Nonreciprocal Magnetoacoustic Waves in Dipolar-Coupled Ferromagnetic Bilayers

M. Küß, M. Heigl, L. Flacke, A. Hörner, M. Weiler, A. Wixforth, and M. Albrecht

Phys. Rev. Applied 15, 034060 – Published 19 March 2021

Abstract

We study the interaction of surface acoustic waves (SAWs) with spin waves (SWs) in a ${Co}_{40} {Fe}_{40} B_{20}$ / $Au$ / ${Ni}_{81} {Fe}_{19}$ system composed of two ferromagnetic layers separated by a nonmagnetic $Au$ spacer layer. Because of interlayer magnetic dipolar coupling between the two ferromagnetic layers, a symmetric and an antisymmetric SW mode form, which both show a highly nondegenerate dispersion relation for oppositely propagating SWs. Due to magnetoacoustic SAW-SW interaction, we observe highly nonreciprocal SAW transmission in the piezoelectric-ferromagnetic hybrid device. We experimentally and theoretically characterize the magnetoacoustic wave propagation as a function of frequency, wave vector, and external magnetic field magnitude and orientation. Additionally, we demonstrate that the nonreciprocal SW dispersion of a coupled magnetic bilayer is highly tuneable and not limited to ultrathin magnetic films, in contrast to the nonreciprocity induced by the interfacial Dzyaloshinskii-Moriya interaction. Therefore, magnetoacoustic coupling in ferromagnetic multilayers provides a promising route towards building efficient acoustic isolators.

Received 22 December 2020
Revised 9 February 2021
Accepted 15 February 2021

DOI:https://doi.org/10.1103/PhysRevApplied.15.034060

Physics Subject Headings (PhySH)

Dipolar interaction Magnetoacoustic effect Spin dynamics Spin waves

Magnetic multilayers

T-symmetry

Landau-Lifschitz-Gilbert equation Surface acoustic wave

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Küß ^1,*, M. Heigl², L. Flacke ^3,4, A. Hörner¹, M. Weiler^3,4,5, A. Wixforth¹, and M. Albrecht ²

¹Experimental Physics I, Institut of Physics, University of Augsburg, Augsburg 86135, Germany
²Experimental Physics IV, Institut of Physics, University of Augsburg, Augsburg 86135, Germany
³Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Garching 85748, Germany
⁴Physics Department, Technical University Munich, Garching 85748, Germany
⁵Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Kaiserslautern 67663, Germany

^*matthias.kuess@physik.uni-augsburg.de

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Vol. 15, Iss. 3 — March 2021

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Images

Figure 1
Illustration of the investigated magnetoacoustic hybrid device and the coordinate system used. The nonreciprocity of the MASW in the magnetic bilayer $Py$ (20 nm)/ $Au$ (5 nm)/ $Co Fe B$ (5 nm) is characterized by different transmission magnitudes of oppositely propagating waves $k_{S 21}$ and $k_{S 12}$ . A symmetric ( $↿↾$ ) and an antisymmetric ( $↿⇂$ ) SW mode can be excited in the magnetic bilayer. This is schematically shown by the trajectory of the precessing magnetic moments (black arrows).
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Figure 2
Illustration of the nonreciprocity (a),(b) in a magnetic single layer and (c),(d) in a dipolar-coupled magnetic bilayer for $ϕ_{0} = 89^{\circ}$ . Whereas the SW dispersion relation of the single layer (a) is reciprocal, the SW dispersion relation of the bilayer (c) is nonreciprocal (highlighted by shaded areas) and is composed of a high-frequency symmetric mode ( $↿↾$ ) and a low-frequency antisymmetric mode ( $↿⇂$ ). MASWs form in the vicinity of the SAW-SW dispersion intersection points, which are experimentally observed by a decrease in the SAW transmission $S_{i j}$ (b),(d). Additionally, the SAW-SW helicity mismatch effect is present in both samples and induces different transmission magnitudes $S_{21} \neq S_{12}$ at resonance.
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Figure 3
Change of the SAW transmission $Δ S_{21}$ (upper row) and $Δ S_{12}$ (lower row) of (a) a $Co Fe B$ (5)/ $Pt$ (3) [12] magnetic single-layer sample, (b) a $Py$ (20)/ $Au$ (5) magnetic single-layer sample, and (c) a $Py$ (20)/ $Au$ (5)/ $Co Fe B$ (5) magnetic bilayer sample as a function of orientation and magnitude of the external magnetic field at 6.77, 6.86, and 6.87 GHz. The numbers in parentheses are the nominal film thicknesses in nanometers. To compensate for the greater length of the $Co Fe B$ (5)/ $Pt$ (3) film (750 $μ m$ instead of $500 μ m$ ), the response of the $Co Fe B$ (5)/ $Pt$ (3) film is scaled by 2/3 [39]. The low response of $Py$ (20)/ $Au$ (5) is multiplied by a factor of ten. (d) Simulated response of the magnetic bilayer. The discrete appearance of the low-field resonance in (c),(d) is an artifact, which is caused by the incremental step size of $ϕ_{H} = {3.6}^{\circ}$ .
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Figure 4
(a) The resonance (res.) fields $μ_{0} H_{res}^{S 21}$ of the experiment (false-color plot) and simulation (scatter plot) are in very good agreement. The symmetry of the simulated SW mode is given by the color of the simulated data points. (b) Simulated influence of the spacer layer thickness $d_{s}$ on the resonance fields for $Py$ (20)/ $Au$ ( $d_{s}$ )/ $Co Fe B$ (5) magnetic bilayer films. The numbers in parentheses are the nominal film thicknesses in nanometers. (c) Nonreciprocal splitting of the resonance fields $Δ (μ_{0} H_{res})$ for the low- and high-field resonance and for positive magnetic fields [see (a)]. For the points inside the dashed ellipses, no resonance is observed for either $S_{21}$ or $S_{12}$ , for which $μ_{0} H_{res} = 0$ is used. (d) Nonreciprocity of the transmission magnitude $Δ S$ and insertion loss ${IL}_{Δ}$ for positive resonance fields. For the low-field resonance a strong nonreciprocity of 37 dB and simultaneously low ${IL}_{Δ}$ of 0.8 dB are observed (green stars).
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Figure 5
Change of the experimentally determined SAW transmission $Δ S_{21}$ as a function of the external magnetic field and frequency, respectively wave vector, for $ϕ_{H} = 9^{\circ}$ (a), ${21.6}^{\circ}$ (b), and $81^{\circ}$ (c). The green points indicate the simulation results.
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