Artificial spin ices are arrays of correlated nano-scale magnetic islands that prove an excellent playground in which to study the role of topology in critical phenomena. Here, we investigate a continuum of spin ice geometries, parameterised by rotation of the islands. In doing so, we morph from the classic square ice to the recently studied pinwheel geometry, with the rotation angle acting as a proxy for controlling inter-island interactions. We experimentally observe a change in ground state magnetic order from antiferromagnetic to ferromagnetic across this class of geometries using Lorentz transmission electron microscopy on thermally annealed cobalt arrays. The change in ordering leads to an apparent change in the nature of the defects supported: from one-dimensional strings in the antiferromagnetic phase to two-dimensional vortex-like structures in the ferromagnetic one, consistent with the scaling predicted by the Kibble-Zurek mechanism. Our results show how magnetic order in artificial spin ices can be tuned by changes in geometry so that a truly frustrated ice-rule phase is possible in two-dimensional systems. Furthermore, we demonstrate this system as a testbed to investigate out-of-equilibrium dynamics across phases.
Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasi-static and equilibrium behavior of the spin-ice lattice. Here we study the eigenmode dynamics of such defects in a square lattice consisting of stadium-like thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitative…
We report here the results of micromagnetic simulations of square artificial spin ice (ASI) systems with defects. The defects are introduced by misaligning of a nanomagnet at the vertex. In these defective systems, we are able to stabilize emergent monopole-like state by applying a small external field. We observe a systematic change of dipolar energies of the systems with varying misalignment angle. The fields at which the emergent monopoles are created vary linearly with the dipolar energies of the systems. Our results clearly show that the magnetization reversal of the ASI systems is intric…
We investigate spin dynamics of artificial spin ice (ASI) where topological defects confine magnon modes in Ni$_{81}$Fe$_{19}$ nanomagnets arranged on an interconnected kagome lattice. Brillouin light scattering microscopy performed on magnetically disordered states exhibit a series of magnon resonances which depend on topological defect configurations detected by magnetic force microscopy. Nanomagnets on a Dirac string and between a monopole-antimonopole pair show pronounced modifications in magnon frequencies both in experiments and simulations. Our work is key for the creation and annihilat…
We report angular-dependent spin-wave spectroscopy on kagome artificial spin ice made of large arrays of interconnected Ni80Fe20 nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic in-plane angular dependencies. Micromagnetic simulations allow us to interpret characteristic resonances of a two-step magnetization reversal of the nanomagnets. The dynamic properties are consistent with topological defects that are provoked via a magnetic field applied at specific angles. Simulations that we performed on previously investigated kagome artif…
We report broadband spin-wave spectroscopy on kagome artificial spin ice (ASI) made of large arrays of interconnected Ni$_{80}$Fe$_{20}$ nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic magnetic field dependencies. Making use of micromagnetic simulations, we identify resonances that reflect the spin-solid-state and monopole-antimonopole pairs on Dirac strings. The latter resonances allow for the generation of highly-charged vertices in ASIs via microwave assisted switching. Our findings open further perspectives for fundamental studi…
In artificial spin ice systems, an interplay of defects and dipolar interactions is expected to play important roles in stabilizing different collective magnetic states. In this work, we investigated the magnetization reversal of individual defective square artificial spin ice vertices where defects break four-fold rotational symmetry of the system. By varying the angle between the applied field and the geometrical axis of the vertices, we observe a change in energy landscape of the system resulting into the stabilization of collective low-energy magnetic states. We also observe that by changi…
In this theoretical investigation we address the effect of defects on thermal excitations in square-lattice dipolar arrays. The geometry of the nanomagnets, adopted from recent experiments [A. Farhan \textit{et al.}, Nature Phys.\ \textbf{9} (2013) 375], allows for thermal activation at room temperature. It turns out that excitations can efficiently be pinned at defects. Furthermore, ferromagnetic strings of nanomagnets that connect a pair of defects can be produced; their lengths are closely related to the distance of the defects and the topology of the magnetic ground-state configuration. We…
Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying frustration, where lithographically patterned bar magnets mimic the frustrated interactions in real materials but are also amenable to direct characterization. Here, we introduce controlled topological defects into square artificial spin ice lattices in the form of lattice edge dislocations and directly observe the resulting spin configurations. We find the p…
Artificial spin ices are ideal frustrated model systems in which to explore or design emergent phenomena with unprecedented characterization of the constituent degrees of freedom. In square spin ice, violations of the ice rule are topological excitations essential to the kinetics of the system, providing an ideal testbed for studying the dynamics of such defects under varied quench rates. In this work we describe the first test of the Kibble-Zurek mechanism and critical coarsening in colloidal square and colloidal hexagonal ice under quenches from a weakly interacting liquid state into a stron…
