Materials with interacting magnetic degrees of freedom display a rich variety of magnetic behaviour that can lead to novel collective equilibrium and out-of-equilibrium phenomena. In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour. Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory. We use low energy muon spectroscopy to probe the dynamic behaviour of the interacting nanomagnets and observe peaks in the muon relaxation rate that can be identified with the critical temperatures of the predicted phase transitions. This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

Two-dimensional magnetic systems with continuous spin degrees of freedom exhibit a rich spectrum of thermal behaviour due to the strong competition between fluctuations and correlations. When such systems incorporate coupling via the anisotropic dipolar interaction, a discrete symmetry emerges, which can be spontaneously broken leading to a low-temperature ordered phase. However, the experimental realisation of such two-dimensional spin systems in crystalline materials is difficult since the dipolar coupling is usually much weaker than the exchange interaction. Here we realise two-dimensional magnetostatically coupled XY spin systems with nanoscale thermally active magnetic discs placed on square lattices. Using low-energy muon-spin relaxation and soft X-ray scattering, we observe correlated dynamics at the critical temperature and the emergence of static long-range order at low temperatures, which is compatible with theoretical predictions for dipolar-coupled XY spin systems. Furthermore, by modifying the sample design, we demonstrate the possibility to tune the collective magnetic behaviour in thermally active artificial spin systems with continuous degrees of freedom.

This work explores the applicability of atomic layer deposition (ALD) in producing highly oriented crystalline gallium oxide films on foreign substrates at low thermal budgets. The effects of substrate, deposition temperature, and annealing process on formation of crystalline gallium oxide are discussed. The Ga 2 O 3 films exhibited a strong preferred orientation on the c-plane sapphire substrate. The onset of formation of crystalline gallium oxide is determined, at which only two sets of planes, i.e., α-Ga 2 O 3 (006) and β-Ga 2 O 3 (4̅ 02), are present parallel to the surface. More specifically, this work reports, for the first time, that epitaxial gallium oxide films on sapphire start to form at deposition temperatures ≥ 190 °C by using an optimized plasma-enhanced ALD process such that α-Ga 2 O 3 (006)∥α-Al 2 O 3 (006) and β-Ga 2 O 3 (2̅ 01)∥α-Al 2 O 3 (006). Both α-Ga 2 O 3 (006) and β-Ga 2 O 3 (2̅ 01) planes are polar planes (i.e., consisting of only one type of atom, either Ga or O) and, therefore, favorable to form by ALD at such low deposition temperatures. Ellipsometry and van der Pauw measurements confirmed that the crystalline films have optical and electrical properties close to bulk gallium oxide. The film grown at 277 °C was determined to have superior properties among as-deposited films. Using TEM to locate α-Ga 2 O 3 and β-Ga 2 O 3 domains in the as-deposited crystalline films, we proposed a short annealing scheme to limit the development of α-Ga 2 O 3 domains in the film and produce pure β-Ga 2 O 3 films via an energy-efficient process. A pure β-Ga 2 O 3 phase on sapphire with β-Ga 2 O 3 (2̅ 01)∥α-Al 2 O 3 (006) was successfully achieved by using the proposed process at the low annealing temperature of 550 °C preceded by the low deposition temperature of 190 °C. The results of this work enable epitaxial growth of gallium oxide thin films, with superior material properties offered by ALD, not only with potential applications as a high-performance material in reducing global energy consumption but also with an energyefficient fabrication process.