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We demonstrate the presence of an emergent magnetic anisotropy in square lattices of circular mesospins. An external field is used to saturate the magnetization along the [10] and [11] directions before quantifying the magnetic textures at remanence. A clear directional dependence was obtained. The concomitant changes in the interactions are argued to cause the observed anisotropy and, thereby, the directional dependence in the transition temperature of the mesospins.

Amorphous metals have unusual magnetic properties that arise due to the disordered atomic arrangement. We show that Co-x(Al70Zr30)(100-x) (65 < x < 92 at.%) amorphous alloys have a distribution in the local magnetic coupling and ordering temperature, which can be explained by nanoscale composition variations. We use competing anisotropies induced by the substrate and an applied field during growth to probe the Co concentration distribution. Only regions with high enough Co concentration develop a magnetic anisotropy along the magnetic field during growth, whereas regions of low Co concentration have an anisotropy dictated by the substrate. A Gaussian distribution in the Co concentration of width 5.1 at.% is obtained from the variation in anisotropy. The results demonstrate the importance of composition variations for emergent magnetic properties and have far reaching implications for the properties of disordered materials in general.

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.

In this work we present a temperature and angular dependent study of the structural and magnetic properties in highly crystalline V2O3/Ni/Zr magnetic heterostructure films. Our investigation focuses on the coupling between the ferromagnetic Ni layer and V2O3 layer which undergoes an antiferromagnetic/paramagnetic phase transition coupled to the structural phase transition of the material at around 150 K. Structural investigations using x-ray diffraction reveal highly crystalline films of a quality which has previously not been reported in the literature. The Ni layers display an absence of in-plane magnetic anisotropy owing to the highly textured (1 1 1) layering of the Ni films on the underlying V2O3(0 0 0 1) oriented layer. During the transition we observe a strain related enhancement of the coercivity and the onset of a weak exchange bias for cooling under an external magnetic field. Heating the films to above the transition temperature, the exchange bias in the Ni is removed and can be reversed upon subsequent cooling under an inverted external magnetic field. Using temperature dependent polarized neutron reflectometry we investigate the film structure at the interface, capturing the magnetic and nuclear profiles.

Spin and spatial dimensionalities are universal concepts, essential for describing both phase transitions and dynamics in magnetic materials. Lately, these ideas have been adopted to describe magnetic properties of metamaterials, replicating the properties of their atomic counterparts as well as exploring properties of ensembles of mesospins belonging to different universality classes. Here, we take the next step when investigating magnetic metamaterials not conforming to the conventional framework of continuous phase transitions. Instead of a continuous decrease in the moment with temperature, discrete steps are possible, resulting in a binary transition in the interactions of the elements. The transition is enabled by nucleation and annihilation of vortex cores, shifting topological charges between the interior and the edges of the elements. Consequently, the mesospins can be viewed as shifting their spin dimensionality, from 2 (XY-like) to 0 (vortices), at the transition. The results provide insight into how dynamics at different length scales couple, which can lead to thermally driven topological transitions in magnetic metamaterials.

The strength of the interlayer exchange coupling in [Fe/MgO]N(001) superlattices with 2 <= N <= 10 depends on the number of bilayer repeats (N). The exchange coupling is antiferromagnetic for all the investigated thicknesses while being nine times larger in a sample with N = 4 as compared to N = 2. The sequence of the magnetic switching in two of the samples (N = 4, N = 8) is determined using polarized neutron reflectometry. The outermost layers are shown to respond at the lowest fields, consistent with having the weakest interlayer exchange coupling. The results are consistent with the existence of quantum well states defined by the thickness of the Fe and the MgO layers as well as the number of repeats (N) in [Fe/MgO]N(001)superlattices.