-J.; Arnold, C. Quantum Theory of Spontaneous and Stimulated Emission of Surface Plasmons. Phys. Rev. B 2010, 82, 035411. (9) Tame, M. S.; McEnery, K. R.; Özdemir, Ş. K.; Lee, J.; Maier, S. A.; Kim, M. S. Quantum Plasmonics. Nat. Phys. 2013, 9, 329–340. (10) Tielrooij, K. J.; Orona, L.; Ferrier, A.; Badioli, M.; Navickaite, G.; Coop, S.; Nanot, S.; Kalinic, B.; Cesca, T.; Gaudreau, L.; Ma, Q.; Centeno, A.; Pesquera, A.; Zurutuza, A.; de Riedmatten, H.; Goldner, P.; García de Abajo, F. J.; Jarillo-Herrero, P.; Koppens, F. H. L. Electrical Control of Optical Emitter Relaxation Pathways Enabled By Graphene. Nat. Phys. 2015, 11, 281–287. (11) Filter, R.; Mühlig, S.; Eichelkraut, T.; Rockstuhl, C.; Lederer, F. Controlling the Dynamics of Quantum Mechanical Systems Sustaining Dipole-Forbidden Transitions via Optical Nanoantennas. Phys. Rev. B 2012, 86, 035404. (12) Coheur, P. F.; Carleer, M.; Colin, R. The Absorption Cross Sections of C60 and C70 in the Visible-UV Region. J. Phys. B: At. Mol. Opt. Phys. 1996, 29, 4987–4995. (13) McWeeny, R. Spins in Chemistry; Dover Publications: Mineola, N.Y, 2004.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website: The details of methods, symmetry analysis, calculated oscillator strengths, as well as additional spectra and images.

AUTHOR INFORMATION

(14) Benz, F.; Schmidt, M. K.; Dreismann, A.; Chikkaraddy, R.; Zhang, Y.; Demetriadou, A.; Carnegie, C.; Ohadi, H.; de Nijs, B.; Esteban, R.; Aizpurua, J.; Baumberg, J. J. Single-Molecule Optomechanics in “Picocavities”. Science 2016, 354, 726–729. (15) Cotton, F. A. Chemical Applications of Group Theory; Wiley:  New York, 1990.   (16) Xie, Z.; Duan, S.; Wang, C.-K.; Luo, Y. Lighting Up Long-Range Charge-Transfer States By a Localized Plasmonic Field. Nanoscale 2017, 9, 18189–18193.   (17) Dong, Z.-C.; Zhang, X.-L.; Gao, H.-Y.; Luo, Y.; Zhang, C.;  Chen, L.G.; Zhang, R.; Tao, X.; Zhang, Y.; Yang, J.-L.; Hou, J.-G. Generation of Molecular Hot Electroluminescence By Resonant Nanocavity Plasmons. Nat. Photon. 2010, 4, 50–54.  

Corresponding Author

*[email protected] Notes

The authors declare no competing financial interest.

(18) Kneipp, K. Surface-Enhanced Raman Scattering. Phys. Today 2007, 60, 40–46.  

ACKNOWLEDGMENT

(19) Cang, H.; Labno, A.; Lu, C.; Yin, X.; Liu, M.; Gladden, C.; Liu, Y.; Zhang, X. Probing the Electromagnetic Field of a 15-Nanometre Hotspot By Single Molecule Imaging. Nature 2011, 469, 385–388.  

This work is supported by the Ministry of Science and Technology of China (2017YFA0303500), by the National Natural Science Foundation of China (21633007, 21790350), by Anhui Initiative in Quantum Information Technologies (AHY090000), and Swedish Research Council (VR). The Swedish National Infrastructure for Computing (SNIC) was acknowledged for computer time.

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Optomagnetic Effect Induced by Magnetized Nanocavity Plasmon

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