Integrated Circuits (ICs) are present in all electronic devices around us. In an effort to make these devices faster and cheaper, the smallest IC building blocks need to be scaled down. This further downscaling of transistors based on CMOS technology results however in a higher heat dissipation. An alternative for today’s transistors is the spin wave majority gate, which is expected to have a low power dissipation when miniaturized. Genuine spin waves originate from deviations of individual, single spins with respect to the perfectly ordered ground state of a ferromagnet in which all spins are aligned parallel to each other. The waves that are propagating such deviations through the lattice of the ferromagnet are called spin waves and, as such, they can be excited only at very low temperatures. However, at room temperature one may excite similar waves, corresponding to the spatial variation of the macroscopic magnetization vector that locally deviates from the spontaneous magnetization. Although the basic quantum theory of ferromagnetism has been established already in the previous century, various fundamental problems are left unsolved or remain to be highly controversial, especially those concerning low-dimensional magnets. Rather than relying on semi-classical theories and simulation programs, this project will focus on the fundamental physics of the spin dynamics of two-dimensional ferromagnets.

More specifically, this project addresses the
time-dependent evolution of the magnetization and related quantities in order
to mimic the propagation of the basic excitations and/or magnetization waves
through low-dimensional magnets, such as spin wave buses or other (ultra)thin
magnetic layers. Aiming at a full quantum dynamical treatment of
low-dimensional spin systems, this project involves extensive computational
effort, both numerically and on the theory side, where the shortcomings of
commonly used classical dynamics based on the LLG equations need to be
superseded. The questions that can be dealt with are: How does the local magnetization
evolve in time and space? How to trigger the (phase-coherent?) propagation of
elementary excitations (spin waves or spin wave-like deviations)? To which extent
can we superimpose the propagation of magnetization waves, knowing that spin
waves are no bosons and can therefore not be simply superimposed to generate
all possible eigenstates? How detrimental is the effect of decoherence
(spin-phonon interactions, spin-spin scattering...)? Simulating the spin wave behavior in a spin wave majority gate is a very challenging task, due to its complex shape, multitude of interactions between different materials and the magnetic finite temperature excitations. Nevertheless, studying the ferromagnet at zero temperature using a simple geometry can provide already many of the desired insights. More specifically, the ferromagnet can be described as a saturated spin lattice with a Heisenberg spin Hamiltonian. Displacing some spins from their equilibrium orientation initiates a spin wave, whose dynamics is described using the Heisenberg equation of motion. The geometry itself can range from a finite spin chain up to an infinite two-dimensional lattice.

This project will involve both analytical and numerical calculations in the domains of quantum mechanics and magnetism.