Surface Plasmon-Mediated Nanoscale Localization of Laser-Driven

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Surface plasmon-mediated nanoscale localization of laserdriven sub-THz spin dynamics in magnetic dielectrics Alexander Chekhov, Alexander I. Stognij, T. Satoh, Tatiana V. Murzina, I. Razdolski, and Andrzej Stupakiewicz Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00416 • Publication Date (Web): 11 Apr 2018 Downloaded from http://pubs.acs.org on April 11, 2018

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Surface Plasmon-Mediated Nanoscale Localization of Laser-Driven sub-THz Spin Dynamics in Magnetic Dielectrics Alexander L. Chekhov,∗,†,‡,¶ Alexander I. Stognij,§ Takuya Satoh,k Tatiana V. Murzina,† Ilya Razdolski,∗,¶ and Andrzej Stupakiewicz‡ Department of Physics, Moscow State University, 119991 Moscow, Russia, Faculty of Physics, University of Bialystok, 15-245 Bialystok, Poland, Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany, Scientific-Practical Materials Research Centre of the NASB, 220072 Minsk, Belarus, and Department of Physics, Kyushu University, 819-0395 Fukuoka, Japan E-mail: [email protected]; [email protected]

Abstract We report spatial localization of the effective magnetic field generated via the inverse Faraday effect employing surface plasmon polaritons (SPPs) at Au/rare-earth iron garnet interface. Analyzing, both numerically and analytically, the electric field of the SPPs at this interface, we corroborate our study with a proof-of-concept experiment showing efficient SPP-driven excitation of coherent spin precession with 0.41 THz ∗

To whom correspondence should be addressed Department of Physics, Moscow State University, 119991 Moscow, Russia ‡ Faculty of Physics, University of Bialystok, 15-245 Bialystok, Poland ¶ Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany § Scientific-Practical Materials Research Centre of the NASB, 220072 Minsk, Belarus k Department of Physics, Kyushu University, 819-0395 Fukuoka, Japan †

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frequency. We argue that the sub-diffractional confinement of the SPP electric field enables strong spatial localization of the SPP-mediated excitation of spin dynamics. We demonstrate a two orders of magnitude enhancement of the excitation efficiency at the surface plasmon resonance within a 100 nm layer of a dielectric garnet. Our findings broaden the horizons of ultrafast spin-plasmonics and open pathways towards non-thermal opto-magnetic recording on the nanoscale.

Keywords ultrafast spin dynamics, surface plasmon-polariton, inverse Faraday effect, rare-earth iron garnet, nonlinear optics, magnetoplasmonics Ultrafast all-optical control of spins with femtosecond laser pulses is a trending topic at the crossroads of photonics and magnetism with a direct impact on future magnetic recording. Unveiling light-assisted recording mechanisms for increasing the bit density beyond the diffraction limit without excessively heating the recording medium is an open challenge. The development of the next generation magnetic memory devices will be driven by the demand for fast magnetization switching, low energy consumption and high-density recording. 1 In spite of addressing the foremost issue, all-optical magnetization switching with femtosecond laser pulses in various metallic systems 2–5 requires heating close to the Curie temperature. Recently, new routes for non-thermal magnetization reversal in a dielectric garnet with the ultrafast magnetic recording event accompanied by extremely low heat load were demonstrated. 6 It is now widely accepted that the future of high-density all-optical magnetic recording depends on the achievements of sub-diffractional nanophotonics 7–11 featuring light localization on the nanoscale by surface plasmon resonances. As such, the fundamental understanding of the interactions of high-frequency coherent spin dynamics with plasmonic excitations on both nanometer and sub-picosecond scales in opto-magnetic media is highly desirable.

