Spin pumping in strongly coupled magnon-photon systems

H. Maier-Flaig, M. Harder, R. Gross, H. Huebl, and S. T. B. Goennenwein

Phys. Rev. B 94, 054433 – Published 30 August 2016

Abstract

We experimentally investigate magnon polaritons arising in ferrimagnetic resonance experiments in a microwave cavity with a tunable quality factor. To this end, we simultaneously measure the electrically detected spin pumping signal and the microwave reflection (the ferrimagnetic resonance signal) of a yttrium iron garnet (YIG)/platinum (Pt) bilayer in the microwave cavity. The coupling strength of the fundamental magnetic resonance mode and the cavity is determined from the microwave reflection data. All features of the magnetic resonance spectra predicted by first principle calculations and an input-output formalism agree with our experimental observations. By changing the decay rate of the cavity at constant magnon-photon coupling rate, we experimentally tune in and out of the strong coupling regime and successfully model the corresponding change of the spin pumping signal and microwave reflection. Furthermore, we observe the coupling and spin pumping of several spin wave modes and provide a quantitative analysis of their coupling rates to the cavity.

Received 22 January 2016
Revised 2 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.054433

Physics Subject Headings (PhySH)

Magnons Phonons Spin pumping Spintronics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Maier-Flaig^1,2,*, M. Harder³, R. Gross^1,2,4, H. Huebl^1,2,4, and S. T. B. Goennenwein^1,2,4,†

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
²Physik-Department, Technische Universität München, 85748 Garching, Germany
³Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
⁴Nanosystems Initiative Munich, Schellingstraße 4, 80799 München, Germany

^*hannes.maier-flaig@wmi.badw.de
^†Current address: Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany.

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Issue

Vol. 94, Iss. 5 — 1 August 2016

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Images

Figure 1
Block diagram of the experimental setup including low noise voltage amplifer (LNA), vector network analyzer (VNA), and sample mounting. (Inset) Schematic of the coupling scheme illustrating cavity decay due to intrinsic losses ( $κ_{i}$ ) and losses to the feed line ( $κ_{e}$ ) and spin system decay consisting of intrinsic damping ( $γ_{i}$ ) and spin pumping damping ( $γ_{sp}$ ) as well the collective coupling rate $g_{eff}$ .
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Figure 2
(b),(c) Reflection parameter $S_{11}$ recorded while sweeping the magnetic field and the microwave frequency. Strong coupling of the collective spin excitations is indicated by a clear anticrossing and spin wave modes to the low field side of the main resonance are visible. (e),(f) Simultaneously recorded DC voltage. Fundamental and spin wave modes are visible where the latter couple less strongly and thus pump spin current more efficiently. (a),(d) Line cuts at $H_{0} = \pm 267.5 mT$ show the symmetry under field reversal for $S_{11}$ (a) and $V_{DC}$ (d). (g),(h) Detail of the $n = 7$ spin wave mode in microwave reflection (g) and as voltage detected spectrum (h). Superimposed is the dispersion relation of the strong coupling between the fundamental FMR mode and the cavity as solid red line. The anticrossing of this hybrid and the $n = 7$ spin wave mode is displayed as dashed white lines.
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Figure 3
(a) Half width at half maximum linewidths (light blue) from fits of a Lorentzian to frequency cuts at fixed fields. Fitting Eq. (2) for each spin wave resonance enables extraction of the coupling strength for weakly coupled spin waves [34]. (b) For the more strongly coupling spin wave modes ( $n = 7, 9$ ), the model of Eq. (2) overestimates the coupling strength. Instead, the sum of two Lorentzian absorption peaks (dashed, sum as solid dark blue line) are fitted to a cut at constant field $μ_{0} H_{0} = 266.17 mT$ (light blue); the splitting of the centers is equal to $2 g_{eff} / 2 π$ . (c) Spin wave-cavity coupling strength $g_{eff}^{n}$ and spin decay rate $γ_{s}^{n}$ as a function of the inverse mode number. Also displayed is the predicted $1 / n$ behavior. Inset: A homogeneous excitation microwave field $h_{1}$ couples only to the part of the dynamic magnetization of a spin wave mode that has no corresponding $π$ -phase shifted component. For the shown pinned boundary conditions only odd modes can be excited, where the effective magnetization (blue) scales as $1 / n$ .
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Figure 4
Increasing the coupling of the cavity to the feed line (from left to right) increases the cavity loss rate $κ_{c}$ and thus linewidth $Δ ω / 2 π$ . This enables experimental control of the transition between strong and weak coupling. (b)–(d) Microwave reflection. (f)–(h) DC voltage. (a),(e) Line cuts at fixed field ( $H_{0} = \pm 267.5 mT$ ) are shown for the different coupling regimes (R, G, B and corresponding colors) in both reflection (a) and voltage (e) measurements. They clearly show the merging of the two dispersion curves during the strong/weak transition. Cuts at positive field (intense colors) and negative field (pale colors) again confirm the symmetry, $V (- H_{0}) = - V (H_{0})$ and $S_{11} (- H_{0}) = S_{11} (H_{0})$ .
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Figure 5
Line cuts of (a) reflection parameter and (b) DC voltage at the resonator frequency $ω_{c} (H_{0} = 0) = 9.651 GHz$ . In the strongly coupled magnon-photon case (blue lines, cavity and feed line are critically coupled) the only indication of the fundamental mode ( $n = 1$ ) is the large slope in $| S_{11} |$ whereas in the weakly coupled case (red lines, cavity and feed line are highly overcoupled) the magnon spectrum is accurately and clearly reproduced. Inset: Spin wave resonance fields extracted from the weakly coupled case (blue squares) and resonance fields anticipated with values from literature [31, 32, 33] (green dashed line).
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