title: Dynamic magnetism and magnetisation topology in artificial spin ice
Creators: name: Li, Yue
Publisher: name: University of Glasgow
Year: 2018
Subjects: subject: Artificial spin ice, magnetisation dynamics, magnetisation topology, micromagnetic simulation, Lorentz TEM.

description: Artificial spin ice (ASI) is a class of magnetic patterned arrays consisting of interacting ferromagnetic nanomagnets. The nano-scale size and the elongated shape of each nanomagnet ensure the formation of a single domain, which behaves as a ‘macrospin’ and results in only two possible magnetisation directions along the long axis of the nanomagnet.
ASI system has the potential ability not only as a magnonic crystal because of the microwave properties being associated with its intrinsically intricate magnetisation topologies and inter-element interaction, but as a tool to model the microstructure of atomic scale allowing its fundamental physics to be studied.
This thesis addresses the field-induced properties of the static and dynamic magnetisation in square and pinwheel ASI. Firstly, the magnetic properties of the square ASI specimens were characterised using alternating gradient force magnetometry, Brillouin light scattering and ferromagnetic resonance. Micromagnetic simulations were employed to assist in understanding the experimental results. Secondly, the field-induced evolution of the magnetisation configuration in a finite-size pinwheel ASI array was imaged using Lorentz transmission electron microscopy.
The square structure of the square ASI lattices allows a comparison of the response of the spin-wave modes in the two groups of magnetic elements which are orthogonally aligned to one another. The frequency of the spin-wave mode is dependent on the direction of the applied field, either along the easy or hard axes of the nanomagnet. It has been found that more spin-wave modes are found when the magnetic field lies along the hard axis of the nanomagnet compared to when the field is aligned with the easy axis of the island. This attributes to the formation of more edge modes of standing spin waves in the former case. The experimental behaviour of the static and dynamic magnetisation can be well described via the micromagnetic simulations where only an individual island is considered with an assumption that the inter-island interaction is negligible. Additionally, the field direction with respect to the square ASI lattices is also responsible for the changes in spin-wave frequencies. The results imply that the square ASI could act as a reconfigurable microwave resonator due to its spin-wave frequency being dependent on the changes in magnetisation configuration that were controlled by the applied field.
The dependence of the nanomagnet thickness on the static and the dynamic properties of the square ASI was studied. The nanomagnet thickness is found to be responsible for the coercivity and the number of observed spin-wave modes of the square ASI array. The thicker ASI array has a larger coercive field and produces more spin-wave modes. Micromagnetic simulations suggest that the inter-island coupling contributes weakly to the coercivity and the spin-wave frequency of the thicker array whereas it is negligible for a thinner array. Furthermore, fitting to ferromagnetic resonance data allows for access to information on ferromagnetic parameters, such as gyromagnetic ratio and saturation magnetisation.
Finally, static and dynamic magnetisation topologies in a pinwheel ASI is explored as a function of magnetic field. The pinwheel ASI is a square ASI modified by rotating each nanomagnet 45° around its central axis in the same direction. The energy spread between the pinwheel vertices significantly decreased as the geometrical structure transforms from the square vertices to the pinwheel vertices. The ferromagnetic magnetisation process shows the domain growth mediated via the propagation of domain walls. Intriguingly, some of the observed mesoscopic domain-wall topologies resemble the Néel and the crosstie walls seen in natural ferromagnetic films, while others mimic the configurations of the charged walls found in the ferroelectric materials. In addition, a rotational-field demagnetisation was carried out in order to anneal the pinwheel ASI to the ground state. The results show that the net moment of the entire array decreases and the short-range ground state is attained through the presence of the vortices (Type III) and antivortices (Type IV) vertices, rather than the global Landau-like flux closure structure predicted by Monte Carlo simulations.