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Figure 1: (a) Effective static magnetic field induced by a propagating SPP at the Au/magnetic garnet interface. The spatial localization of the SPP electric field results in the interfacial confinement of HyIFE on the scale of 100 nm (governed by the optical properties of the dielectric medium). Numerical simulations of the spatial distributions of the SPP electric field |Ez |2 (b) and effective magnetic field HyIFE (c) at the SPP resonance at 1450 nm wavelength and 34 degrees angle of incidence. The inset in (c) illustrates the spatial localization of the laterally-averaged HyIFE in the garnet layer (z < 0) on the scale of 100 nm. (d) Spectral dependence of the reflectivity R (solid black line) and SPP-induced effective magnetic field HyIFE (blue) calculated using the Finite Difference Time Domain method. Experimental reflectivity spectrum is shown with a black dashed line. Here, we show that surface plasmon-polaritons in hybrid metal-dielectric structures can provide spatial confinement of the inverse Faraday effect, mediating the excitation of localized coherent spin precession with 0.41 THz frequency. We demonstrate a two orders of magnitude enhancement of the excitation efficiency at the surface plasmon resonance within a 100 nm layer of a dielectric garnet. Our findings broaden the horizons of ultrafast spin-plasmonics and open pathways towards non-thermal opto-magnetic recording on the nanoscale. Enabling the excitation of spin eigenmodes by circularly polarized femtosecond light pulses via the inverse Faraday effect (IFE), 12–16 the interaction of the spin excitations and light (optical field E) is described by the free energy F ∝ −δεij Ei Ej∗ , where δεij is the

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variation of the dielectric permittivity ε by magnons. Introducing a phase shift ϕ between Ei and Ej , for the resulting projection of the effective magnetic field HkIFE we get:

HkIFE = −

∂F ∝ κijk (Ei Ej∗ − Ei∗ Ej ) ∝ κijk |E|2 sin ϕ, ∂Mk

(1)

where κijk is the magneto-optical constant, εij = iκijk Mk . This field exerts a torque on the magnetization M and triggers its precessional motion. Since for circularly polarized light in transparent media ϕ = ±π/2, the sign of HkIFE is governed by the helicity of light polarization. For any linear polarization ϕ = 0 and the IFE vanishes. Microscopically, bearing a notable similarity 17 to the second-order optical rectification, an impulsive stimulated Raman scattering (ISRS) 18 employs two optical fields at frequencies ω1 , ω2 contained in the spectrum of the femtosecond laser pulse for the excitation of a spin eigenmode at Ω = ω1 − ω2 . 19,20 The explicit phase dependence in Eq. (1) reveals its key role for the ultrafast optomagnetic phenomena. Modern nanophotonics provides effective tools for engineering electric fields in nano-confined volumes, enabling resonant control of their amplitudes and phases. The spinphoton coupling can thus be mediated by collective electronic excitations, i.e. plasmons. The excitation of propagating surface plasmon polaritons (SPPs) at the metal-dielectric interface imposes a rigid phase shift ϕ between the in-plane x (parallel to the SPP propagation direction) and out-of-plane z components of the electric field: 21 Ez /Ex = ikx0 /kz00 . Here kx0 is q εm εd ω √ εd ω 00 SPP 0 00 the real part of the SPP wavenumber k = c εm +εd = kx + ikx and kz = Im c εm +εd , where εm , εd refer to the permittivities of the metal and dielectric, respectively. It is seen that although the SPPs are excited with linearly polarized light, in the SPP TM-wave there is a ϕ = π/2 phase shift between Ex and Ez . 22 Notably, despite the oscillatory spatial de0

pendence of these fields ∝ eikx x , the phase shift remains constant, giving rise to the static effective magnetic field HyIFE (Fig. 1a):

HyIFE

∝

0 2 kx −2(kx00 x−kz00 z) κijk |Ex | 00 e . kz

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(2)

