Geometrically frustrated materials, such as spin ice or kagome lattice, are known to exhibit exotic Hall effect phenomena due to spin chirality. We explore Hall effect mechanism in an artificial honeycomb spin ice of Nd--Sn element using Hall probe and polarized neutron reflectivity measurements. In an interesting observation, a strong enhancement in Hall signal at relatively higher temperature of $T$ $\sim$ 20 K is detected. The effect is attributed to the planar Hall effect due to magnetic moment configuration in spin ice state in low field application. In the antiferromagnetic state of neodymium at low temperature, applied field induced coupling between atomic Nd moments and conduction electrons in underlying lattice causes distinct increment in Hall resistivity at very modest field of $H$ $\sim$ 0.015 T. The experimental findings suggest the development of a new research vista to study the planar and the field induced Hall effects in artificial spin ice.
We model the dynamics of magnetization in an artificial analog of spin ice specializing to the case of a honeycomb network of connected magnetic nanowires. The inherently dissipative dynamics is mediated by the emission, propagation and absorption of domain walls in the links of the lattice. These domain walls carry two natural units of magnetic charge, whereas sites of the lattice contain a unit magnetic charge. Magnetostatic Coulomb forces between these charges play a major role in the physics of the system, as does quenched disorder caused by imperfections of the lattice. We identify and de…
Artificial spin ice is a frustrated magnetic two-dimensional nano-material, recently employed to study variety of tailor-designed unusual collective behaviours. Recently proposed extensions to three dimensions are based on self-assembly techniques and allow little control over geometry and disorder. We present a viable design for the realization of a three-dimensional artificial spin ice with the same level of precision and control allowed by lithographic nano-fabrication of the popular two-dimensional case. Our geometry is based on layering already available two-dimensional artificial spin ic…
We report the experimental and theoretical characterization of the angular-dependent spin dynamics in arrays of ferromagnetic nanodisks arranged on a honeycomb lattice. The magnetic field and microwave frequency dependence, measured by broadband ferromagnetic resonance, reveal a rich spectrum of modes that is strongly affected by the microstate of the network. Based on symmetry arguments with respect to the external field, we show that certain parts of the ferromagnetic network contribute to the detected signal. A comparison of the experimental data with micromagnetic simulations reveals that …
Artificial magnetic honeycomb lattice provides a two-dimensional archetypal system to explore novel phenomena of geometrically frustrated magnets. According to theoretical reports, an artificial magnetic honeycomb lattice is expected to exhibit several phase transitions to unique magnetic states as a function of reducing temperature. Experimental investigations of permalloy artificial honeycomb lattice of connected ultra- small elements, ~ 12 nm, reveal a more complicated behavior. First, upon cooling the sample to intermediate temperature, T ~ 175 K, the system manifests a non-unique state wh…
In 1935, Pauling estimated the residual entropy of water ice with remarkable accuracy by considering the degeneracy of the ice rule {\it solely at the vertex level}. Indeed, his estimate works well for both the three-dimensional pyrochlore lattice and the two-dimensional six-vertex model, solved by Lieb in 1967. The case of honeycomb artificial spin ice is similar: its pseudo-ice rule, like the ice rule in Pauling and Lieb's systems, simply extends a degeneracy which is already present in the vertices to the global ground state. The anisotropy of the magnetic interaction limits the design of i…
Artificial magnetic honeycomb lattices are expected to exhibit a broad and tunable range of novel magnetic phenomena that would be difficult to achieve in natural materials, such as long-range spin ice, entropy-driven magnetic charge-ordered state and spin-order due to the spin chirality. Eventually, the spin correlation is expected to develop into a unique spin solid state density ground state, manifested by the distribution of the pairs of vortex states of opposite chirality. Here we report the creation of a new artificial permalloy honeycomb lattice of ultra-small connecting bonds, with a t…
We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically-interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice topology to previously-studied 'artificial spin ice' systems composed of in-plane moments. The two systems show striking similarities in the development of moment pair correlations, demonstrating a univ…
We present the electronic band structures of states with the same symmetry as the three-sublattice planar antiferromagnetic order of the triangular lattice. Such states can also be defined on the honeycomb lattice provided the spin density waves lie on the bonds. We identify cases which are consistent with observations on twisted bilayer graphene: a correlated insulator with an energy gap, yielding a single doubly-degenerate Fermi surface upon hole doping. We also discuss extensions to metallic states which preserve spin rotation invariance, with fluctuating spin density waves and bulk $\mathb…
Magnetic nanoarray with special geometries exhibits nontrivial collective behaviors similar to those observed in the spin ice materials. Here we present a novel circuit model to describe the complex magnetotransport phenomena in artificial kagome spin ice. In this picture, the system can be viewed as a resistor network driven by voltage sources that are located at vertices of the honeycomb array. The differential voltages across different terminals of these sources are related to the ice-rules that govern the local magnetization ordering. The circuit model relates the transverse Hall voltage o…
