Magnonic Band Structure in Vertical Meander-Shaped <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>Co</mml:mi><mml:mn>40</mml:mn></mml:msub></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>Fe</mml:mi><mml:mn>40</mml:mn></mml:msub></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="normal">B</mml:mi></mml:mrow></mml:mrow><mml:mn>20</mml:mn></mml:msub></mml:math> Thin Films
Gianluca Gubbiotti, Alexandr Sadovnikov, Evgeny Beginin, Sergey Nikitov, Danny Wan, Anshul Gupta, Shreya Kundu, Giacomo Talmelli, Robert Carpenter, Inge Asselberghs, Iuliana P. Radu, Christoph Adelmann, Florin Ciubotaru
Abstract
Exploring the third dimension in magnonic systems is essential for the investigation of alternative physical phenomena and for the control of spin-wave propagation at the nanoscale. Here, the characteristics of spin waves in vertical meander-shaped ${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$ thin films consisting of nanosegments located at 90\ifmmode^\circ\else\textdegree\fi{} angles with respect to each other are investigated by Brillouin-light-scattering spectroscopy over four Brillouin zones in reciprocal space. We reveal the dispersion relations and the periodic character of several dispersive branches as well as alternating frequency bands, where spin waves are allowed or forbidden to propagate. Between each couple of successive modes, frequency band gaps exist only for wave numbers k = 2m\ensuremath{\pi}/a, where m is an integer number and a is the size of the meander unit cell, whereas the spectra show propagating modes in the orthogonal film segments for all the other wave numbers. Micromagnetic simulations and analytical calculations are used to understand and explain the results in terms of the mode spatial localization and symmetry. We show that the width and the center frequency of the magnonic band gaps can be controlled by changing the geometrical parameters of the meander-shaped film. The investigated samples behave as three-dimensional waveguides where spin waves propagate in the film segments located at 90\ifmmode^\circ\else\textdegree\fi{} angles with respect to each other, thus making possible vertical spin-wave transport for multilayer magnonic architectures and signal processing.