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This repository holds the first release of TetraX. The recent version is found atgitlab.hzdr.de/micromagnetic-modeling/tetrax. TetraX is a package for finite-element-method (FEM) micromagnetic modeling of magnetization statics and dynamics with the aim to provide user friendly and flexible workflows. Apart from energy minimizers and an LLG solver, it provides implementations of several FEM dynamic-matrix approaches to numerically calculate the normal modes and associated frequencies for magnetic specimen of different geometries such as confined samples, infinitely long waveguides, or infinitely extended multilayers. Next to support for ferromagnets, TetraX will also provide the first full micromagnetic package for antiferromagnets. TetraX is a package for finite-element-method (FEM) micromagnetic modeling of magnetization statics and dynamics with the aim to provide user friendly and flexible workflows. Apart from energy minimizers and an LLG solver, it provides implementations of several FEM dynamic-matrix approaches to numerically calculate the normal modes and associated frequencies for magnetic specimen of different geometries such as confined samples, infinitely long waveguides, or infinitely extended multilayers. Next to support for ferromagnets, TetraX will also provide the first full micromagnetic package for antiferromagnets.

Spin waves are considered as promising candidates to carry information in future technology applications, therefore in the last decades they have been studied intensively in ferromagnetic thin films. Recent developments in material research enabled the manufacturing of more complex structures than planar thin films; especially nanotubes and bent structures of varying curvature can be produced. It has recently been shown by theory that in nanotubes the curvature has an impact on both the domain wall and spin-wave propagation [1][2]. Moreover, the dispersion relation in nanotubes is non-reciprocal regarding the sign of the propagation vector. These effects are attributed to the lack of local inversion symmetry due to the curved surface of the nanotube [3]. As predicted by theory the spin-wave dynamics is fundamentally different from that known from thin films. Here, we studied the spin-wave propagation and the spin-wave dispersion in bent Permalloy thin-film stripes in the form of quarter-tubes, half-tubes and threequarter tubes. Compared to nanotubes, these systems only posses the curvature but not the specific boundary condition of nanotubes. For the simulations we used our GPU accelerated Finite Element micromagnetic code TetraMag [4]. The partial tubes had a homogenous magnetization along the circumference or azimuthal direction in cylindrical coordinates. The spin waves are excited with an external field applied in the radial direction at the middle of the sample. Therefore the spin waves propagate toward the ends of the considered structures, in a Damon-Eshbach geometry. For a given frequency the simulation is run until the steady state is reached. The wave vector correponding to this excitation frequency is determined by a Fourier analysis of the radial component of the magnetization along the z-axis, using a given snapshot in time. The resulting dispersion relations show a non-reciprocity regarding the sign of the propagation vector, similarly to those reported for nanotubes. The spin wave assymetry, defined as the ratio between the difference of the frequencies and their sum for a given wave vector but with opposite signs, can be as high as 5%. This is equivalent to a difference of about 500MHz for spin waves travelling with a given wave vector but opposite signs. We believe this assymetry can be verified experimentally, providing further prospects for research. [1] M. Yan et al., Appl. Phys. Lett. 99, 122505 (2011) [2] M. Yan et al., Appl. Phys. Lett. 100, 25402 (2012) [3] R. Hertel, SPIN 3, 1340009 (2013) [4] A. Kakay et al., IEEE Trans. Magn. 46, 2303 (2010)

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