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Strong Interlayer Magnon-Magnon Coupling in Magnetic Metal-Insulator Hybrid Nanostructures

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Strong Interlayer Magnon-Magnon Coupling in Magnetic Metal-Insulator Hybrid Nanostructures PHYSICAL REVIEW LETTERS 120, 217202 (2018) Strong Interlayer Magnon-Magnon Coupling in Magnetic Metal-Insulator Hybrid Nanostructures Jilei Chen,1,* Chuanpu Liu,1,* Tao Liu,2,* Yang Xiao,3,* Ke Xia,4 Gerrit E. W. Bauer,5,6 Mingzhong Wu,2 and Haiming Yu1,† 1Fert Beijing Institute, BDBC, School of Electronic and Information Engineering, Beihang University, Xueyuan Road 37, Beijing 100191, China 2Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA 3Department of Applied Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 4Department of Physics, Beijing Normal University, Beijing 100875, China 5Institute for Materials Research, WPI-AIMR and CSNR, Tohoku University, Sendai 980-8577, Japan 6Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands (Received 2 October 2017; revised manuscript received 7 February 2018; published 23 May 2018) We observe strong interlayer magnon-magnon coupling in an on-chip nanomagnonic device at room temperature. Ferromagnetic nanowire arrays are integrated on a 20-nm-thick yttrium iron garnet (YIG) thin film strip. Large anticrossing gaps up to 1.58 GHz are observed between the ferromagnetic resonance of the nanowires and the in-plane standing spin waves of the YIG film. Control experiments and simulations reveal that both the interlayer exchange coupling and the dynamical dipolar coupling contribute to the observed anticrossings. The coupling strength is tunable by the magnetic configuration, allowing the coherent control of magnonic devices. DOI: 10.1103/PhysRevLett.120.217202 Strong couplings between photons and spins, atoms, separated nanomagnets offers new functionalities towards and superconducting qubits lie at the heart of realizing the magnon transistors [31] or spin-wave logic [32]. quantum manipulation in quantum dots, nitrogen-vacancy A schematic of the nanomagnonic device is shown in centers, and mechanical oscillators [1–5]. Cavity magnon Fig. 1(a). YIG thin films with thickness t1 20 nm were ¼ polaritons [6–12], i.e., the hybrid state of a cavity photon grown on Gd3Ga5O12 substrates by magnetron sputtering and a spin-wave excitation in a magnet in the cavity, and patterned by ion beam etching to form a magnon have been evidence of such coupling at both ultralow and waveguide of 90 μm width. Magnetic nanowire arrays were room temperatures. Strong couplings have been observed deposited on top of a YIG waveguide by electron beam in submillimeter-sized yttrium iron garnet (YIG) spheres evaporation with a thickness of t2 (20-nm-thick nickel or [10–12], which obeyedffiffiffiffi the size scaling law proposed by Dicke [13], i.e., g ∝ pN with N the number of spins. (a) z ’ (c) However, Dicke s law implies weak couplings when a x n = 8 magnets become small in nanomagnonic devices [14–22], y 10 disqualifying microwaves for coherent control at the Ni Ni nanoscale. YIG n = 6 Here, we report the realization of strong coupling of magnons not in photonic but magnonic cavities with (b) (GHz) 5 f standing magnon modes. This is an analog to the magnon H polariton, but the cavity mode is magnonic rather than n = 4 photonic, and it happens on a smaller length scale. We k observe anticrossing gaps as large as 1.58 GHz at a -1000 0 1000 frequency of about 7.5 GHz in heterostructures consisting field (Oe) of a metallic ferromagnet wire array on top of a thin-film magnetic insulator YIG. This large anticrossing gap FIG. 1. (a) Sketch of a hybrid magnetic nanostructure based on approaches the ultrastrong coupling regime, comparable a YIG thin film. The applied field H is in plane and parallel to the to what is observed for macroscopic cavity magnon polar- nanowires. (b) An SEM image (scale bar 500 nm) of the Ni-based nanowire array on YIG thin film. (c) Color-coded reflection itons [11]. We can control the coupling by the magneti- spectra S11 measured on the Ni/YIG hybrid nanostructures by a zation alignments, analogous to the tunable band gaps of coplanar waveguide. The arrows highlight anticrossing modes magnonic crystals [23–30] that would be difficult to realize induced by different in-plane standing spin-wave modes with in photonic devices. The strong coupling between spatially mode numbers n 4,6,8. ¼ 0031-9007=18=120(21)=217202(6) 217202-1 © 2018 American Physical Society PHYSICAL REVIEW LETTERS 120, 217202 (2018) (c) 30-nm-thick cobalt) [33]. a stands for the center-to-center 10 (a) (b) 0.2 9 distance of two neighboring nanowires, i.e., the period of 0.06 the array. A scanning electron microscope (SEM) image of 9 2g (GHz) (GHz) f the nanomagnonic arrays with a 600 nm is shown in g ¼ 8.5 Fig. 1(b). An external magnetic field was applied (initially) 0.1 0.04 8 parallel to the nanowires. We excite and detect spin waves 1000 1200 1400 -5 0 5 468 S (arb. unit) using coplanar waveguides (CPWs) integrated on top of the field (Oe) 11 mode number n (e) 1 nanowire arrays. The scattering parameter S11 for reflection (d) 7.0 is measured by a vector network analyzer (VNA) connected to the CPW (Fig. S1) [33,37–40]. The nanowire arrays on (GHz) top of the YIG thin film act as Bragg scattering gratings to f 6.5 form in-plane standing spin waves (ISSWs) with large NiYIG Ni n = 8 0 wave numbers as illustrated in Fig. 1(a). 