The interactions between an excitation (similar to a pair of Nambu monopoles) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the "imperfect" island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We have shown that the two extreme points of a malformed island behave like two opposite magnetic charges. Then, the effective intera…
Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in X-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a programmed topological defect, a double edge dislocation, imparts OAM to scattered X-rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AF) ground state. The topological charge of the defect differs with respect to the structural and m…
We experimentally demonstrate that arrays of interacting nanoscale ferromagnetic islands, known as artificial spin ice, develop reproducible microstates upon cycling an applied magnetic field. The onset of this memory effect is determined by the strength of the applied field relative to the array coercivity. Specifically, when the applied field strength is almost exactly equal to the array coercivity, several training cycles are required before the array achieves a nearly completely repeatable microstate, whereas when the applied field strength is stronger or weaker than the array coercivity, …
The spin-wave dynamics of the ferromagnetic nanoarrays termed artificial spin ice (ASI) are known to vary depending on their magnetic microstate. However, little work has been done to characterise this relationship. Recent advances in control over the magnetic configuration of ASI bring designs harnessing the interplay between spin-wave eigenmodes and the microstate within reach, offering diverse applications including reconfigurable magnonic crystals, microwave filters and microstate read-out probes. These designs hinge on a strong understanding of the underlying spin wave-microstate correspo…
Artificial ices enable the study of geometrical frustration by design and through direct observation. However, it has proven difficult to achieve tailored long-range ordering of their diverse configurations, limiting both fundamental and applied research directions. We designed an artificial spin structure that produces a magnetic charge ice with tunable long-range ordering of eight different configurations. We also developed a technique to precisely manipulate the local magnetic charge states and demonstrate write-read-erase multifunctionality at room temperature. This globally reconfigurable…
Although initially introduced to mimic the spin-ice pyrochlores, no artificial spin ice has yet exhibited the expected degenerate ice-phase with critical correlations similar to the celebrated Coulomb phase in the pyrochlore lattice. Here we study a novel artificial spin ice based on a vertex-frustrated rather than pairwise frustrated geometry and show that it exhibits a quasicritical ice phase of extensive residual entropy and, significantly, algebraic correlations. Interesting in its own regard as a novel realization of frustration in a vertex system, our lattice opens new pathways to study …
Using extensive numerical simulations, we probe the magnetization switching in two-dimensional artificial spin ice (ASI) system consisting of peanut-shaped nanomagnets. We also investigated the effect of the external magnetic field on the degeneracy of the magnetic states in such a system. The switching field is found to be one order smaller in the proposed ASI system with peanut-shaped nanomagnets as compared to the conventionally used highly-anisotropic nanoisland such as elliptically shaped nanomagnets. The metastable 2-in/2-out (Type II) magnetic state is robust at the remanence. We are al…
Relaxation pathways and emergence of domains in square artificial spin ice
CIC nanoGUNE BRTA；Department of Physics, School of Science, Loughborough University（拉夫堡大学理学院物理系）；Department of Physics and Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文系）；Elettra-Sincrotrone Trieste S.C.p.A.（的里雅斯特电子同步加速器公司）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯基克巴斯克科学基金会）
A domain wall (DW) in a ferromagnetic nanowire is composed of elementary topological bulk and edge defects with integer and fractional winding numbers, respectively, whose relative spatial arrangement determines the chirality of the DW. Here we show how we can understand and control the trajectory of DWs in magnetic branched networks, composed of connected nanowires, by considering their fractional elementary topological defects and how they interact with those innate to the network. We first develop a highly reliable mechanism for the injection of a DW of a given chirality into a nanowire and…
Recent progress in nanofabrication has led to the emergence of three-dimensional magnetic nanostructures as a vibrant field of research. This includes the study of three-dimensional arrays of interconnected magnetic nanowires with tunable artificial spin-ice properties. Prominent examples of such structures are magnetic buckyball nanoarchitectures, which consist of ferromagnetic nanowires connected at vertex positions corresponding to those of a C60 molecule. These structures can be regarded as prototypes for the study of the transition from two- to three-dimensional spin-ice lattices. In spit…
Fractional diffusion without disorder in two dimensions
Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；TCM Group, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室 TCM 组）；Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg（奥格斯堡大学物理学院电子相关与磁性中心理论物理第三系）；University of Cambridge（剑桥大学）；University of Augsburg（奥格斯堡大学）
