Temperature-dependent magnetic damping of yttrium iron garnet spheres

H. Maier-Flaig, S. Klingler, C. Dubs, O. Surzhenko, R. Gross, M. Weiler, H. Huebl, and S. T. B. Goennenwein

Phys. Rev. B 95, 214423 – Published 27 June 2017

Abstract

We investigate the temperature-dependent microwave absorption spectrum of an yttrium iron garnet sphere as a function of temperature (5 to $300 K$ ) and frequency (3 to $43.5 GHz$ ). At temperatures above $100 K$ , the magnetic resonance linewidth increases linearly with temperature and shows a Gilbert-like linear frequency dependence. At lower temperatures, the temperature dependence of the resonance linewidth at constant external magnetic fields exhibits a characteristic peak which coincides with a non-Gilbert-like frequency dependence. The complete temperature and frequency evolution of the linewidth can be modeled by the phenomenology of slowly relaxing rare-earth impurities and either the Kasuya-LeCraw mechanism or the scattering with optical magnons. Furthermore, we extract the temperature dependence of the saturation magnetization, the magnetic anisotropy, and the $g$ factor.

Received 29 March 2017
Revised 2 June 2017

DOI:https://doi.org/10.1103/PhysRevB.95.214423

Physics Subject Headings (PhySH)

Ferrimagnets Magnetic systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Maier-Flaig^1,2,*, S. Klingler^1,2, C. Dubs³, O. Surzhenko³, R. Gross^1,2,4, M. Weiler^1,2, H. Huebl^1,2,4, and S. T. B. Goennenwein^1,2,4,5,6

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
²Physik-Department, Technische Universität München, 85748 Garching, Germany
³INNOVENT e.V. Technologieentwicklung, 07745 Jena, Germany
⁴Nanosystems Initiative Munich, 80799 München, Germany
⁵Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany
⁶Center for Transport and Devices of Emergent Materials, Technische Universität Dresden, 01062 Dresden, Germany

^*hannes.maier-flaig@wmi.badw.de

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Issue

Vol. 95, Iss. 21 — 1 June 2017

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Images

Figure 1
The coplanar waveguide (CPW), on which the YIG sphere and a DPPH marker are mounted (right), is inserted into a magnet cryostat (left). The microwave transmission through the setup is measured phase sensitively using a vector network analyzer (VNA). As the Oersted field $h_{MW}$ (red) around the center conductor of the CPW extends into the YIG sphere and the DPPH, we can measure the microwave response spectra of both samples. A superconducting magnet provides the static external magnetic field $H_{0}$ (orange) at the location of the sample. Also shown are the lines corresponding to the specified 1‰ homogeneity of the field for an on-axis deviation from the center of magnet (com).
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Figure 2
Eigenmode spectra of the YIG sphere at (a) $290 K$ and (b) $20 K$ . The (110) and (440) MSMs are marked with red dashed lines. The change in their slope gives the change of the $g$ factor of YIG. Their splitting ( $Δ f_{M}$ , red arrow) depends linearly on the YIG magnetization. The increase in $M_{s}$ towards lower temperatures is already apparent from the increased splitting $Δ f_{M}$ . Marked in orange is the offset of the resonance frequency $Δ f_{A}$ extrapolated to $H_{0} = 0$ resulting from anisotropy fields $H_{ani}$ present in the sphere. The green marker denotes the position of the DPPH resonance line, which increases in amplitude considerably towards lower temperatures. Inset: $S_{21}$ parameter (data points) and fit (lines) at $μ_{0} H = 321 mT$ and $T = 20 K$ .
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Figure 3
(a) YIG magnetization as function of temperature extracted from the (110) and (440) mode dispersions using Eq. (4). The purple line shows the fit to a Bloch model (cf. parameters in the main text). (b) YIG anisotropy field $μ_{0} H_{ani} (T) = \frac{2 π}{γ} Δ f_{ani}$ . Red squares: Same procedure applied to the DPPH dispersion as reference. (c) YIG $g$ -factor (blue circles). For reference, the extracted DPPH $g$ -factor is also shown (red squares). The gray numbers indicate the relative change of the $g$ -factors from the lowest to the highest measured temperature (gray horizontal lines). As we use the YIG (110) mode as the magnetic field reference, the extracted value of $g$ and $H_{ani}$ at $300 K$ are fixed to the values determined in the room temperature setup [16].
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Figure 4
(a) Full width at half maximum (FWHM) linewidth $Δ f_{res}^{110}$ of the (110) mode as a function of frequency for different temperatures. A linear Gilbert-like interpretation is justified in the high- $T$ case ( $T > 100 K$ ) only. Below $100 K$ , the slope of $Δ f^{110} (f_{res}^{110})$ is not linear so that a Gilbert type interpretation is no longer applicable. (b) FWHM linewidth as a function of temperature for two different fixed external magnetic fields. The linewidth peaks at a magnetic-field-dependent temperature that can be modeled using the phenomenology of rare-earth impurities resulting in $T_{\max}$ (vertical dotted lines).
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Figure 5
(a) Gilbert damping parameter $α$ determined from the slope of a linear fit to the $Δ f (f, T)$ data for frequencies above $20 GHz$ . The red line shows the linear dependence of the linewidth with temperature expected from the Kasuya-LeCraw process. (b) Inhomogeneous linewidth $Δ f_{0}$ (intersection of the aforementioned fit with $f_{res}^{110} = 0$ ) as a function of temperature. The inhomogeneous linewidth shows a slight increase with decreasing temperature down to $100 K$ . In the region where the slow relaxor dominates the linewidth (gray shaded area, cf. Fig. 4), the linear fit is not applicable and unphysical damping parameters and inhomogeneous linewidths are extracted.
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Figure 6
Full map of the FWHM linewidth of the (110) mode as function of temperature and field or resonance frequency $f_{res}^{110}$ . At low temperatures, only the slow relaxor peak is visible, while at high temperatures the Gilbert-like damping becomes dominant. The position of the peak in the linewidth modeled by a slow relaxor is shown as a dashed orange line. The model parameters are taken from Clarke [29] and taking $δ_{a} = 2.50 meV$ . The dotted lines indicate the deviation of the model for $0.5 δ_{a}$ (lower $T^{\max}$ ) and $2 δ_{a}$ (higher $T^{\max}$ ).
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