Configurable Artificial Spin Ice with Site-Specific Local Magnetic Fields.

We demonstrate ground state tunability for a hybrid artificial spin ice composed of Fe nanomagnets which are subject to site-specific exchange-bias fields, applied in integer multiples of the lattice along one sublattice of the classic square artificial spin ice. By varying this period, three distinct magnetic textures are identified: a striped ferromagnetic phase; an antiferromagnetic phase attainable through an external field protocol alone; and an unconventional ground state with magnetically charged pairs embedded in an antiferromagnetic matrix. Monte Carlo simulations support the results of field protocols and demonstrate that the pinning tunes relaxation timescales and their critical behavior.

Emergent dynamic chirality in a thermally driven artificial spin ratchet.

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice can lead to specific collective behaviour, including emergent magnetic monopoles, charge screening and transport, as well as magnonic response. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells.

Spin-Wave Chirality and Its Manifestations in Antiferromagnets.

As first demonstrated by Tang and Cohen in chiral optics, the asymmetry in the rate of electromagnetic energy absorption between left and right enantiomers is determined by an optical chirality density. Here, we demonstrate that this effect can exist in magnetic spin systems. By constructing a formal analogy with electrodynamics, we show that in antiferromagnets with broken chiral symmetry, the asymmetry in local spin-wave energy absorption is proportional to a spin-wave chirality density, which is a direct counterpart of optical zilch. We propose that injection of a pure spin current into an antiferromagnet may serve as a chiral symmetry breaking mechanism, since its effect in the spin-wave approximation can be expressed in terms of additional Lifshitz invariants. We use linear response theory to show that the spin current induces a nonequilibrium spin-wave chirality density.

Spin Wave Power Flow and Caustics in Ultrathin Ferromagnets with the Dzyaloshinskii-Moriya Interaction.

The Dzyaloshinskii-Moriya interaction in ultrathin ferromagnets can result in nonreciprocal propagation of spin waves. We examine theoretically how spin wave power flow is influenced by this interaction. We show that the combination of the dipole-dipole and Dzyaloshinskii-Moriya interactions can result in unidirectional caustic beams in the Damon-Eshbach geometry. Morever, self-generated interface patterns can also be induced from a point-source excitation.

Nanoscale Mapping of the Magnetic Properties of (111)-Oriented La(0.67)Sr(0.33)MnO3.

Spatially resolved analysis of magnetic properties on the nanoscale remains challenging, yet strain and defects on this length-scale can profoundly affect a material's bulk performance. We present a detailed investigation of the magnetic properties of La0.67Sr0.33MnO3 thin films in both free-standing and nanowire form and assess the role of strain and local defects in modifying the films' magnetic properties. Lorentz transmission electron microscopy is used to measure the magnetocrystalline anisotropy and to map the Curie temperature and saturation magnetization with nanometric spatial resolution. Atomic-scale defects are identified as pinning sites for magnetic domain wall propagation. Measurement of domain wall widths and crystalline strain are used to identify a strong magnetoelastic contribution to the magnetic anisotropy. Together, these results provide unique insight into the relationship between the nanostructure and magnetic functionality of a ferromagnetic complex oxide film.

Narrow Magnonic Waveguides Based on Domain Walls.

The channeling of spin waves with domain walls in ultrathin ferromagnetic films is demonstrated theoretically and through micromagnetics simulations. It is shown that propagating excitations localized to the wall, which appear in the frequency gap of bulk spin wave modes, can be guided in curved geometries and propagate in close proximity to other channels. For Néel-type walls arising from a Dzyaloshinskii-Moriya interaction, the channeling is strongly nonreciprocal and group velocities can exceed 1 km/s in the long wavelength limit for certain propagation directions. The channeled modes represent an unusual analogy of whispering gallery waves that are one dimensional and nonreciprocal with this interaction. Moreover, a sufficiently strong Dzyaloshinskii-Moriya interaction can create a degeneracy of channeled and propagating modes at a critical wave vector.

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying "diamagnetic" angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields.

Target motion misjudgments reflect a misperception of the background; revealed using continuous psychophysics.

Determining the velocities of target objects as we navigate complex environments is made more difficult by the fact that our own motion adds systematic motion signals to the visual scene. The flow-parsing hypothesis asserts that the background motion is subtracted from visual scenes in such cases as a way for the visual system to determine target motions relative to the scene. Here, we address the question of why backgrounds are only partially subtracted in lab settings. At the same time, we probe a much-neglected aspect of scene perception in flow-parsing studies, that is, the perception of the background itself. Here, we present results from three experienced psychophysical participants and one inexperienced participant who took part in three continuous psychophysics experiments. We show that, when the background optic flow pattern is composed of local elements whose motions are congruent with the global optic flow pattern, the incompleteness of the background subtraction can be entirely accounted for by a misperception of the background. When the local velocities comprising the background are randomly dispersed around the average global velocity, an additional factor is needed to explain the subtraction incompleteness. We show that a model where background perception is a result of the brain attempting to infer scene motion due to self-motion can account for these results.

Continuous psychophysics for two-variable experiments; A new "Bayesian participant" approach.

Interest in continuous psychophysical approaches as a means of collecting data quickly under natural conditions is growing. Such approaches require stimuli to be changed randomly on a continuous basis so that participants can not guess future stimulus states. Participants are generally tasked with responding continuously using a continuum of response options. These features introduce variability in the data that is not present in traditional trial-based experiments. Given the unique weaknesses and strengths of continuous psychophysical approaches, we propose that they are well suited to quickly mapping out relationships between above-threshold stimulus variables such as the perceived direction of a moving target as a function of the direction of the background against which the target is moving. We show that modelling the participant in such a two-variable experiment using a novel "Bayesian Participant" model facilitates the conversion of the noisy continuous data into a less-noisy form that resembles data from an equivalent trial-based experiment. We also show that adaptation can result from longer-than-usual stimulus exposure times during continuous experiments, even to features that the participant is not aware of. Methods for mitigating the effects of adaptation are discussed.