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Owing to the nanoscale SPP field localization and amplification, HyIFE is enhanced and strongly confined in the vicinity of the metal-dielectric interface, which is otherwise unattainable in a transparent dielectric media. The inherently nonlinear-optical origin of HyIFE enables its twice as strong spatial localization, as compared to the SPP electric fields (Fig. 1,b-c). The sign of HyIFE , governed by the helicity of the light polarization in IFE, is now determined by the SPP propagation direction. Recently, a similar mechanism was discussed in other plasmonic systems 23,24 and was suggested to drive the nonlinear self-modulation of SPPs at magnetic interfaces. 25 These considerations are supported by the results of numerical simulations performed for the SPP excited at a model metal/dielectric interface (see Supporting Information). It is seen that the SPP excitation prominently enhances the electric fields Ex , Ez in the dielectric medium (Fig. 1b) and enables sizeable effective magnetic field HyIFE localized in the 100 nmthick dielectric layer adjacent to the interface (Fig. 1c). The rather complicated structure of the |Ez |2 and HyIFE distributions stems from the interference between the SPP and nonresonantly transmitted fields (see Supporting Information for details). To account for the spatial averaging within the laser spot (on the order of 50 µm), we consider laterally averaged values of the HyIFE (see inset in Fig. 1c). Exerting a torque on Mx , a short (given by the SPP lifetime, i.e. sub-ps) SPP-driven burst of HIFE can be observed experimentally as the SPP-mediated excitation of coherent spin precession in the dielectric employing p-polarized light, i.e. when the direct IFE is inactive. We have complemented a 380 µm-thick Gd-Yb-doped bismuth iron garnet single crystal (Gd4/3 Yb2/3 BiFe5 O12 , GdYbBIG) with a periodically perforated 50 nm-thick Au overlayer (800 nm period), allowing for the excitation of the SPPs at both Au/air and Au/garnet interfaces 26–28 (Fig. 2a). The grooves of the gold grating were oriented perpendicularly to the plane of incidence. The uniaxial anisotropy field in the GdYbBIG crystal was Hu = 0.62 kOe, the Curie temperature TC = 573 K, and the Gilbert damping α = 0.02, as obtained from the ferromagnetic resonance (FMR) spectroscopy. 29 GdYbBIG crystals strongly absorb

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Figure 2: (a) SPP dispersion map of a Au/garnet hybrid magneto-plasmonic crystal with a spatial periodicity of 800 nm, grooves depth of 50 nm and width of 100 nm. The dashed blue and red lines indicate the calculated dispersions of, correspondingly, Au/air and Au/garnet SPPs with the numbers corresponding to the diffraction order. The open circles and diamonds indicate the SPP resonances obtained from the experimentally measured reflectivity spectra. The purple vertical stripe and the red circle show the spectral tunability and width of the pump and probe pulses, respectively, as well as their angles of incidence in the experiments (34◦ and 25◦ , respectively). (b) Typical transient variations of the Faraday rotation. The red and green dashed lines indicate background contributions obtained within the data fitting procedure (see Supporting Information). The blue line illustrates the resulted fit to the experimental data. The inset exemplifies the exchange resonance dynamics of the magnetic moments of the rare earth (RE) and transition metal (TM) subsystems. (c) Experimental data with the background removed together with the fit lines. The green data points illustrate the spin dynamics excitation with circularly polarized light for comparison purposes. (d,e) Amplitude A and phase ψ of the spin precession as a function of the incident pump polarization, as extracted from the fitting procedure. The λ/4 wave plate angle of 0 degrees corresponds to the p-polarized excitation. The colored circles correspond to the data shown in (c) with respective colors.

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light in the visible range due to the presence of bismuth and rare-earth ions. 16 To that end, the geometrical parameters of the Au lattice were chosen such that the grating excitation in the near-IR range enables low-loss first-order Au/garnet SPPs. From the linear reflectivity spectra of the sample in the visible (halogen lamp) and in near-IR (Nd:YAG seeded optical parametric oscillator) ranges for the p-polarized light we obtained a dispersion map for the SPPs at the two interfaces as shown in Fig. 2a. A characteristic near-IR reflectivity spectrum for 34 degrees incidence is shown in Fig. 1d with the black dashed curve. The spin dynamics in hybrid plasmonic structure was studied in the pump-probe measurements using a Ti:Sa ultrafast amplifier (Ace, SpectraPhysics) with 800 nm output. Employing an optical parametric oscillator (TOPAS, SpectraPhysics), the pump beam wavelength was converted into the range of 1100-1500 nm. A delay line (Newport) in the probe channel was used to control the delay time between the pump and probe pulses. Intense 50 fs near-IR pump pulses were incident at 34 degrees on the sample exciting an SPP and inducing an effective static magnetic field HIFE - which drove a high-frequency (fex = 0.41 THz) exchange resonance mode in GdYbBIG. 16 The microscopic excitation mechanism is similar to that discussed in Ref. 15 A polarizer and a λ/4 wave plate were used to continuously control the polarization state of the pump beam from linear to circular. An external in-plane magnetic field of 1.2 kOe was applied along the SPP propagation direction with the help of an electromagnet. The pump fluence was set to 10 mJ/cm2 , while the probe fluence was about 100 times smaller. The sketch of the experimental scheme is shown in Fig. S1. In order to verify the SPP role in the excitation of the exchange resonance mode, we performed comparative measurements at the SPP resonance and away from it, taking advantage of the tunability of the pump wavelength (Fig. 2a). Figure 2b shows the characteristic transient variations of the Faraday rotation. Having removed the background, we fitted a decaying sine function to the oscillatory part of the data (Fig. 2c) and extracted the fit parameters. Figure 2d-e shows the amplitude A and phase ψ of the oscillations as a function of the pump polarization set by a λ/4 wave plate. For the off-resonant case (black), a

