ARTICLE https://doi.org/10.1038/s41467-019-10545-x OPEN Strongly coupled magnon–phonon dynamics in a single nanomagnet Cassidy Berk 1, Mike Jaris1, Weigang Yang1, Scott Dhuey2, Stefano Cabrini2 & Holger Schmidt1 Polaritons are widely investigated quasiparticles with fundamental and technological sig- nificance due to their unique properties. They have been studied most extensively in semi- conductors when photons interact with various elementary excitations. However, other fi 1234567890():,; strongly coupled excitations demonstrate similar dynamics. Speci cally, when magnon and phonon modes are coupled, a hybridized magnon–phonon quasiparticle can form. Here, we report on the direct observation of coupled magnon–phonon dynamics within a single thin nickel nanomagnet. We develop an analytic description to model the dynamics in two dimensions, enabling us to isolate the parameters influencing the frequency splitting. Fur- thermore, we demonstrate tuning of the magnon–phonon interaction into the strong coupling regime via the orientation of the applied magnetic field. 1 School of Engineering, University of California Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA. 2 Molecular Foundry, University of California Berkeley, 67 Cyclotron Road, Berkeley, CA 94720, USA. Correspondence and requests for materials should be addressed to C.B. (email: [email protected]) NATURE COMMUNICATIONS | (2019) 10:2652 | https://doi.org/10.1038/s41467-019-10545-x | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10545-x agnonics is an extremely active research area which ab Mexploits the wave nature of magnons, the quanta of spin Spins waves, in order to advance data storage, communica- tion, and information processing technology. However, a current drawback in the excitation, manipulation, and detection of magnons exists due to relatively low conversion efficiencies1. 100 nm Coupling to the phononic system is a less explored avenue for the Phonons manipulation of magnons, and has been shown to be a promising means of lowering the switching energy of nanoelements2,3. With cd e this in mind, a more thorough understanding of the coupling 18 H z between the spin and phonon systems in nanostructures is 16 MS necessary. 14 (2,0) M – 12 Because of this, the magnon phonon interaction has recently (1,1) X H been the focus of increased research, specifically as it is applied to 10 – 8 (1,0) surface acoustic wave ferromagnetic resonance (SAW-FMR)4 7. M k Frequency (GHz) Frequency fi 6 mp y Signi cant effects of optically excited SAWs on the magnetization 2 3452 3 4 5 k dynamics of patterned nanomagnet arrays have been demon- H (kOe) H (kOe) strated8. In these systems, the SAW frequencies arise from the geometric arrangement of the elements9, with the SAW energy Fig. 1 Experimental illustrations and colormaps. a Scanning electron located in the substrate layer below the nanoelements. Due to the microscope image of 330 x 330 x 30 nm Ni nanomagnet. b When the pump magneto-elastic coupling, the magnetic resonance is pinned at the pulse (400 nm) irradiates the sample, the deposited heat causes the SAW frequency. This effect was used to extract the Gilbert element to thermally expand, which causes the element to vibrate at damping parameter in a nanomagnet10. In these structures, the eigenfrequencies determined by the geometry and material properties. In dynamics are akin to a driven oscillation rather than to two addition, the heat perturbs the magnetization causing the spins to precess coupled oscillators11. Another exciting development was the around the effective field. Due to magnetostriction, the spin and phonon experimental demonstration of magnons transferring spin to the systems are coupled to one another. A probe pulse (800 nm) which is phonon system12. Despite all of this progress, observation, and delayed in time monitors the dynamics following excitation. c Fourier quantification of the hybridized magnon–phonon modes itself amplitude spectra normalized for each field bin of the magnetic and (d) the remain challenging tasks13, and so far dynamics of the hybridized non-magnetic detection channels. The arrows and dotted lines are modes have not been resolved spectroscopically in relevant indicators of the phononic eigenfrequencies. The positions of these structures14. frequencies match in the magnetic and non-magnetic spectra. In this article, we utilize the vibrational modes of a single, e Experimental geometry. The x and y axes are defined to be the in-plane isolated Ni nanostructure to optically initiate phononic dynamics directions along the edges of the nanomagnet and the z-axis in the direction fi θ = in the GHz frequency