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The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order1–6, collective low-energy dynamics7,8 and emergent magnetic properties5, 9,10 in, for example, artificial spin-ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here, we introduce a new approach: single interaction modifiers, using slave mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane11. We show that by placing these on the vertices of square artificial spin-ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule-obeying states in square artificial spin-ice structures, enabling the exploration of thermal dynamics in a spin-liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.

Artificial spin ice structures can be designed that allow for the induction of thermal fluctuations, with dynamics that depend on the material and the lattice geometry. Artificial spin ice systems have been proposed as a playground for the study of monopole-like magnetic excitations 1 , 2 , similar to those observed in pyrochlore spin ice materials 3 . Currents of magnetic monopole excitations have been observed 4 , demonstrating the possibility for the realization of magnetic-charge-based circuitry. Artificial spin ice systems that support thermal fluctuations can serve as an ideal setting for observing dynamical effects such as monopole propagation and as a potential medium for magnetricity investigations 1 , 2 . Here, we report on the transition from a frozen to a dynamic state in artificial spin ice with a square lattice. Magnetic imaging is used to determine the magnetic state of the islands in thermal equilibrium. The temperature-induced onset of magnetic fluctuations and excitation populations are shown to depend on the lattice spacing and related interaction strength between islands. The excitations are described by Boltzmann distributions with their factors in the frozen state relating to the blocking temperatures of the array. Our results provide insight into the design of thermal artificial spin ice arrays where the magnetic charge density and response to external fields can be studied in thermal equilibrium.

We present a study of V 2 O 3 thin films grown on c -plane Al 2 O 3 substrates by reactive dc-magnetron sputtering. Our results reveal three distinct types of films displaying different metal–insulator transitions dependent on the growth conditions. We observe a clear temperature window, spanning 200 ∘ C, where highly epitaxial films of V 2 O 3 can be obtained wherein the transition can be tuned by controlling the amount of interstitial oxygen in the films through the deposition conditions. Although small structural variations are observed within this window, large differences are observed in the electrical properties of the films with strong differences in the magnitude and temperature of the metal–insulator transition which we attribute to small changes in the stoichiometry and local strain in the films. Altering the sputtering power we are able to tune the characteristics of the metal–insulator transition suppressing and shifting the transition to lower temperatures as the power is reduced. Combined results for all the films fabricated for the study show a preferential increase in the a lattice parameter and reduction in the c lattice parameter with reduced deposition temperature with the film deviating from a constant volume unit cell to a higher volume.

We present a direct experimental investigation of the thermal ordering in an artificial analogue of an asymmetric two-dimensional Ising system composed of a rectangular array of nano-fabricated magnetostatically interacting islands. During fabrication and below a critical thickness of the magnetic material the islands are thermally fluctuating and thus the system is able to explore its phase space. Above the critical thickness the islands freeze-in resulting in an arrested thermalized state for the array. Determining the magnetic state we demonstrate a genuine artificial two-dimensional Ising system which can be analyzed in the context of nearest neighbor interactions.

We demonstrate a lossless switching between vortex and collinear magnetic states in circular FePd disks arranged in a square lattice. Above a bifurcation temperature we show that thermal fluctuations are enough to facilitate flipping between the two distinctly different magnetic states. We find that the temperature dependence of the vortex annihilation and nucleation fields can be described by a simple power law relating them to the saturation magnetization.

We investigate the design of magnetic ordering in one-dimensional mesoscopic magnetic Ising chains by modulating long-range interactions. These interactions are affected by geometrical modifications to the chain, which adjust the energy hierarchy and the resulting magnetic ground states. Consequently, the magnetic ordering can be tuned between antiferromagnetic and dimer antiferromagnetic phases. These phases are experimentally observed in chains fabricated using both conventional electron-beam lithography and ion implantation techniques, demonstrating the feasibility of controlling magnetic properties at the mesoscale. The ability of attaining these magnetic structures by thermal annealing, underlines the potential of using such systems instead of simulated annealers in tackling combinatorial optimization tasks.

We study experimentally the impact of the additive fabrication method on the magnetic properties of Fe\\(^+\\)-implanted Pd square artificial spin ice lattices. Our findings show that the lattices exhibit a higher ordering temperature than their continuous film counterparts. This behavior is attributed to the additive fabrication process, which induces an inhomogeneous Fe concentration within the lattice building blocks. Moreover, the implantation process creates a magnetic depth profile, enabling temperature-dependent tunability of the magnetic thickness. These additional internal degrees of freedom broaden the design possibilities for magnetic metamaterials, allowing precise fine-tuning of their static and dynamic properties to achieve complex and customizable behaviors.

The topic of this thesis is the investigation of the magnetic properties of artificially created magnetic structures. Applying different characterization techniques, ranging from direct imaging methods to reciprocal space techniques, the properties of lithographically patterned arrays of magnetic thin film and multilayer elements are investigated by exploring their magnetic state, extending from the atomic scale up to collective ordering phenomena of nano-magnetic elements.Laterally patterned amorphous multilayer arrays of combined circular and ellipsoidal islands were investigated. The arrays contain a variety of length scales, ranging from their nanometer scale multilayer structure to their lateral periodicity in the micrometer range. The attributes of these arrays are explored using different techniques, applicable for addressing the magnetization at different length scales, including magneto-optical techniques, micromagnetic simulations and x-ray resonant magnetic scattering.Arrays of dipole interacting elongated magnetic elements composed of Pd(Fe) thin films were investigated. Pd(Fe) films have a low Curie temperature which can be tuned by the thickness of the Fe layer embedded in Pd. By this, the interaction and the shape anisotropy energies can be brought down to energy scales comparable to room temperature enabling the possibility of investigating the effect of thermal excitations on such arrays. The temperature dependent magnetization of an artificial square spin ice array was investigated by magneto-optical measurements demonstrating the possibility of observing an order-disorder transition in an artificial square spin ice system. The role of dipolar interactions and the possibility of achieving thermal ground state ordering was then further investigated by magnetically sensitive photoemission electron microscopy imaging of ring arrangements of elongated Pd(Fe) elements. The results reveal a high probability of achieving a thermal ground state ordering of the magnetization of the islands.

The switching mechanisms in artificial spin ice systems are investigated with focus on shakti and modified shakti lattices. Minimum energy paths are calculated using the geodesic nudged elastic band (GNEB) method implemented with a micromagnetic description of the system, including the internal magnetic structure of the islands and edge modulations. Two switching mechanisms, uniform magnetization rotation and domain wall formation, are found to have comparable activation energy. The preference for one over the other depends strongly on the saturation magnetization and the magnetic ordering of neighboring islands. Surprisingly, these mechanisms can coexist, leading to an enhanced probability of magnetization reversal. These results provide valuable insight that can help control internal magnetization switching processes in spin ice systems and help predict their thermodynamic properties.

We investigate the design of magnetic ordering in one-dimensional mesoscopic magnetic Ising chains by modulating long-range interactions. These interactions are affected by geometrical modifications to the chain, which adjust the energy hierarchy and the resulting magnetic ground states. Consequently, the magnetic ordering can be tuned between antiferromagnetic and dimer antiferromagnetic phases. These phases are experimentally observed in chains fabricated using both conventional electron-beam lithography and ion implantation techniques, demonstrating the feasibility of controlling magnetic properties at the mesoscale. The ability of attaining these magnetic structures by thermal annealing, underlines the potential of using such systems instead of simulated annealers in tackling combinatorial optimization tasks.