Spin-wave localization and guiding by magnon band structure engineering in yttrium iron garnet

Rouven Dreyer, Niklas Liebing, Eric R. J. Edwards, Andreas Müller, and Georg Woltersdorf

Phys. Rev. Materials 5, 064411 – Published 21 June 2021

Abstract

In spintronics, the propagation of spin-wave excitations in magnetically ordered materials can also be used to transport and process information. One of the most popular materials in this regard is the ferrimagnetic insulator yttrium iron garnet due its exceptionally small spin-wave damping parameter. While the small relaxation rate allows for large propagation length of magnetic excitations, it also leads to nonlocality of the magnetic properties. By imaging spin waves, their band structure is mapped with high-frequency resolution using a magneto-optic super-Nyquist sampling technique. In doing so, wave-vector selection is shown to suppress dispersion effects to a large extent, allowing for local measurements of spin relaxation. Moreover, we demonstrate even higher control of magnon propagation by employing the wave-vector selectivity near an avoided crossing of different spin-wave modes where the group velocity approaches zero. Here the local engineering of the dispersion allows us to construct magnonic waveguides, and at the same time it reveals the local relaxation properties.

Received 2 March 2021
Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.064411

Physics Subject Headings (PhySH)

Magnetism Magnetization dynamics Methods in magnetism Spin dynamics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Rouven Dreyer, Niklas Liebing, Eric R. J. Edwards^*, Andreas Müller, and Georg Woltersdorf ^†

Institute of Physics, Martin Luther University Halle-Wittenberg, 06120 Halle, Germany

^*Present address: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA.
^†georg.woltersdorf@physik.uni-halle.de

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Issue

Vol. 5, Iss. 6 — June 2021

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Images

Figure 1
(a) Geometry of the experiments. Spatial resolved images of spin waves in DE and BV configurations with their corresponding wavelength are shown in the gap. (b) The frequency comb generated by a femtosecond laser is given by multiples of the laser repetition rate $f_{rep}$ . The excitation frequency $f_{rf}$ aliases back to the Nyquist frequencies (red dotted lines). The lowest aliasing frequency corresponds to the difference frequency $ɛ$ between $f_{rf}$ and the nearest comb line.
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Figure 2
Extracted spin-wave dispersion for a fixed external field of 79 mT. The dispersion curves were computed with the recipe by Kalinikos and Slavin [40, 58] as discussed in the supplemental material. The red solid lines indicate the DE and BV dispersion. The dotted red line shows an angular orientation of nearly flat dispersion. The black solid line depicts the dispersion branch for the first PSSW. The top left inset shows the spin-wave profile in the vicinity of the avoided mode crossing recorded in the gap of the CPW. The top right inset shows a magnified view of the avoided mode crossing with the calculated mode repulsion [40, 58].
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Figure 3
(a) Angular dependence of the local field swept measurements of the rf-susceptibility measured with an excitation frequency of 4.0 GHz. A clear minimum of the dispersion around a magnetic field direction of 55 degrees is visible. The inset shows the nearly uniform spatial distribution of the magnetic excitation across the gap recorded at the dispersion minimum. (b)–(e) Detailed measurement of the spin-wave dispersion minimum for frequencies between 3 and 6 GHz. The inset in panel (e) depicts the extracted linewidth of the 5.6 GHz measurement as a function of in-plane field orientation clearly showing a minimum at nearly flat dispersion.
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Figure 4
(a) Frequency dependence of the linewidth for FMR measurements (black cross) and at the dispersion minimum (red dots). The blue data points show the calculated linewidth in the vicinity of the avoided crossing. Solid lines are fits to extract the Gilbert damping. (b) Gilbert damping for localized spin-wave modes for different frequency. The dotted black line indicates the average damping parameter, while the gray area is the standard deviation. The orange star marks the data point taken within the magnonic waveguide presented in Fig. 5.
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Figure 5
Parts (a) and (b) show the magnonic band gap for an external field of 79 mT at positions next to and within the magnonic waveguide, respectively. In (b) the dispersion is slightly shifted toward larger frequencies. Here we find a regime where in contrast to the band state in (c), the propagation of DE spin-wave modes is only possible within the waveguide (gap state) as observed in (d).
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