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Rotating all islands in square artificial spin ice (ASI) uniformly about their centers gives rise to the recently reported pinwheel ASI. At angles around 45, the antiferromagnetic ordering changes to ferromagnetic and the magnetic configurations of the system exhibit near degeneracy, making it particularly sensitive to small perturbations. We investigate through micromagnetic modeling the influence of dipolar fields produced by physically extended islands in field-driven magnetization processes in pinwheel arrays and compare the results to hysteresis experiments performed in situ using Lorentz transmission electron microscopy. We find that magnetization end states induce a Heisenberg pseudoexchange interaction that governs both the interisland coupling and the resultant array reversal process. Symmetry reduction gives rise to anisotropies and array-corner mediated avalanche reversals through a cascade of nearest-neighbor (NN) islands. The symmetries of the anisotropy axes are related to those of the geometrical array but are misaligned to the array axes as a result of the correlated interactions between neighboring islands. The NN dipolar coupling is reduced by decreasing the island size and, using this property, we track the transition from the strongly coupled regime towards the pure point dipole one and observe modification of the ferromagnetic array reversal process. Our results shed light on important aspects of the interactions in pinwheel ASI and demonstrate a mechanism by which their properties may be tuned for use in a range of fundamental research and spintronic applications.

We report on the crossover from the thermal to the athermal regime of an artificial spin ice formed from a square array of magnetic islands whose lateral size, 30 nm × 70 nm, is small enough that they are dynamic at room temperature. We used resonant magnetic soft x-ray photon correlation spectroscopy as a method to observe the time-time correlations of the fluctuating magnetic configurations of spin ice during cooling, which are found to slow abruptly as a freezing temperature of T0=178±5 K is approached. This slowing is well described by a Vogel-Fulcher-Tammann law, implying that the frozen state is glassy, with the freezing temperature being commensurate with the strength of magnetostatic interaction energies in the array. The activation temperature, TA=40±10 K, is much less than that expected from a Stoner-Wohlfarth coherent rotation model. Zero-field-cooled/field-cooled magnetometry reveals a freeing up of fluctuations of states within islands above this temperature, caused by variation in the local anisotropy axes at the oxidised edges. This Vogel-Fulcher-Tammann behavior implies that the system enters a glassy state upon freezing, which is unexpected for a system with a well-defined ground state.

We present a comparative study of the spin wave properties in two magnetic films patterned into an artificial square spin ice-like geometry. The array elements are rectangular islands with the same lateral dimensions but with different thicknesses: 10 nm and 30 nm. Using Brillouin light scattering, the frequencies of spin wave excitations were measured as a function of the magnetic field going from positive to negative saturation. We find substantial changes with thickness to spin wave mode frequencies and the number of detected modes. Frequencies of spin waves localized at element edges are observed to evolve non-monotonically with magnetic fields and soften at critical fields. These critical fields enable us to extract information of the magnetization reversal of individual islands within the array. Finally, we discuss the effects of separation between islands and examine the possibilities for dynamic coupling through the overlap of collective edge modes.

We report the results, from experimental and micromagnetic studies, of the magnetic normal modes in artificial square spin ice systems consisting of ferromagnetic-monodomain islands. Spin-wave properties are measured by Brillouin light scattering. The mode spectra contain several branches whose frequencies are sensitive to the magnitude and in-plane orientation of an applied magnetic field. We also identify soft modes that exhibit different behaviours depending on the direction of the applied magnetic field. The obtained results are well described with micromagnetic simulations of independent magnetic elements arranged along two sublattices.

The spin-orbit interaction is an inherent part of magnetism, which links up the independent world of spins to the atomic lattice, thus controlling many functional properties of magnetic materials. In the widely used 3d transition metal ferromagnetic films, the spin-orbit interaction is relatively weak, due to low atomic number. Here we show that it is possible to enhance and tune the spin-orbit interaction by adding 5d platinum dopants into permalloy (Ni81Fe19) thin films by a cosputtering technique. This is achieved without significant changes of the magnetic properties, due to the vicinity of Pt to meeting the Stoner criterion for the ferromagnetic state. The spin-orbit interaction is investigated by means of transport measurements (the anisotropic magnetoresistance and anomalous Hall effect), ferromagnetic resonance measurements to determine the Gilbert damping, as well as by measuring the x-ray magnetic circular dichroism at the L3 and L2 x-ray absorption edges to reveal the ratio of orbital to spin magnetic moments. It is shown that the effective spin-orbit interaction increases with Pt concentration within the 0%-10% Pt concentration range in a way that is consistent with theoretical expectations for all four measurements.

