Emergent tri-criticality in magnetic metamaterials

Metallic discs engineered on the 100 nm scale have an internal magnetic texture which varies from a fully magnetized state to a vortex state with zero moment. The interplay between this internal structure and the inter-disc interactions is studied in magnetic metamaterials made of square arrays of the magnetic discs. The texture is modeled by a mesospin of varying length with O(2) symmetry and the inter-disc interaction by a nearest neighbour coupling between mesospins. The thermodynamic properties of the model are studied numerically and an ordering transition is found which varies from Kosterlitz-Thouless to first order via an apparent tri-critical point. The effective critical exponent characterising the finite size magnetization evolves from the value for the 2D-XY model to less than half this value at the tri-critical point. The consequences for future experiments both in and out of equilibrium are discussed.Comment: 10 pages, 9 figure

Phase transitions in magnetic metamaterials

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

Phase transitions in magnetic metamaterials

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

Thermal excitations within and among mesospins in artificial spin ice

We provide experimental and numerical evidence for thermal excitations within and among magnetic mesospins, forming artificial spin ice structures. At low temperatures, a decrease in magnetization and increase in susceptibility is observed with increasing temperature, interpreted as an onset of thermal fluctuations of the magnetic texture within the mesospins. At elevated temperatures a pronounced susceptibility peak is observed, related to thermally induced flipping of the mesospins and a collapse of the remanent state. The fluctuations, while occurring at distinct length and energyscales, are shown to be tunable by the interaction strength of the mesospins

Emergent anisotropy and textures in two dimensional magnetic arrays

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

The influence of diameter on the magnetic saturation in Fe 84 Cu 16 /MgO [001] multilayered islands

The saturation field of circular islands, consisting of [Fe84Cu16/MgO]9Fe84Cu16 multilayers, increases with decreasing diameter of the islands. When the diameter of the islands is below 450 nm the field induced changes are dominated by a coherent rotation of the moment of the Fe84Cu16 layers. For diameters of 2 μm and larger, a signature of domain nucleation and evolution is observed. The changes in the saturation field with diameter of the islands are ascribed to the interplay between interlayer exchange coupling, stray field coupling at the edges and the crystalline anisotropy of the Fe84Cu16 layers

Temperature-induced collapse of spin dimensionality in magnetic metamaterials

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