Stray-Field Imaging of a Chiral Artificial Spin Ice during Magnetization Reversal.

Artificial spin ices are a class of metamaterials consisting of magnetostatically coupled nanomagnets. Their interactions give rise to emergent behavior, which has the potential to be harnessed for the creation of functional materials. Consequently, the ability to map the stray field of such systems can be decisive for gaining an understanding of their properties. Here, we use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image the magnetic stray field distribution of an artificial spin ice system exhibiting structural chirality as a function of applied magnetic fields at 4.2 K. The images reveal that the magnetostatic interaction gives rise to a measurable bending of the magnetization at the edges of the nanomagnets. Micromagnetic simulations predict that, owing to the structural chirality of the system, this edge bending is asymmetric in the presence of an external field and gives rise to a preferred direction for the reversal of the magnetization. This effect is not captured by models assuming a uniform magnetization. Our technique thus provides a promising means for understanding the collective response of artificial spin ices and their interactions.

Magnetization dynamics of weakly interacting sub-100 nm square artificial spin ices.

Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements, provides a fascinating opportunity to observe the physics of out-of-equilibrium systems. Initial studies concentrated on the static, frozen state, whilst more recent studies have accessed the out-of-equilibrium dynamic, fluctuating state. This opens up exciting possibilities such as the observation of systems exploring their energy landscape through monopole quasiparticle creation, potentially leading to ASI magnetricity, and to directly observe unconventional phase transitions. In this work we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. We have investigated the effect of the interaction strength on the magnetization dynamics at different temperatures in the range where the nanomagnets are thermally active. We have observed that they follow an Arrhenius-type Néel-Brown behaviour. An unexpected negative correlation of the average blocking temperature with the interaction strength is also observed, which is supported by Monte Carlo simulations. The magnetization relaxation measurements show faster relaxation for more strongly coupled nanoelements with similar dimensions. The analysis of the stretching exponents obtained from the measurements suggest 1-D chain-like magnetization dynamics. This indicates that the nature of the interactions between nanoelements lowers the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to quantify the effective interaction energy of a square ASI system, and compare it to the interaction energy computed with micromagnetic simulations.

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.

Ground state search, hysteretic behaviour, and reversal mechanism of skyrmionic textures in confined helimagnetic nanostructures.

Magnetic skyrmions have the potential to provide solutions for low-power, high-density data storage and processing. One of the major challenges in developing skyrmion-based devices is the skyrmions' magnetic stability in confined helimagnetic nanostructures. Through a systematic study of equilibrium states, using a full three-dimensional micromagnetic model including demagnetisation effects, we demonstrate that skyrmionic textures are the lowest energy states in helimagnetic thin film nanostructures at zero external magnetic field and in absence of magnetocrystalline anisotropy. We also report the regions of metastability for non-ground state equilibrium configurations. We show that bistable skyrmionic textures undergo hysteretic behaviour between two energetically equivalent skyrmionic states with different core orientation, even in absence of both magnetocrystalline and demagnetisation-based shape anisotropies, suggesting the existence of Dzyaloshinskii-Moriya-based shape anisotropy. Finally, we show that the skyrmionic texture core reversal dynamics is facilitated by the Bloch point occurrence and propagation.

Mixed modes of surface polaritons in a PML-type magnetoelectric multiferroic with canted spins.

We present a theoretical discussion of surface polaritons on a ferroelectric-antiferromagnet with magnetoelectric coupling which allows the magnetic subsystem to be canted. Canting of the antiferromagnet results in weak ferromagnetism. The surface polaritons for a semi-infinite film are calculated for a propagation parallel to the uniaxial easy axis, leading to mixed modes. A superposition of two plane waves is needed to generate mixed surface modes. We find two branches, one near the magnon resonance frequency and the other near the phonon resonance frequency. We also find that the surface modes are non-reciprocal due to magnetoelectric interaction, such that ω(k) ≠ ω(-k), where ω is the frequency and k is the propagation vector.

Exchange bias using a spin glass.

Exchange bias is commonly manifested as the hysteresis-loop shift observed when a ferromagnet is in contact with an antiferromagnet. Here, we report observations of exchange bias with unusual features of a ferromagnet in contact with a spin glass, demonstrating that this is a phenomenon of greater generality. The easily measured properties of the ferromagnet allow access to the internal magnetic degrees of freedom of the glass to which they are coupled. Our results show that a Co/CuMn bilayer system exhibits all the rich phenomena of coercivity enhancement, bias-field shifts and training effects associated with a conventional ferromagnet/antiferromagnet system. Nevertheless, striking differences arise, such as an orientation reversal of the bias field in a small temperature range just below the blocking temperature. We argue that all features can be understood within the context of a random-field model for long-ranged oscillatory Ruderman-Kittel-Kasuya-Yosida (RKKY) coupled spins.

A simple Hebbian/anti-Hebbian network learns the sparse, independent components of natural images.

Slightly modified versions of an early Hebbian/anti-Hebbian neural network are shown to be capable of extracting the sparse, independent linear components of a prefiltered natural image set. An explanation for this capability in terms of a coupling between two hypothetical networks is presented. The simple networks presented here provide alternative, biologically plausible mechanisms for sparse, factorial coding in early primate vision.