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Figure 3: (a-b) Spectral dependencies of the amplitude A and phase ψ of the exchange resonance mode for the circular (black) and close-to-linear (red, 4◦ λ/4 plate) pump excitation. A prominent feature at about 1400 nm corresponds to the SPP excitation at the Au/garnet interface. A smaller feature at about 1200 nm is pertinent to the interplay of the SPP at the Au/air interface and a 2nd order SPP at the Au/garnet interface. A phase shift of π is mathematically identical to the amplitude sign reversal, which is illustrated by red dashed curves. (c-d) Calculated efficiency of the SPP-driven excitation of the exchange resonance mode in thin garnet films. The HyIFE values are normalized to that obtained for the semi-infinite garnet film. The solid black line in (c) shows the SPP dispersion shift. The dashed vertical line at the garnet thickness of dcrit = 100 nm indicates the threshold below which the SPP-mediated IFE in hybrid metal-dielectric magneto-plasmonic systems becomes inefficient. parabolic shape of A and a step in ψ is registered, consistent with the usual IFE mechanism. However, at the SPP resonance (red) the A shape distortion and ψ step shift indicates a strong SPP-induced contribution coexisting with the one originating from the helicity of the pump polarization. A clear shift of ≈ 4◦ between the resonant (1380 nm) and off-resonant (1300 nm) dependencies highlights the importance of the SPP-driven contribution to the IFE effective magnetic field. In order to unambiguously associate this additional IFE contribution to the SPP excitation, we performed spectral measurements at a close-to-linear pump polarization where both helicity- and SPP-induced contributions are of comparable magnitude. The spectral dependencies of A and ψ of the oscillations (Fig. 3a-b) for the circular pump polarization (black) show no significant variations across a broad range of wavelengths. The absence of sharp 8


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features for the circularly polarized pump pulse hints at negligible variations of the magnetooptical coefficients of the garnet in the spectral region of interest. In striking contrast, the ψ spectrum under illumination with a close-to-linearly polarized pump exhibits a large resonant peak centered at around λpump = 1380 nm, corresponding to the SPP excitation at the Au/garnet interface. The SPP-mediated excitation mechanism is further corroborated by a similar resonant modulation in the A spectrum (Fig. 3b). Numerical simulations reveal a clear correlation between the SPP excitation and non-zero HyIFE as well as a good agreement between the simulated and experimental reflectivity spectra (Fig. 1d). We note that the spectral width of the SPP resonance observed both in the linear reflectivity spectrum (Fig. 1d) and in the high-frequency precession phase and amplitude spectra (Fig. 3a,b) is in a good agreement with the results of numerical calculations (Fig. 1d). This is indicative of a good quality of both Au perforation and Au/garnet interface 30 as well as negligible role of surface roughness as a limiting factor for the experimentally achieved magnitude of HIFE . With these data in hand, the importance of the SPP-induced contribution to the IFE excitation of the coherent exchange resonance mode is confirmed. Notably, opposite to the homogeneous action of a circularly polarized pump beam in transparent GdYbBIG, the SPPmediated excitation is localized in the dSPP ≈ 100-nm-thick layer adjacent to the interface (see Fig. 1c). Considering the Faraday rotation θF proportional to the effective thickness of the optically active medium d (in the homogeneous case dbulk = 380 µm), and estimating the SPP-driven precession amplitude to be ≈ 10% of the one excited with the circular polarized pump (cf. Fig. 3b), for the SPP enhancement of the excitation efficiency σ one gets:

σ=

ASPP dbulk ≈ 4 · 102 . Abulk dSPP

(3)

