Micromagnetic simulations for boolean and non-boolean logic

In the last decades, the downscaling of the CMOS transistor has led to an exponential growth in computing unit performances. However, when the transistor size reached the nanometer dimensions, this downscaling became increasingly challenging. As a result, recently, there has been a strong search for beyond-CMOS computing schemes that allow for further improvement of computing unit performances. One promising alternative computing methodology is called wave computing which utilizes waves and waveguides instead of electric currents and transistors. In the wave computing framework, different logic building blocks can be designed which have higher functional density than traditional transistors. Nevertheless, every computing framework has its own advantages and disadvantages and, therefore, the wave computing scheme is not expected to replace the complete CMOS ecosystem. Instead, it is predicted to complement the current CMOS-based computing architecture and thereby forming a hybrid CMOS-wave computing system.

There are several types of waves that can be utilized to realize wave computing circuits. In this work, we focus on spin and magnetoelastic waves as they are scalable and have low intrinsic energies. These waves are only present in magnetic materials and thus magnetoelectric transducers are required to connect the electric and magnetic domain in the hybrid CMOS-wave computing system. However, currently, there is a lack of understanding of the wave properties and the transducer behavior at nanoscale dimensions. Therefore, in this work, we study the underlying physics of inductive antenna and strain-based magnetoelectric transducers as well as spin and magnetoelastic waves at the nanometer scale and RF frequencies.

In the first part, we derive theoretical models of the magnetoelectric transducers and assess their efficiency and scalability relations. In addition, the models are applied to specific use cases to gain more understanding and order of magnitude estimates of their actual performance. These models result in general guidelines to determine the optimal transducer material and device configurations.

In the second part, we study spin and magnetoelastic waves in nanoscale waveguides. The nanoscale dimension results in strongly modified wave properties because the boundary influence cannot be neglected anymore. It is shown that the shape anisotropy increases for nanoscale dimensions which leads to different spin-wave modes with tilted mode profiles and modified dispersion relations. Moreover, at these nanoscale dimensions and for nonuniform magnetization dynamics, the presence of edge modes is also illustrated.

Besides pure spin waves, also magnetoelastic waves in nanoscale waveguides are investigated. A theoretical model is derived which allows to calculate the dispersion relation and eigenstates of plane magnetoelastic waves in thin films. For magnetoelastic waves in thin waveguides, a new numerical module is developed which considers the boundary conditions and magnetoelastic interaction between the elastic and magnetic domains. This solver is incorporated in mumax3 and utilized to study magnetoelastic waves in nanoscale waveguides. The results show the presence of additional magnetoelastic coupling terms that originate from the confinement and illustrate mode-dependent coupling between the elastic and magnetic modes.

In the last part, the coupling between the dynamics inside the magnetoelectric transducer and the dynamics inside the waveguide is investigated by combining the comsol and mumax3 simulation platforms. The understanding of this coupling is crucial for achieving hybrid magnetoelectric systems. The study investigates two interaction schemes that act simultaneously but have different origins. From this, it is shown that only the shear strain components result in strong magnetoelastic interaction for the considered geometries.

The results obtained in this work contribute to the fundamental understanding of scalable magnetoelectric transducers and waves in nanoscale magnetostrictive waveguides. The theory gives fundamental physical insight and provides transducer efficiency estimates. On the other hand, the simulations help in understanding the dynamics and provide insight into the design of next-generation wave-based circuits.