range (5 GHz–25 GHz) along with the of the surface normal. The external eld H is applied at H 60° with intrinsic magnetic resonances of the magnet. Access to this higher respect to the surface normal. This cants the magnetization vector MS out θ frequency range has been a limiting factor in resolving the mode of the plane to an angle M with respect to the surface normal and to an in- φ x splitting in previous experiments using interdigital transducers14. plane angle, M from the -axis. The phononic modes k are characterized φ φ The confined geometry of the magnetic nanostructure isolates the by their mode indices and their in-plane angle, k. mp is the in-plane angle phononic modes much like semiconductor microcavities control between MS and k excitonic states. Using an external magnetic field in the appro- priate geometries, the magnonic mode is tuned through the arise due to the coupling to the phononic system. Confirmation of phononic resonances and the avoided crossings characteristic of this is seen in the non-magnetic spectra (Fig. 1d), where the coupled systems is observed15,16. frequencies are all H-field independent and match the positions of the magnetic channel’s field independent frequencies. These spectra look similar to those observed in patterned arrays8. Results However, in the single isolated nanomagnet, the coupling Hybridized magnon–phonon dynamics. The magnon–phonon between the two systems is stronger and more direct. It arises dynamics of the nanomagnet (Fig. 1a) were measured using a within the element itself rather than with surface acoustic waves two-color TR-MOKE setup using a balanced photodiode detec- located in the substrate, leading to qualitatively different behavior tion scheme which enables us to measure the magnetic system around the crossovers between resonances. 17 The in-plane components of the phononic mode’s k-vector are and the non-magnetic (phononic) system at the same time (see π ¼ nx;y the Methods section). When the pump pulse hits the nano- k ; , where lx,y is the dimension of the nanoelement along x y lx;y magnet, the energy is absorbed by the electron system which then the x or y directions. Therefore, the phononic mode is equilibrates with the phonon systems within a few picoseconds characterized by the indices (nx,ny) and the in-plane angle from according to the two-temperature model18. This excites the spin φ = −1 the x-axis, k tan (ny/nx) (Fig. 1e). Because the material is and phonon systems concurrently within the nanomagnet elastically isotropic, it can be characterized by the Lamé (Fig. 1b). constants, λ=Ev/(1+v)(1−2v) and μ=E/(2(1+v)), where E is In Fig. 1, colormaps from the magnetic (c) and non-magnetic the Young’s Modulus and v is the Poisson ratio19. We assume the fi (d) channels are displayed. Each eld represents a different TR- density of Ni, ρ = 8900 kg/m3 and v = 0.3120 and fit E to the MOKE scan that has been transformed into the frequency experimentally measured phononic modes using the relation domain using an FFT algorithm. The colors represent the frequency components present at that field. In order to see the ðÞ2λ þ 3μ k2 frequency variation more clearly, the frequency amplitude was ω2 ¼ ð Þ ph ρ 1 normalized for each field bin. The magnetic channel displays a 2 dominant frequency which changes as the external field changes fi fi þ31 (Fig. 1c). In addition, there are eld independent modes which derived in Supplementary Note 2. The tted value was 209À29 2 NATURE COMMUNICATIONS | (2019) 10:2652 | https://doi.org/10.1038/s41467-019-10545-x | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10545-x ARTICLE GPa, in excellent agreement with the range of values reported in Where 21 ref. γM In order to extract the relevant magnetic parameters, an ω4 ¼ S ðÞω þ ω 2 ð Þ C ρ 1C2 2C1 k 4 identical magnetic film was grown next to the nanostructures. Its precession resonances were measured at various fields and angles, with γ fi 22 and and MS were t to the Kittel formula C ¼ sin2 2θ b2 cos2 φ cos2 φ þ sin2 φ sin2 φ ω2 ¼ ω ω ð Þ 1 M 1 k mp k mp M 1 2 2 ð5Þ þ 3 φ φ þ 1 2 2 φ ω ¼ γðÞÀ π ðÞþθ ðÞθ À θ ω ¼ γ b1b2 sin 2 k sin 2 mp b2 sin 2 mp where 1 4 MS cos 2 M H cos H M , 2 4 2 ðÞÀ π ðÞþθ ðÞθ À θ fi 4 MS cos 2 M H cos H M , H is the applied eld θ θ magnitude, M and H are the angles of the magnetization vector C ¼ sin2 θ b2 sin2 2φ þ 2b2 cos2 2φ ð6Þ and the applied field with respect to the surface normal, γ is 2 M 1 mp 2 mp the gyromagnetic ratio, and MS is the saturation magnetization. The frequency peaks were selected from the (1,1) and (2,0) fi γ ¼ : þ0:02 ´ 7 fi The tted frequencies yielded values of 1 98À0:01 10 modes and t simultaneously using Eq.