Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Toroidic phase transitions in a direct-kagome artificial spin ice

Ferrotoroidicity-the fourth form of primary ferroic order-breaks both space and time-inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a cross-over to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.

Crystallizing Kagome Artificial Spin Ice

Artificial spin ices are engineered arrays of dipolarly coupled nanobar magnets. They enable direct investigations of fascinating collective phenomena from their diverse microstates. However, experimental access to ground states in the geometrically frustrated systems has proven difficult, limiting studies and applications of novel properties and functionalities from the low energy states. Here, we introduce a convenient approach to control the competing diploar interactions between the neighboring nanomagnets, allowing us to tailor the vertex degeneracy of the ground states. We achieve this by tuning the length of selected nanobar magnets in the spin ice lattice. We demonstrate the effectiveness of our method by realizing multiple low energy microstates in a kagome artificial spin ice, particularly the hardly accessible long range ordered ground state-the spin crystal state. Our strategy can be directly applied to other artificial spin systems to achieve exotic phases and explore new emergent collective behaviors.

Controlling degeneracy and magnetization switching in an artificial spin ice system of peanut-shaped nanomagnets

Using extensive numerical simulations, we probe the magnetization switching in a two-dimensional artificial spin ice (ASI) system consisting of peanut-shaped nanomagnets. We also investigated the effect of 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 two-in/two-out (Type II) magnetic state is robust at the remanence. We are also able to access the other possible microstate corresponding to Type II magnetic configurations by carefully varying the external magnetic field. It implies that one can control the degeneracy of the magnetic state by an application of suitable magnetic field. Interestingly, the magnetic charge neutrality at the vertex breaks due to the defects induced by removing nanomagnets. In such a case, the system also appears to have one-out/three-in or three-out/one-in (Type III) spin state, reminiscent of magnetic monopole at the vertex. We believe that our study is highly desirable in the context of developing the next-generation spintronics-based devices for future technologies.

Experimental Realization of the 1D Random Field Ising Model

We have measured magnetic-field-induced avalanches in a square artificial spin ice array of interacting nanomagnets. Starting from the ground state ordered configuration, we imaged the individual nanomagnet moments after each successive application of an incrementally increasing field. The statistics of the evolution of the moment configuration show good agreement with the canonical one-dimensional random field Ising model. We extract information about the microscopic structure of the arrays from our macroscopic measurements of their collective behavior, demonstrating a process that could be applied to other systems exhibiting avalanches.

Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice

Designing and constructing model systems that embody the statistical mechanics of frustration is now possible using nanotechnology. We have arranged nanomagnets on a two-dimensional square lattice to form an artificial spin ice, and studied its fractional excitations, emergent magnetic monopoles, and how they respond to a driving field using X-ray magnetic microscopy. We observe a regime in which the monopole drift velocity is linear in field above a critical field for the onset of motion. The temperature dependence of the critical field can be described by introducing an interaction term into the Bean-Livingston model of field-assisted barrier hopping. By analogy with electrical charge drift motion, we define and measure a monopole mobility that is larger both for higher temperatures and stronger interactions between nanomagnets. The mobility in this linear regime is described by a creep model of zero-dimensional charges moving within a network of quasi-one-dimensional objects.

Superferromagnetism and Domain-Wall Topologies in Artificial "Pinwheel" Spin Ice

For over ten years, arrays of interacting single-domain nanomagnets, referred to as artificial spin ices, have been engineered with the aim to study frustration in model spin systems. Here, we use Fresnel imaging to study the reversal process in "pinwheel" artificial spin ice, a modified square ASI structure obtained by rotating each island by some angle about its midpoint. Our results demonstrate that a simple 45° rotation changes the magnetic ordering from antiferromagnetic to ferromagnetic, creating a superferromagnet which exhibits mesoscopic domain growth mediated by domain wall nucleation and coherent domain propagation. We observe several domain-wall configurations, most of which are direct analogues to those seen in continuous ferromagnetic films. However, charged walls also appear due to the geometric constraints of the system. Changing the orientation of the external magnetic field allows control of the nature of the spin reversal with the emergence of either one- or two-dimensional avalanches. This property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.