Originating in the prominent SPP-driven increase of the electric fields in a dielectric medium, this two orders of magnitude enhancement can be further improved by photonic optimization of the hybrid metal-dielectric system. In particular, we can estimate the magnitude of the 9


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effective HIFE from the experimentally registered amplitude of the spin precession. First, we note that for a bare garnet film, circularly polarized 50 fs-long pump pulses used in this work result in the relative precession amplitude (ratio between dynamic and static Faraday rotation values) of about 10−4 . Using the uniaxial anisotropy field Hu and a typical gyromagnetic ratio in garnets, 31 we obtain 32 an effective magnetic field of about 800 Oe. A similar order of magnitude estimation (∼700 Oe) can be derived directly from Eq. (1). As such, the SPP-mediated enhancement of the IFE by two orders of magnitude enables optical generation of highly localized, few Tesla-large effective magnetic fields. In the light of recently discovered magnetic recording via coherent spin precession, 6 strong SPP-mediated confinement of the excitation of coherent spin dynamics holds a high promise for increasing the recording density in thin dielectric films. In order to look at the indepth confinement of HIFE upon reducing the GdYbBIG thickness, we simulated the spectra of the SPP-induced HIFE in thin GdYbBIG films. Illustrating the effective SPP-induced magnetic field HyIFE , Fig. 3,c-d indicate the critical garnet thickness dcrit of about 100 nm: below dcrit , HyIFE and the quality of a potential SPP-based transducer deteriorates quickly, mostly due to the smearing out of the SPP dispersion (see Supporting Information). A model magneto-plasmonic system analyzed here serves as a starting point towards tailoring the local interaction of spins with photons for industrial needs. For instance, stronger confinement of the SPP-mediated excitation can be achieved in a transparent media with an even higher dielectric function εd , paving a way for further material optimization. To summarize, we have experimentally demonstrated the possibility to control the spin states in a dielectric with the effective static magnetic field of a surface plasmon polariton. The excitation efficiency of sub-THz spin precession was resonantly enhanced by two orders of magnitude via the excitation of an SPP. Our calculations show that the proposed method allows for the localization of the spin dynamics excitation in a surface layer with 100 nm thickness. Approaching the commercially attractive dimensions of a single bit, the demonstrated confinement mechanism holds a great potential for future switching and recording

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applications, as well as sheds light on the fundamental spatio-temporal aspects of the spinplasmon coupling on ultrashort timescales. These results break new ground in laser-induced coherent spin dynamics, enabling spatial localization of the excitation and thus opening the path towards high-density, low-loss opto-magnetism.

Supporting Information Available Supporting Information contains details about sample fabrication, experimental methods, data fitting methods and numerical simulations for semi-infinite and thin garnet film. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgements The authors thank A. Melnikov and T. Kampfrath for fruitful discussions, as well as M. Wolf and A. Maziewski for their continuous support. We acknowledge support from the National Science Centre Poland (grant DEC-2017/25/B/ST3/01305), G-RISC grant 2017a-18, JSPS KAKENHI grant (JP26103004) and JSPS Core-to-Core Program (A. Advanced Research Networks).

Notes The authors declare no competing financial interest.

Author contribution I.R. and A.S. conceived and designed the experiment. T.S. provided the garnet crystal. A.I.S. fabricated the Au grating. A.L.C., I.R. and A.S. carried out the time-resolved Faraday effect measurements. A.L.C. and I.R. performed numerical simulations. A.L.C., T.V.M., I.R. and

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A.S. discussed and analyzed the data. A.L.C. and I.R. wrote the manuscript with the help of the co-authors.

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quality Au/BIG/GGG magnetoplasmonic crystals fabricated by a combined ion-beam etching technique. Optical Materials Express 2015, 5, 1647–1652. (31) Wijn, H., Ed. Magnetic Properties of Non-Metallic Inorganic Compounds Based on Transition Elements. Garnets; Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III; Springer-Verlag Berlin Heidelberg, 1991; Vol. 27E. (32) Kozhaev, M. A.; Chernov, A. I.; Savochkin, I. V.; Kuz’michev, A. N.; Zvezdin, A. K.; Belotelov, V. I. Peculiarities of the inverse Faraday effect induced in iron garnet films by femtosecond laser pulses. JETP Letters 2016, 104, 833–837.

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Surface Plasmon-Mediated Nanoscale Localization of Laser-Driven

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