Theory and simulations are used to demonstrate implementation of a variational Bayes algorithm called "active inference" in interacting arrays of nanomagnetic elements. The algorithm requires stochastic elements, and a simplified model based on a magnetic artificial spin ice geometry is used to illustrate how nanomagnets can generate the required random dynamics. Examples of tracking and PID control are demonstrated and shown to be consistent with the original stochastic differential equation formulation of active inference. Interestingly, nonlinear response in the form of spikes and spike trains not predicted by the original theory can appear in the nanomagnet system for certain temperature regimes. A theoretical approach using a mean-field approximation for spin systems is proposed, which describes the transition to nonlinear response. Finally, the possibility to create simple magnetic arrays using realistic models is shown with micromagnetic simulations of a simple 17 element array of nanomagnets that include magnetic anisotropies, and exchange and dipolar interactions. Possible applications are simulated to illustrate how nanomagnetic arrays can be used as the stochastic element for feedback control of processes, investigation and control of magnetic state evolution, and as a method to optimize pulsed field magnetic switching protocols.

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., Competing Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2023.)

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., Competing Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article., (© The Author(s) 2023.)

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years., (Creative Commons Attribution license.)

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.

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.

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.

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.

We report dissipative magnon-photon coupling caused by the cavity Lenz effect, where the magnons in a magnet induce a rf current in the cavity, leading to a cavity backaction that impedes the magnetization dynamics. This effect is revealed in our experiment as level attraction with a coalescence of hybridized magnon-photon modes, which is distinctly different from level repulsion with mode anticrossing caused by coherent magnon-photon coupling. We develop a method to control the interpolation of coherent and dissipative magnon-photon coupling, and observe a matching condition where the two effects cancel. Our work sheds light on the so-far hidden side of magnon-photon coupling, opening a new avenue for controlling and utilizing light-matter interactions.

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.

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.

A technique is presented whereby the performance of a microwave device is evaluated by mapping local field distributions using Lorentz transmission electron microscopy (L-TEM). We demonstrate the method by measuring the polarisation state of the electromagnetic fields produced by a microstrip waveguide as a function of its gigahertz operating frequency. The forward and backward propagating electromagnetic fields produced by the waveguide, in a specimen-free experiment, exert Lorentz forces on the propagating electron beam. Importantly, in addition to the mapping of dynamic fields, this novel method allows detection of effects of microwave fields on specimens, such as observing ferromagnetic materials at resonance.

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.

Theoretical analysis and Lorentz transmission electron microscopy (LTEM) investigations in an FeGe wedge demonstrate that chiral twists arising near the surfaces of noncentrosymmetric ferromagnets [Meynell et al., Phys. Rev. B 90, 014406 (2014)] provide a stabilization mechanism for magnetic Skyrmion lattices and helicoids in cubic helimagnet nanolayers. The magnetic phase diagram obtained for freestanding cubic helimagnet nanolayers shows that magnetization processes differ fundamentally from those in bulk cubic helimagnets and are characterized by the first-order transitions between modulated phases. LTEM investigations exhibit a series of hysteretic transformation processes among the modulated phases, which results in the formation of the multidomain patterns.

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.

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.

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.

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.

Recent studies on surface reflection illustrate how light beams can be laterally shifted from the position predicted by geometrical optics, the so called Goos-Hänchen effect. In antiferromagnets this shifts can be controlled with an external magnetic field. We show that a configuration in which spins cant in response to applied magnetic fields enhance possibilities of field controlled shifts. Moreover, we show that nonreciprocal displacements are possible, for both oblique and normal incidence, due to inherent nonreciprocity of the polariton phase with respect to the propagation direction. In the absence of an external field, reciprocal displacements occur.

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.

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.

Quenched disorder affects how nonequilibrium systems respond to driving. In the context of artificial spin ice, an athermal system comprised of geometrically frustrated classical Ising spins with a twofold degenerate ground state, we give experimental and numerical evidence of how such disorder washes out edge effects and provide an estimate of disorder strength in the experimental system. We prove analytically that a sequence of applied fields with fixed amplitude is unable to drive the system to its ground state from a saturated state. These results should be relevant for other systems where disorder does not change the nature of the ground state.

We detail measurements of field-driven expansion and zero-field relaxation of magnetic mirror domains in antiferromagnetically coupled perpendicularly magnetized ultrathin Co layers. The zero-field stability of aligned ('mirror') domains in such systems results from non-homogeneous dipolar stray fields which exist in the vicinity of the domain walls. During field-driven domain expansion, we evidence a separation of the domain walls which form the mirror domain boundary. However, the walls realign, thereby reforming a mirror domain, if their final separation is below a critical distance at the end of the field pulse. This critical distance marks the point at which the effective net interaction between the walls changes from attractive to repulsive.

We report a novel approach to the question of whether and how the ground state can be achieved in square artificial spin ices where frustration is incomplete. We identify two sources of randomness that affect the approach to ground state: quenched disorder in the island response to fields and randomness in the sequence of driving fields. Numerical simulations show that quenched disorder can lead to final states with lower energy, and randomness in the sequence of driving fields always lowers the final energy attained by the system. We use a network picture to understand these two effects: disorder in island responses creates new dynamical pathways, and a random sequence of driving fields allows more pathways to be followed.