Spin Solid versus Magnetic Charge Ordered State in Artificial Honeycomb Lattice of Connected Elements

The nature of magnetic correlation at low temperature in two-dimensional artificial magnetic honeycomb lattice is a strongly debated issue. While theoretical researches suggest that the system will develop a novel zero entropy spin solid state as T → 0 K, a confirmation to this effect in artificial honeycomb lattice of connected elements is lacking. This study reports on the investigation of magnetic correlation in newly designed artificial permalloy honeycomb lattice of ultrasmall elements, with a typical length of ≈12 nm, using neutron scattering measurements and temperature-dependent micromagnetic simulations. Numerical modeling of the polarized neutron reflectometry data elucidates the temperature-dependent evolution of spin correlation in this system. As temperature reduces to ≈7 K, the system tends to develop novel spin solid state, manifested by the alternating distribution of magnetic vortex loops of opposite chiralities. Experimental results are complemented by temperature-dependent micromagnetic simulations that confirm the dominance of spin solid state over local magnetic charge ordered state in the artificial honeycomb lattice with connected elements. These results enable a direct investigation of novel spin solid correlation in the connected honeycomb geometry of 2D artificial structure.

New Description of Evolution of Magnetic Phases in Artificial Honeycomb Lattice

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, [Formula: see text] 12 nm, reveal a more complicated behavior. First, upon cooling the sample to intermediate temperature, [Formula: see text] 175 K, the system manifests a non-unique state where the long range order co-exists with short-range magnetic charge order and weak spin ice state. Second, at much lower temperature, [Formula: see text] 6 K, the long-range spin solid state exhibits a re-entrant behavior. Both observations are in direct contrast to the present understanding of this system. New theoretical approaches are needed to develop a comprehensive formulation of this two dimensional magnet.

Fabrication of high-resolution nanostructures of complex geometry by the single-spot nanolithography method

The paper presents a method for the high-resolution production of polymer nanopatterns with controllable geometrical parameters by means of a single-spot electron-beam lithography technique. The essence of the method entails the overexposure of a positive-tone resist, spin-coated onto a substrate where nanoscale spots are exposed to an electron beam with a dose greater than 0.1 pC per dot. A single-spot enables the fabrication of a nanoring, while a chain of spots placed at distance of 5-30 nm from each other allows the production of a polymer pattern of complex geometry of sub-10 nm resolution. We demonstrate that in addition to the naturally oxidized silicon substrates, gold-coated substrates can also successfully be used for the single-spot nanopattering technique. An explanation of the results related to the resist overexposure was demonstrated using Monte Carlo simulations. Our nanofabrication method significantly accelerates (up to 10 times) the fabrication rate as compared to conventional lithography on positive-tone resist. This technique can be potentially employed in the electronics industry for the production of nanoprinted lithography molds, etching masks, nanoelectronics, nanophotonics, NEMS and MEMS devices.

Nucleation of iron oxide nanoparticles mediated by Mms6 protein in situ

Biomineralization proteins are widely used as templating agents in biomimetic synthesis of a variety of organic-inorganic nanostructures. However, the role of the protein in controlling the nucleation and growth of biomimetic particles is not well understood, because the mechanism of the bioinspired reaction is often deduced from ex situ analysis of the resultant nanoscale mineral phase. Here we report the direct visualization of biomimetic iron oxide nanoparticle nucleation mediated by an acidic bacterial recombinant protein, Mms6, during an in situ reaction induced by the controlled addition of sodium hydroxide to solution-phase Mms6 protein micelles incubated with ferric chloride. Using in situ liquid cell scanning transmission electron microscopy we observe the liquid iron prenucleation phase and nascent amorphous nanoparticles forming preferentially on the surface of protein micelles. Our results provide insight into the early steps of protein-mediated biomimetic nucleation of iron oxide and point to the importance of an extended protein surface during nanoparticle formation.

Artificial ferroic systems: novel functionality from structure, interactions and dynamics

Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 μm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.

Direct observation of thermal relaxation in artificial spin ice

We study the thermal relaxation of artificial spin ice with photoemission electron microscopy, and are able to directly observe how such a system finds its way from an energetically excited state to the ground state. On plotting vertex-type populations as a function of time, we can characterize the relaxation, which occurs in two stages, namely a string and a domain regime. Kinetic Monte Carlo simulations agree well with the temporal evolution of the magnetic state when including disorder, and the experimental results can be explained by considering the effective interaction energy associated with the separation of pairs of vertex excitations.