Magnetic order and energy-scale hierarchy in artificial spin ice

In order to explain and predict the properties of many physical systems, it is essential to understand the interplay of different energy-scales. Here we present investigations of the magnetic order in thermalised artificial spin ice structures, with different activation energies of the interacting Ising-like elements. We image the thermally equilibrated magnetic states of the nano-structures using synchrotron-based magnetic microscopy. By comparing results obtained from structures with one or two different activation energies, we demonstrate a clear impact on the resulting magnetic order. The differences are obtained by the analysis of the magnetic spin structure factors, in which the role of the activation energies is manifested by distinct short-range order. This demonstrates that artificial spin systems can serve as model systems, allowing the definition of energy-scales by geometrical design and providing the backdrop for understanding their interplay.Comment: 8 pages, 5 figures (+ supplementary 6 pages, 4 figures

Використання кавітаційних пристроїв в харчовій промисловості

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

Multiple energy scales in mesospin systems : the vertex-frustrated Saint George lattice

The interplay between topology and energy hierarchy plays a vital role in the collective magnetic order in artificial ferroic systems. Here we investigate, experimentally, the effect of having one or two activation energies of interacting Ising-like magnetic islands—mesospins—in thermalized, vertex-frustrated lattices. The thermally arrested magnetic states of the elements were determined using synchrotron-based magnetic microscopy after cooling the samples from temperatures above the Curie temperature of the material. Statistical analysis of the correlations between mesospins across several length scales reveals changes in the magnetic order, reflecting the amount of ground state plaquettes realized for a vertex-frustrated lattice. We show that the latter depends on the presence, or not, of different activation energies

The importance of the weak: Interaction modifiers in artificial spin ices

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics, and emergent magnetic properties, in e.g. 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 plane. 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.Comment: 17 pages, including methods, 4 figures. Supplementary information contains 16 pages and 15 figure

Tailoring the magnetic order in mesoscopic spin systems

Mesoscopic spin systems can be designed and fabricated using modern nano-fabrication techniques. These systems can contain large numbers of patterned ferromagnetic elements, for which the shape will generally determine their effective mesospin dimensionality. The lateral arrangement of these mesospins can be further used to tune the interactions between them. With an appropriate choice of material, it is possible to define a temperature range where thermal fluctuations of these mesospins are experimentally accessible. To actively define this range, we use δ-doped Palladium, a three-layer system of Palladium—Iron—Palladium, for which the Curie-temperature scales with the Iron layer thickness. The patterned mesoscopic elements used in this work have a stadium-like shape that promotes a single magnetic domain state, thus making these islands behave as one-dimensional Ising-like mesospins that can be observed using magnetic imaging techniques. We investigate the impact on the magnetic order resulting from modifications of the square spin ice geometry. By adding, removing and merging elements in the square artificial spin ice architecture, energy-landscape variations can be realized. Firstly, an added interaction modifier is used to equilibrate the interactions between the mesospins at the vertex level, which can restore the degenerate ground state of the square spin ice model. Secondly, the removal of elements can lead to topologically frustrated spin systems, as not all building blocks can simultaneously be in their lowest energy state. Furthermore, the merging results in multiple element sizes in the mesospin system. As the magnetization reversal barrier is dependent on the element size, these mesospin systems have different energy barriers. The thermal ordering process in such a system differs from a single-size element system with its unique energy barrier. Using reciprocal space analysis tools like the magnetic spin structure factor we show that systems with multiple element sizes achieve a higher short-range order then their single-size element references. The magnetic order in mesoscopic spin systems could successfully be tailored by modifications of the lattice geometry

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

Magnetic properties and thermal stability of B2 and bcc phases in AlCoCrFeMnxNi

Alloys of AlCoCrFeMnxNi (x = 0.0, 0.04, 0.08, 0.12 and 0.16) have been synthesized through arc–melting and gas atomisation (x = 0.0 and 0.16) to investigate the effect of Mn additions to AlCoCrFeNi. Here, the structure, magnetic properties and the thermal stability of the alloys is presented. Electron microscopy confirmed the elemental composition and revealed the microstructure to consist of two spinodally decomposed phases. Rietveld analysis of standard powder X-ray diffraction showed the arc-melted samples consisted of two phases, a B2 phase and a bcc phase while the gas atomised powders consisted of a single-phased B2 structure. Magnetic measurements revealed an increase in the saturation magnetisation at room temperature by 68% for AlCoCrFeMnNi compared to AlCoCrFeNi. The thermal stability of the alloys was investigated using magnetometry, differential scanning calorimetry and in–situ X-ray diffraction, which showed that an increase in Mn content adversely effected the thermal stability of the alloy

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

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