A detailed investigation of magnetic impurity-mediated interlayer exchange coupling observed in Cu(0.94)Mn(0.06)/Co multilayers using polarized neutron reflectometry and magnetic x-ray techniques is reported. Excellent descriptions of temperature and magnetic field dependent biquadratic coupling are obtained using a variant of the loose spin model that takes into account the distribution of the impurity Mn ions in three dimensions. Positional disorder of the magnetic impurities is shown to enhance biquadratic coupling via a new contribution J(2)(fluct), leading to a temperature dependent canting of magnetic domains in the multilayer. These results provide measurable effects on RKKY coupling associated with the distribution of impurities within planes parallel to the interfaces.

We present a theory for surface polaritons on ferroelectric-antiferromagnetic materials with canted spin structure. A small uniform canted moment is allowed, resulting in a weak ferromagnetism directed in the plane parallel to the surface. Surface and bulk polariton modes for a semi-infinite film are calculated for the case of transverse electric (TE) and transverse magnetic (TM) polarization. Example results are presented using parameters appropriate for BaMnF(4). We find that the surface modes are non-reciprocal for the TE polarization due to the magnetoelectric interaction, and the non-reciprocity can be controlled by an applied electric field. Example results for attenuated total reflection (ATR) are calculated. The magnetoelectric interaction also gives rise to 'leaky' surface modes in the case of TM polarization. These are pseudo-surface waves that exist in the pass band, and dissipate energy into the bulk of the material. We show that these pseudo-surface mode frequencies and properties can be modified by temperature and the application of external electric or magnetic fields.

Local magnetic ordering in artificial spin ices is discussed from the point of view of how geometrical frustration controls dynamics and the approach to steady state. We discuss the possibility of using a particle picture based on vertex configurations to interpret the time evolution of magnetic configurations. Analysis of possible vertex processes allows us to anticipate different behaviors for open and closed edges and the existence of different field regimes. Numerical simulations confirm these results and also demonstrate the importance of correlations and long-range interactions in understanding particle population evolution. We also show that a mean-field model of vertex dynamics gives important insights into finite size effects.

We demonstrate experimentally dynamic interface binding in a system consisting of two coupled ferromagnetic layers. While domain walls in each layer have different velocity-field responses, for two broad ranges of the driving field H, walls in the two layers are bound and move at a common velocity. The bound states have their own velocity-field response and arise when the isolated wall velocities in each layer are close, a condition which always occurs as H→0. Several features of the bound states are reproduced using a one-dimensional model, illustrating their general nature.

Magnetic relaxation experiments have been used to investigate the non-equilibrium dynamics of FePt nanoparticles. The system exhibits ageing at low temperatures, as well as a narrow energy distribution of the barrier to reversal. These properties were found susceptible to being affected by particle size, matrix and applied field strength. An analysis based on broad rate distributions is presented and compared with results obtained using energy barrier and viscosity interpretations. We find that a single broad distribution of relaxation times suggestive of cooperative effects is sufficient to explain the experimental results.

We report on the control of magnetization reversal in exchange-biased Co/CoO nanorings resulting from the competition between field-cooling-induced unidirectional anisotropy at the Co/CoO interface and shape anisotropy of the elongated Co nanorings. We observed that the magnetization reversal mechanisms and magnitudes of exchange bias fields are strongly dependent on the strength and orientation of the cooling field relative to the major axis of the nanorings. Our results demonstrate a convenient technique to control the magnetization reversal modes in ferromagnetic nanorings.

We report on magnetic domain-wall velocity measurements in ultrathin Pt/Co(0.5-0.8 nm)/Pt films with perpendicular anisotropy over a large range of applied magnetic fields. The complete velocity-field characteristics are obtained, enabling an examination of the transition between thermally activated creep and viscous flow: motion regimes predicted from general theories for driven elastic interfaces in weakly disordered media. The dissipation limited flow regime is found to be consistent with precessional domain-wall motion, analysis of which yields values for the damping parameter, alpha.

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.

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.

As a magnetic domain wall propagates under small fields through a random potential, it roughens as a result of weak collective pinning, known as creep. Using Kerr microscopy, we report experimental evidence of a surprising deroughening of wall pairs in the creep regime, in a 0.5 nm thick Co layer with perpendicular anisotropy. A bound state is found in cases where two rough domains nucleated far away from one another and first growing under the action of a magnetic field eventually do not merge. The two domains remain separated by a strip of unreversed magnetization, characterized by flat edges and stabilized by dipolar fields. A creep theory that includes dipolar interactions between domains successfully accounts for (i) the domain wall deroughening as the width of the strip decreases and (ii) the quasistatic and dynamic field dependence of the strip width s.