Letter pubs.acs.org/NanoLett
Cite This: Nano Lett. 2018, 18, 2970−2975
Surface Plasmon-Mediated Nanoscale Localization of Laser-Driven sub-Terahertz Spin Dynamics in Magnetic Dielectrics Alexander L. Chekhov,*,†,‡,¶ Alexander I. Stognij,§ Takuya Satoh,∥ 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 ∥ Department of Physics, Kyushu University, 819-0395 Fukuoka, Japan ‡
S Supporting Information *
ABSTRACT: We report spatial localization of the effective magnetic field generated via the inverse Faraday effect employing surface plasmon polaritons (SPPs) at Au/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 SPPdriven excitation of coherent spin precession with 0.41 THz frequency. We argue that the subdiffractional confinement of the SPP electric field enables strong spatial localization of the SPP-mediated excitation of spin dynamics. We demonstrate 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 toward nonthermal optomagnetic recording on the nanoscale. KEYWORDS: Ultrafast spin dynamics, surface plasmon−polariton, inverse Faraday effect, rare-earth iron garnet, nonlinear optics, magnetoplasmonics
U
the inverse Faraday effect, mediating the excitation of localized coherent spin precession with 0.41 THz frequency. We demonstrate 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 toward nonthermal 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 - ∝ −δεijEiE*j , where δεij is the variation of the dielectric permittivity ε by magnons. By introducing a phase shift φ between Ei and Ej, for the resulting projection of the effective magnetic field HIFE k we get:
ltrafast 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, lowenergy consumption, and high-density recording.1 Despite addressing the foremost issue, all-optical magnetization switching with femtosecond laser pulses in various metallic systems2−5 requires heating close to the Curie temperature. Recently, new routes for nonthermal 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 subdiffractional nanophotonics7−11 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 subpicosecond scales in opto-magnetic media is highly desirable. Here, we show that surface plasmon−polaritons in hybrid metal−dielectric structures can provide spatial confinement of © 2018 American Chemical Society
HkIFE = −
∂∝ ϰijk (EiE*j − Ei*Ej) ∝ ϰijk |E|2 sin φ ∂Mk
(1)
where ϰijk is the magneto-optical constant, εij = iϰijkMk. This field exerts a torque on the magnetization M and triggers its Received: January 29, 2018 Revised: April 4, 2018 Published: April 11, 2018 2970
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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 HIFE y 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 HIFE y (c) at the SPP resonance at 1450 nm wavelength and 34° angle of incidence. The inset in (c) illustrates the spatial localization of the laterally averaged HIFE y 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 HIFE y (blue) calculated using the finite difference time domain method. Experimental reflectivity spectrum is shown with a black dashed line.
precessional motion. Because for circularly polarized light in transparent media φ = ±π/2, the sign of HIFE k is governed by the helicity of light polarization. For any linear polarization, φ = 0 and the IFE vanishes. Microscopically, bearing a notable similarity17 to the second-order optical rectification, an impulsive stimulated Raman scattering (ISRS)18 employs two optical fields at frequencies ω1 and 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 nanoconfined volumes, enabling resonant control of their amplitudes and phases. The spin-photon coupling can thus be mediated by collective electronic excitations, that is, 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 = ikx′/kz″. Here kx′ is the real part of the SPP wavenumber kSPP =
ω c
HyIFE ∝ ϰijk |Ex|2
(2)
Owing to the nanoscale SPP field localization and amplification, HIFE y 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 HIFE y enables its twice as strong spatial localization, as compared to the SPP electric fields (Figure 1b,c). The sign of HIFE y , 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 systems23,24 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 (Figure 1b) and enables sizable effective magnetic field HIFE y localized in the 100 nm thick dielectric layer adjacent to the interface (Figure 1c). The rather complicated distributions stems from the structure of the |Ez|2 and HIFE y 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 HIFE y (see inset in Figure 1c). Exerting a torque on Mx, a short (given by the SPP lifetime, that is, subps) 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, that is, when the direct IFE is inactive. We have complemented a 380 μm thick Gd-Yb-doped bismuth iron garnet single crystal (Gd4/3Yb2/3BiFe5O12, GdYbBIG) with a periodically perforated 50 nm thick Au overlayer (800 nm period), allowing for the excitation of the SPPs at both Au/air
εmεd = k′x + ik″x εm + εd
⎛ω k″z = Im⎜⎜ ⎝c
kx′ −2(kx″x − kz″z) e kz″
⎞ εd ⎟⎟ εm + εd ⎠
where εm and 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 dependence of these fields ∝ eikx′x, the phase shift remains constant, giving rise to the static effective magnetic field HIFE y (Figure 1a) 2971
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Figure 2. (a) SPP dispersion map of a Au/garnet hybrid magnetoplasmonic 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° corresponds to the p-polarized excitation. The colored circles correspond to the data shown in (c) with respective colors.
