Band structure engineering of two-dimensional magnonic vortex crystals

Carolin Behncke, Max Hänze, Christian F. Adolff, Markus Weigand, and Guido Meier

Phys. Rev. B 91, 224417 – Published 15 June 2015

Abstract

Magnonic vortex crystals are studied via scanning transmission x-ray microscopy and ferromagnetic-resonance spectroscopy. We investigate a two-dimensional vortex crystal by imprinting waves with tunable wave vectors. The dispersion relation $ω (k)$ is determined via ferromagnetic-resonance spectroscopy with a tunable frequency and wave vector for two vortex core polarization patterns that are adjusted by self-organized state formation prior to the measurement. We demonstrate that the band structure of the crystal is reprogrammed by tuning the vortex polarizations.

Received 20 February 2015
Revised 20 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.224417

Authors & Affiliations

Carolin Behncke^1,*, Max Hänze¹, Christian F. Adolff¹, Markus Weigand², and Guido Meier^3,4

¹Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Universität Hamburg, Jungiusstr. 11, 20355 Hamburg, Germany
²Max-Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany
³Max-Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
⁴The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany

^*cbehncke@physnet.uni-hamburg.de

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Issue

Vol. 91, Iss. 22 — 1 June 2015

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Images

Figure 1
(a) Schematic representation of gyration waves propagating through a two-dimensional vortex crystal imprinted by a phase-shifted excitation of the first two columns of vortices. (b) Scanning electron micrograph of a vortex crystal covered by copper striplines. All three striplines are used to tune the polarization pattern by self-organized state formation. The two thin striplines are used for band structure measurements.
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Figure 2
(a) STXM measurements after state formation with a frequency $f_{state} = 270 MHz, 320 MHz$ , and $330 MHz$ . The white and black dots correspond to $p = 1$ and $p = - 1$ , respectively. Their size depicts the relative gyration amplitude. (b) Absorption spectra of five $50 \times 50$ vortex arrays after state formation with varying frequencies measured with the broad stripline shown in Fig. 1. (c) Selected absorption spectra after state formation at $270 MHz$ (solid dark blue), $320 MHz$ (dashed black), and $330 MHz$ (dotted brown) and Lorentzian fit curves. (d) Absorption spectra calculated within the extended Thiele model corresponding to the following polarization patterns: horizontally striped polarization (solid dark blue), big domains (dashed black), and smaller domains (dotted brown).
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Figure 3
Schematic representation of the measurement setup. The polarization pattern is tuned via an adiabatic reduction of a high frequency magnetic field excitation. The first two columns of vortices are excited via the copper striplines with phase-shifted harmonic high frequency magnetic fields ${\vec{H}}_{1}$ and ${\vec{H}}_{2}$ . Phase and amplitude of the excitation are controlled and adjusted with the signal that passed the sample. The power absorption is determined with the help of a reference measurement at $μ_{0} H = 60 mT$ .
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Figure 4
(a) Measured absorption intensity as a function of excitation frequency and phase difference between the fields ${\vec{H}}_{1}$ and ${\vec{H}}_{2}$ for domains of homogeneous polarization (inset) and (b) corresponding calculations based on the extended Thiele model, where $\frac{ω_{0}}{2 π} = 240 MHz$ . (c) Measured absorption intensity for horizontally striped polarization (inset) and (d) corresponding calculations. The red and blue markers and lines indicate the maxima of the absorption obtained from Lorentzian fits.
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Figure 5
Band structure measurements (markers), calculations based on the extended Thiele model including damping (lines), and calculations by Shibata et al. [18] without damping (dashed lines). (a) Homogeneous polarization pattern. (b) Horizontally striped polarization pattern. The gray regions of wave numbers $k$ are experimentally not accessible. The resonance frequency of a single vortex is $\frac{ω_{0}}{2 π} = 240 MHz$ .
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