500 600 Microwaves field (Oe) Figure 1(c) shows reflection spectra S11 measured as a function of the frequency and magnetic field where two FIG. 2. (a) Color-coded reflection spectra S11 for high-order main branches are observed. The lower-frequency branches ISSWs with a mode number of n 8. (b) The line spectrum agree with the spin-wave resonance of a bare YIG film in selects the spectrum indicated by the¼ vertical dotted line in (a) at the Damon-Eshbach (DE) configuration [39], whereas 1200 Oe. The frequency gap in the anticrossing mode reveals the those at higher frequencies are assigned to the ferromag- coupling strength g. (c) g as a function of the mode number netic resonance (FMR) of the Ni wires. The Ni modes can n 4, 6, and 8. Red dots: Experiments. Black squares: Simu- lations.¼ (d) Schematic of the modeled structure. The width of YIG be fitted with an in-plane demagnetization factor Nxx 0.01 [27]. This value is smaller than the expected form¼ and Ni are 500 and 100 nm, respectively. (b) Simulation results of reflection spectra as a function of the in-plane magnetic field for factor of a wire, which has been reported also by Ding, the anticrossing of the Ni FMR mode and the n 8 ISSW YIG Kostylev, and Adeyeye [41]. Dipolar interactions at the mode. The color represents the reflection amplitude¼ with the edges [42] or between neighboring wires could explain the scale definition on the side. observed reduction of the anisotropy. Here we focus on the three pronounced anticrossings (marked with arrows) −16 2 constant λex 3 × 10 m [36], the saturation magneti- observed in the Ni resonances that we attribute to the ¼ zation 4πMS 1766 G [20], film thickness 20 nm, and interlayer coupling between the FMR of Ni and high-order k nπ=a. As¼ a result, these three modes are attributed to ISSWs in YIG as sketched in Fig. 1(a). ISSWs¼ with mode numbers n 4, n 6, and n 8. Spin waves in a periodic potential develop a band Schematic drawings of these three¼ high-order¼ ISSWs¼ are structure with gaps at the Brillouin zone boundaries with shown in the insets in Fig. 1(c). The PSSWs of the YIG wave number π=a, where a is the unit cell length. In the films resonate at frequencies > 35 GHz and are not limit of a strong periodic potential, the superlattice band relevant for the present study. structure becomes dispersionless, the spin waves are all In Figs. 2(a) and 2(b), an anticrossing gap of 120 MHz is localized in each unit cell, and the band index n counts the observed for the n 8 mode. The anticrossing covers a number of nodes. When the frequency of a standing spin broad frequency range,¼ because the Ni FMR mode and the wave in YIG approaches a resonance of the Ni wire array, a n 8 ISSW mode run nearly parallel. The coupling coupling results in a level repulsion or anticrossing [see strength¼ g is defined as half of the minimal peak-to-peak Fig. 2(a)]. When the nanowires are at resonance, the strong frequency spacing in the anticrossing. The coupling magnetization of the relatively hard magnetic material Ni strengths g extracted for all three anticrossings are plotted drives a spin precession in the relatively soft magnetic YIG in Fig. 2(c). For spin-wave resonance of films with thick- through interlayer magnetic coupling. Since the FMR of Ni ness d and pinned surface magnetizationffiffiffi [8,33], the n ensures in-phase precession in all nanowires, the YIG film coupling strength decreases as gð Þ ∝ pd=n, where n is beneath each nanowire precesses in phase as well. The a PSSW mode number. In our case, the driving force is not associated dynamic periodic boundary conditions can be the homogeneous ac field but the localized field beneath Ni fulfilled by in-plane standing spin waves for an even nanowires. Nevertheless, with increasing n the overlap with number of nodes only (n 2, 4, 6). In contrast, only the applied ac magnetic field is increasingly averaged out, odd-numbered perpendicular¼ standing spin waves (PSSWs) leading to a g ∝ 1=n scaling as in conventional spin-wave are observed in the spin-wave resonance of intrinsic thin resonance [8,33,43].
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