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Magnetic metamaterials consisting of arrays of densely packed, two-dimensional nanoscale magnetic islands have degrees of freedom on two separate length scales: inside the islands, and among them. These degrees of freedom can be tuned by e.g. size, shape, island separation and lattice geometry. The material can thereby be tailored to display behavior corresponding to conventional universality classes, wherein small elongated islands behave like Ising spins and circular ones behave like XY-spins. Making the islands larger promotes inner degrees of freedom in the form of inner magnetic textures. Some of these textures, such as magnetic vortices in circular islands, have a critical impact on the interaction between the islands and therefore also on the global order.

In this thesis, the interplay between the inner textures and island-island interactions is explored, anticipating the emergence of behavior beyond that of conventional universality classes. A transition temperature between static and dynamic inner textureswas found in systems with elongated islands. In arrays of circular islands, a collapse from metastable collinear islands to vortex islands was observed, with a dependence on both island size and lattice orientation. Finally, a model was created based on key aspects of the circular islands, and using Monte Carlo calculations, an exotic phase diagram with a tricritical point and first order phase transitions was found. The transition is caused by a mutual dependence on the degrees of freedom inside, and among the elements. The experimental and numerical results presented in this thesis signify the existence of such phase transitions in the multiscale material.

This thesis is focused on exploring and modulating magnetic interactions in metamaterials and amorphous alloys along one-, two-, and three-dimensions. 

First, thin films of alternating Fe and MgO are adapted to modulate magnetic interactions along one dimension. At the remanent state, the Fe layers exist in an antiferromagnetic order, achieved by interlayer exchange coupling originating from spin-polarized tunneling through the MgO layers. Altering the number of repeats can tune the strength of the coupling. This is attributed to the total extension of the samples and beyond-nearest-neighbor interactions. Similarly, decreasing the temperature results in an exponential increase of the coupling strength, accompanied by changes in the reversal character of the Fe layers and magnetic ground state.

Next, magnetic modulations along two dimensions are investigated using lithographically patterned metamaterial consisting of arrays with mesospins - i.e., circular islands. Mesospins have degrees of freedom on two separate length scales, within and between the islands. Changing their size and lateral arrangement alters their behavior. The magnetic texture in small elements can be described as collinear with XY-like behavior, while larger islands result in magnetic vortices. Allowing the islands to interact by densely packing them in a square lattice alters the energy landscape. This is manifested by the interplay of intra- and inter-island interactions and leads to temperature-dependent transitions from a static to a dynamic state. The temperature dependence can be further altered by both element size and lattice orientation, leading to emergent behavior.

The final part of this thesis explores the modulations of interactions in three dimensions through inherent disorder in magnetic amorphous alloys. The atomic distribution in amorphous alloys can be viewed as random. However, local composition at the nanometer scale is, in fact, homogeneous. Variations in the composition of amorphous CoAlZr alloys lead to changes in the local distribution of magnetic amorphous CoAlZr manifested by competing anisotropies. Finally, off-specular scattering performed on a magnetic amorphous FeZr alloy is used to investigate the compositional variations at the nanometer scale. Indeed, correlations are observed at low temperatures due to the sample relaxation.