Measuring the Magnon-Photon Coupling in Shaped Ferromagnets: Tuning of the Resonance Frequency

Sergio Martínez-Losa del Rincón, Ignacio Gimeno, Jorge Pérez-Bailón, Victor Rollano, Fernando Luis, David Zueco, and María José Martínez-Pérez

Phys. Rev. Applied 19, 014002 – Published 3 January 2023

Abstract

Cavity photons and ferromagnetic spin excitations can exchange information coherently in hybrid architectures, at speeds set by their mutual coupling strength. Speed enhancement is usually achieved by optimizing the geometry of the electromagnetic cavity. Here we show that the geometry of the ferromagnet also plays a role, by setting the fundamental frequency of the magnonic resonator. Using focused ion-beam patterning, we vary the aspect ratio of different Permalloy samples reaching operation frequencies above 10 GHz while working at low external magnetic fields. Additionally, we perform broadband ferromagnetic resonance measurements and cavity experiments that demonstrate that the light-matter coupling strength can be estimated using either open transmission lines or resonant cavities, yielding very good agreement. Finally, we describe a simple theoretical framework based on electromagnetic and micromagnetic simulations that successfully accounts for the experimental results. This approach can be used to design hybrid quantum systems exploiting magnetostatic mode excited in ferromagnets of arbitrary size and shape and to tune their operation conditions.

Received 8 July 2022
Revised 13 October 2022
Accepted 27 October 2022

DOI:https://doi.org/10.1103/PhysRevApplied.19.014002

Physics Subject Headings (PhySH)

Circuit quantum electrodynamics Magnetic anisotropy Magnons Quantum circuits Quantum information with hybrid systems Spin optoelectronics Spintronics

Ferromagnets

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Sergio Martínez-Losa del Rincón ^1,2, Ignacio Gimeno ^1,2, Jorge Pérez-Bailón ^1,2, Victor Rollano ^1,2, Fernando Luis ^1,2, David Zueco ^1,2, and María José Martínez-Pérez ^1,2,*

¹Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, Zaragoza, Spain
²Departamento de Física de la Materia Condensada, Universidad de Zaragoza, Zaragoza, Spain

^*pemar@unizar.es

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Vol. 19, Iss. 1 — January 2023

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Images

Figure 1
(a) A constriction of width $w$ is FIB patterned on the central part of a conventional $Nb$ CPW transmission line. The Omniprobe needle is used to transport the ${Si}_{3} N_{4}$ palette with the $Py$ ferromagnet towards the constriction. (b) Broadband FMR experiments are performed by measuring the $S_{21}$ transmission parameter with a VNA while sweeping the external magnetic field $B_{ext}$ applied along the $\hat{x}$ direction so that the microwave field $b_{rms}$ produced by the transmission line is perpendicular to it. In this way, a quasihomogeneous Kittel magnon mode is excited in the ferromagnet (blue rectangle with colored arrows) lying at distance $h$ from the superconductor. (c) Enlarged view of the meander region (left panel) where finger capacitors are opened by FIB (right panel). (d) The resulting CPW resonator, with characteristic frequency $ω_{p}$ , and its coupling to the ferromagnetic sample are characterized using the VNA.
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Figure 2
(a) SEM pictures of samples 1, 2, 3, and 4, highlighted with yellow dashed polygons, placed onto the central line of CPW superconducting transmission lines. (b) Broadband FMR curves of the same samples in derivative mode (see Sec. 5). Fitting the magnon resonance frequency $ω_{m}$ to the general Kittel formula [Eq. (2), dashed] yields the corresponding demagnetizing factors (legend). Color scale in all panels goes from $- 0.1$ to 0.1. The solid dots in panels 3 and 4 correspond to the experimental data points obtained from cavity experiments [see Fig. 3]. (c) Field derivative of the experimental transmission parameter (see Sec. 5) corresponding to sample 2 (dashed blue) measured at different values of $B_{ext}$ and fits based on Eq. (3) (solid red). Vertical scale goes from $- 1 \times 10^{- 3}$ to $1 \times 10^{- 3}$ in all panels.
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Figure 3
(a) Experimental microwave transmission through superconducting resonators containing samples 3 ( $ω_{p} / 2 π = 4.2$ GHz, $T = 4.2$ K) and 4 ( $ω_{p} / 2 π = 10.5$ GHz, $T = 10$ mK). The dashed lines are the broadband FMR curves shown in Fig. 2. (b) Field dependence of the resonance width $κ$ for the same resonators and least-squares fits (dashed lines) to Eq. (4). Data corresponding to sample 3 are shifted 2 mT towards negative fields due to a small remnant field in the superconducting coils. Maxima of $κ$ versus $B_{ext}$ provide two additional experimental points of FMR at $B_{ext} = - 3.9$ and 0.4 mT for sample 3 and $B_{ext} = \pm 23$ mT for sample 4 [see Fig. 2].
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Figure 4
Spatial distribution of the in-plane ( $y$ ) component of $b_{rms}$ (a) and $Δ M$ (b) calculated at the position of the ferromagnet. (c) Solid lines are the numerical $g_{theo}$ (at fixed frequency $ω_{p}$ given above each panel) versus distance $h$ . Data points are the experimental $g_{FMR}$ (dots) and $g_{res}$ (stars). From left to right, our experimental data roughly follow $g \propto ω_{p}$ .
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