Impact of magnetocrystalline anisotropy on static magnetization and spinwave dynamics in nanowires

In the last decades, CMOS technology optimization has been pushing close to its limits, leading to a slowdown of Moore’s law trend. To overcome these limitations, new strategies have been developed : one of the most promising is spintronics. Spintronics aims to build a new encoding of information, relying on the electron spin and magnetization states. In parallel to spintronics evolution, advanced fabrication methods evolution have enable the realization advanced structures, giving rise to a new branch of magnetic texture called three-dimensional magnetism. In this context, novel geometries are investigated for the encoding and transport of information. This thesis work focuses on magnetic nanowires and on the impact of magneto-crystalline anisotropy on the static magnetization and spinwave propagation. The results shown in this thesis are obtained from simulations performed by using TetraX , a finite-element eigenmode solver, developed for the study of dynamic states in nanomagnets. TetraX employs two-dimensional finite-element discretization, which gives an accurate description of complex geometries, keeping the computational cost low with respect to three-dimensional solvers. Thesis results are organized in two main sections. In the first section a statical analysis is carried out. The magnetocristalline anisotropy is defined along the nanowire axis, defining a preferred direction of the magnetization. Negative values of this parameter induces the reorientation of the magnetization from the axial direction toward the section of the wire, resulting in the vortex states formation. A vortex state is a spin texture in which the magnetization in the center is aligned with the axis axial direction and moving towards the radial component the magnetization gradually tilts towards the azimuthal direction, with two possible magnetization circulations. An analytical model, together with a semi-analytical, obtained by fitting methods, are proposed in order to describe the magnetization orientation along the radial direction of the nanowire. Subsequently, the statical characterization includes hysteresis loops obtained by applying an external field in the axial direction. From hysteresis loops is possible to derive anisotropic magnetoresistance measurements, providing a connection with experimental measurements and allowing an experimental estimation of the value of the anisotropy in real systems. The second section focuses the dynamical analysis. A first study is conducted in a nanowire without magnetocrystalline anisotropy. From simulations results form TetraX it is possible to have access to eigenfrequencies and eigenmodes, allowing the construction of a spinwave dispersion spectrum as function of the wavevector. A nomenclature of eigenmodes is introduced, and a classification of different branches in the spectrum is proposed based from shared properties. A second study is carried out in a system with an anisotropy value sufficient to induce the vortex state formation. In this case, the calculated spectrum reveals an asymmetry in the dispersion relation, showing the role of anisotropy in the spinwave propagation. This work aims to validate experimental results that suggest an asymmetric behavior in spinwave propagation related to the magnetocrystalline anisotropy. The numerical results presented establish a computational framework , that may be confirmed by tailored experiments, thus contributing to the understanding of spinwaves in three-dimensional geometries.