Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy

Morley, Sophie A.; Venero, Diego Alba; Porro, José María; Riley, Susan Tania; Stein, Aaron; Steadman, P.; Stamps, R. L.; Langridge, S.; Marrows, C. H.

doi:10.1103/physrevb.95.104422

Cited by 44 publications

(53 citation statements)

References 71 publications

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“…This approach has been used in a number of previous works, addressing both the order and dynamics of magnetic nanostructures [1][2][3][4][5][6][7][8]12 . In the specific case of square artificial spin ice (SASI) this approach has even enabled tailoring of the thermal dynamics and relaxation 8,[13][14][15] , as well as experimental realizations 9 of the degenerate square-ice model 16 . The distance and thereby the coupling strength for nearest and next-nearest neighbours are different in SASI (d 1 = d 2 (see Fig.…”

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confidence: 99%

Interaction modifiers in artificial spin ices

et al. 2018

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The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order [1][2][3][4][5][6] , collective low-energy dynamics 7,8 and emergent magnetic properties 5,9,10 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 plane 11. 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.Lithographic techniques can be used to fabricate magnetic nanoarrays, in which the interaction between the elements can be chosen by, for example, the distance between the islands. This approach has been used in a number of previous works, addressing both the order and dynamics of magnetic nanostructures [1][2][3][4][5][6][7][8]12 . In the specific case of square artificial spin ice (SASI), this approach has even enabled tailoring of the thermal dynamics and relaxation 8,[13][14][15] , as well as experimental realizations 9 of the degenerate square-ice model 16 . The distance and thereby the coupling strength for nearest and nextnearest neighbours are different in SASI (d 1 ≠ d 2 ; see Fig. 1), resulting in the loss of degeneracy. As a consequence, the ice-rule-obeying vertices, with two islands pointing in-two islands pointing out, are split into two groups (T I and T II ) with different energies (E I < E II ). One way to remedy this shortcoming is to shift parts of the lattice in the third dimension 9,17,18 . An alternative way to modify the energy landscape is to introduce an interaction modifier, as illustrated in Fig. 1b. In these modified SASI (mSASI) arrays, all islands have the same distance, or gap G, to the interaction modifier. While a height offset might seem the obvious choice for manipulating the coupling strengths between the islands, the use of interaction modifiers at the vertices of artificial spin-ice structures is not only lithographically much easier to achieve, but also opens up completely new avenues for tailoring their energy landscapes. Instead of having a system consisting of only one type of island, we use two subsystems with widely different shape anisotropies a...

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confidence: 99%

Interaction modifiers in artificial spin ices

et al. 2018

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“…Meanwhile the kagomé pattern has stronger frustration and a richer phase diagram 20,21 , whose phase transitions have been probed by low energy muon spectroscopy 22 . Recent attention has focussed on thermal excitations in these systems 8,[10][11][12]19,[23][24][25][26][27][28][29] , as well as new lattices designed to give rise to novel phenomena 30 . These include the 'shakti' lattice, which displays topologically induced emergent frustration 31 , the 'tetris' lattice, which exhibits an emergent reduction in dimensionality 32 , and artificial charge ices suitable for data storage 33 .…”

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Frustration and thermalization in an artificial magnetic quasicrystal

et al. 2017

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Artificial frustrated systems offer a playground to study the emergent properties of interacting systems. Most work to date has been on spatially periodic systems, known as artificial spin ices when the interacting elements are magnetic. Here we have studied artificial magnetic quasicrystals based on quasiperiodic Penrose tiling patterns of interacting nanomagnets. We construct a low energy configuration from a stepby-step approach that we propose as a ground state. Topologically induced emergent frustration means that this configuration cannot be constructed from vertices in their ground states. It has two parts, a quasi-one-dimensional "skeleton" that spans the entire pattern and is capable of long-range order, surrounding "flippable" clusters of macrospins that lead to macroscopic degeneracy. Magnetic force microscopy imaging of Penrose tiling arrays revealed superdomains that are larger for more strongly coupled arrays, especially after annealing the array above its blocking temperature. G eometrical frustration not only exists in crystalline materials such as the Ice I h phase of water and the rare-earth pyrochlore spin ices 1,2 , but can also be realised in a wide range of artificial systems 3-6 . Since they are built using nanotechnology, the structure of such a system, and the frustrated interactions it embodies, can be designed rather than discovered. When magnetic, such systems are known as artificial spin ices 7 .Two different analogs of the pyrochlores are the square 3,8-13 and kagomé 14-18 ice arrays, which have been widely studied. The square ice array has a long-range ordered antiferromagnetic ground state that is easily accessible through annealing 8,10,19 , although introducing a height offset between islands can restore the extensive degeneracy 13 . Meanwhile the kagomé pattern has stronger frustration and a richer phase diagram 20,21 , whose phase transitions have been probed by low energy muon spectroscopy 22 . Recent attention has focussed on thermal excitations in these systems 8,10-12,19,23-29 , as well as new lattices designed to give rise to novel phenomena 30 . These include the 'shakti' lattice, which displays topologically induced emergent frustration 31 , the 'tetris' lattice, which exhibits an emergent reduction in dimensionality 32 , and artificial charge ices suitable for data storage 33 .These arrays are spatially periodic with discrete translational symmetry. Since artificial systems may be designed arbitrarily, there is no need to always respect this constraint. Indeed, the discovery of quasicrystalline materials 34 shows that nature does not always respect it either. Quasicrystals have structures that lack translational symmetry 35 , and so possess complex forms of magnetic frustration leading to glassy behaviour [36][37][38] . Building artificial magnetic quasicrystals based on Penrose tilings brings the ability to inspect the magnetic configuration at the level of individual macrospins, allowing deeper insight into this frustration and its manifestations. Kite-and-dart tiling...

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“…Below T b , the average time taken for moments to switch is much longer than the measurement time, and the nanomagnets appear to be frozen. For the nanomagnets in artificial spin ice, the switching can occur through a non-uniform process 82 , leading to a much lower T b than is expected for magnets displaying singledomain coherent rotation. Equation 1 still applies, but the energy barrier is modified to replace the true volume We start our discussion of emergent magnetic monopoles in a system consisting of discrete mesoscopic spins in the context of artificial kagome spin ice 6,195 (see the figure, top panels).…”

Section: Thermodynamics and Kineticsmentioning

confidence: 96%

Advances in artificial spin ice

et al. 2019

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Artificial spin ices consist of nanomagnets arranged on the sites of various periodic and aperiodic lattices. They have enabled the experimental investigation of a variety of fascinating phenomena such as frustration, emergent magnetic monopoles and phase transitions that have previously been the domain of bulk spin crystals and theory , as we discuss in this Review. Artificial spin ices also show promise as reprogrammable magnonic crystals and, with this in mind, we give an overview of the measurements of fast dynamics in these magnetic metamaterials. We survey the variety of geometries that have been implemented, in terms of both the form of the nanomagnets and the lattices on which they are placed, including quasicrystalline systems and artificial spin systems in 3D. Different magnetic materials can also be incorporated to modify anisotropies and blocking temperatures, for example. With this large variety of systems, the way is open to discover new phenomena, and we complete this Review with possible directions for the future.

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Vogel-Fulcher-Tammann freezing of a thermally fluctuating artificial spin ice probed by x-ray photon correlation spectroscopy

Cited by 44 publications

References 71 publications

Interaction modifiers in artificial spin ices

Interaction modifiers in artificial spin ices

Frustration and thermalization in an artificial magnetic quasicrystal

Advances in artificial spin ice

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