Emerging new concepts, such as magnetic charge dynamics in two-dimensional magnetic material, can provide novel mechanism for spin based electrical transport at macroscopic length. In artificial spin ice of single domain elements, magnetic charge's relaxation can create an efficient electrical pathway for conduction by generating fluctuations in local magnetic field that couple with conduction electrons spins. In a first demonstration, we show that the electrical conductivity is propelled by more than an order of magnitude at room temperature due to magnetic charge defects sub-picosecond relax…
Artificial spin ice offers the possibility to investigate a variety of dipolar orderings, spin frustrations and ground states. However, the most fascinating aspect is the realization that magnetic charge order can be established without spin order. We have investigated magnetic dipoles arranged on a honeycomb lattice as a function of applied field, using magnetic force microscopy. For the easy direction with the field parallel to one of the three dipole sublattices we observe at coercivity a maximum of spin frustration and simultaneously a maximum of charge order of magnetic monopoles with alt…
We report a successful preparation of a purely honeycomb, graphene-like borophene, by using an Al(111) surface as the substrate and molecular beam epitaxy (MBE) growth in ultrahigh vacuum. Our scanning tunneling microscopy (STM) reveals perfect monolayer borophene with planar, non-buckled honeycomb lattice similar as graphene. Theoretical calculations show that the honeycomb borophene on Al(111) is energetically stable. Remarkably, nearly one electron charge is transferred to each boron atom from the Al(111) substrate and stabilizes the honeycomb borophene structure, in contrast to the little …
We use the methods of topological quantum chemistry to explore the topology of phonons on time-reversal symmetric crystals with the structure of the planar honeycomb (layer group $p6/mmm$). This approach is not tied to a particular model of atomic vibrations, but is applied to the most general dynamical matrix constrained only by the symmetries of the system. We show that four distinct fragile topological phonon phases are generically possible. Truncating the dynamical matrix to third nearest neighbors yields a model that realizes the different phonon topologies, characterized by the existence…
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…
The emergent concept of magnetic charge quasi-particle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. We report on the exploration of magnetic phases due to various magnetic charge correlation using the complementary numerical techniques of micromagnetic and distorted wave Born approximation simulations in artificial permalloy honeycomb lattice. The honeycomb element length varies between 10 nm and 100 nm, while the width and thickness are kept within the single domain limit. In addition to the charge ordered loop state, w…
We propose a family of free fermion lattice models that have "Dirac loops", closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply-connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility…
Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of t…
We study planar rectangular-like arrays composed by macroscopic dipoles (magnetic bars with size around a few centimeters) separated by lattice spacing a and b along each direction. Physical behavior of such macroscopic artificial spin ice (MASI) systems are shown to agree much better with theoretical prediction than their micro- or nano-scaled counterparts, making MASI "almost ideal prototypes" for readily naked-eye visualization of geometrical frustration effects.
We present results of ferromagnetic resonance (FMR) experiments and micromagnetic simulations for a distorted, 2D Kagome artificial spin ice. The distorted structure is created by continuously modulating the 2D primitive lattice translation vectors of a periodic honeycomb lattice, according to an aperiodic Fibonacci sequence used to generate 1D quasicrystals. Experimental data and micromagnetic simulations show the Fibonacci distortion causes broadening and splitting of FMR modes into multiple branches, which accompany the increasing number of segment lengths and orientations that develop with…
The change in electrical resistance associated with the application of an external magnetic field is known as the magnetoresistance (MR). The measured MR is quite complex in the class of connected networks of single-domain ferromagnetic nanowires, known as "artificial spin ice", due to the geometrically-induced collective behavior of the nanowire moments. We have conducted a thorough experimental study of the MR of a connected honeycomb artificial spin ice, and we present a simulation methodology for understanding the detailed behavior of this complex correlated magnetic system. Our results de…
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…
The anomalous Hall effect (AHE) can appear in certain antiferromagnetic metals when it is allowed by symmetry. Since the net magnetization is usually small in such anomalous Hall antiferromagnets, it is useful to have other physical indicators of the AHE that have the same symmetry properties as the latter and can be conveniently measured and calculated. Here we propose such indicators named as electronic chiralization (EC), which are constructed using spatial gradients of spin and charge densities in general periodic crystals, and can potentially be measured directly by scattering experiments…