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 Figure 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 (Figure 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 (Figure 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 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 helicityand SPP-induced contributions are of comparable magnitude. The spectral dependencies of A and ψ of the oscillations (Figure 3a,b) for the circular pump polarization (black) show no significant variations across a broad range of wavelengths. The absence of sharp features for the circularly polarized pump pulse hints at negligible variations of the magneto-optical coefficients of the garnet in the spectral region of interest. In striking contrast, the ψ spectrum under illumination with a close-to-linearly polarized
and Au/garnet interfaces26−28 (Figure 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 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 Figure 2a. A characteristic near-IR reflectivity spectrum for 34° incidence is shown in Figure 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° 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. 2972
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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 HIFE y 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 SPPmediated IFE in hybrid metal−dielectric magnetoplasmonic systems becomes inefficient.
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 obtain32 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 SPPmediated enhancement of the IFE by 2 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 in-depth confinement of HIFE upon reducing the GdYbBIG thickness, we simulated the spectra of the SPPinduced HIFE in thin GdYbBIG films. Illustrating the effective SPP-induced magnetic field HIFE y , Figure 3c,d indicates the critical garnet thickness dcrit of about 100 nm; below dcrit, HIFE y 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 magnetoplasmonic system analyzed here serves as a starting point toward 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 applications, as well as sheds light on the fundamental
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 (Figure 3b). Numerical simulations reveal a clear correlation between the SPP excitation and nonzero HIFE y as well as a good agreement between the simulated and experimental reflectivity spectra (Figure 1d). We note that the spectral width of the SPP resonance observed both in the linear reflectivity spectrum (Figure 1d) and in the highfrequency precession phase and amplitude spectra (Figure 3a,b) is in a good agreement with the results of numerical calculations (Figure 1d). This is indicative of a good quality of both Au perforation and Au/garnet interface30 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 SPP-mediated excitation is localized in the dSPP ≈ 100 nm thick layer adjacent to the interface (see Figure 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. Figure 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 effective HIFE from the experimentally registered amplitude of the spin precession. First, we note that for a 2973
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spatiotemporal aspects of the spin-plasmon coupling on ultrashort time scales. These results break new ground in laserinduced coherent spin dynamics, enabling spatial localization of the excitation and thus opening the path toward high-density, low-loss opto-magnetism.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.8b00416. Details about sample fabrication, experimental methods, data fitting methods, and numerical simulations for semiinfinite and thin garnet film (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. ORCID
Alexander L. Chekhov: 0000-0002-4985-0597 Author Contributions
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 A.S. discussed and analyzed the data. A.L.C. and I.R. wrote the manuscript with the help of the coauthors. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank A. Melnikov, T. Kampfrath, A. Kirilyuk, and A.M. Kalashnikova 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 DEC2017/25/B/ST3/01305), G-RISC Grant 2017a-18, JSPS KAKENHI Grant (JP26103004), and JSPS Core-to-Core Program (A. Advanced Research Networks).
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ABBREVIATIONS SPP surface plasmon-polariton IFE inverse Faraday effect GdYbBIG gadolinium ytterbium bismuth iron garnet
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REFERENCES
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