Gauge invariant and gauge dependent aspects of topological walking colloidal bipeds.

Paramagnetic colloidal spheres assemble to colloidal bipeds of various length in an external magnetic field. When the bipeds reside above a magnetic pattern and we modulate the direction of the external magnetic field, the rods perform topologically distinct classes of protected motion above the pattern. The topological protection allows each class to be robust against small continuous deformations of the driving loop of the external field. We observe motion of the rod from a passive central sliding and rolling motion for short bipeds toward a walking motion with both ends of the rod alternately touching down on the pattern for long bipeds. The change of character of the motion occurs in form of discrete topological transitions. The topological protection makes walking a form of motion robust against the breaking of the non symmorphic symmetry. In patterns with non symmorphic symmetry walking is reversible. In symmorphic patterns lacking a glide plane the walking can be irreversible or reversible involving or not involving ratchet jumps. Using different gauges allows us to unravel the active and passive aspects of the topological walks.

Magnetic Domains without Domain Walls: A Unique Effect of He

We show that it is possible to engineer magnetic multidomain configurations without domain walls in a prototypical rare-earth-transition-metal ferrimagnet using keV He^{+} ion bombardment. We additionally show that these patterns display a particularly stable magnetic configuration due to a deep minimum in the energy of the system caused by flux closure and a corresponding reduction of the magnetostatic energy without an increase in energy by exchange and anisotropy terms across the walls. This occurs because light-ion bombardment affects an element's relative contribution to the properties of the ferrimagnet differently. Therefore, it is possible to control the relative contribution from each magnetic subsystem. The selection of material and the use of light-ion bombardment allow us to engineer domain patterns in continuous magnetic films, which open a way to fabricate them in a much smaller scale than currently possible. Our Letter emphasizes that the right criterion to determine the presence or absence of a domain wall is whether there is a rotation of the spin for each sublattice and that changes of the direction of effective magnetization alone do not constitute an appropriate criterion.

Colloidal trains.

Single and double paramagnetic colloidal particles are placed above a magnetic square pattern and are driven with an external magnetic field processing around a high symmetry direction of the pattern. The external magnetic field and that of the pattern confine the colloids into lanes parallel to a lattice vector of the pattern. The precession of the external field causes traveling minima of the magnetic potential along the direction of the lanes. At sufficiently high frequencies of modulation, only the doublets respond to the external field and move in direction of the traveling minima along the lanes, while the single colloids cannot follow and remain static. We show how the doublets can induce a coordinated motion of the single colloids building colloidal trains made of a chain of several single colloids transported by doublets.

Edge transport at the boundary between topologically equivalent lattices.

Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when the system is driven with periodic modulation loops of an external magnetic field. The number of topologically protected particle edge transport modes is not determined by a bulk-boundary correspondence. Instead, we find a rich variety of edge transport modes that depend on the symmetry of both the edge and the modulation loop. The edge transport can be ratchet-like or adiabatic, time or non-time reversal symmetric. The topological nature of the edge transport is classified by a set of winding numbers around bulk fence points extended by winding numbers around edge specific bifurcation points that cannot be deduced from the two bulk lattices.

Lattice symmetries and the topologically protected transport of colloidal particles.

The topologically protected transport of colloidal particles on top of periodic magnetic patterns is studied experimentally, theoretically, and with computer simulations. To uncover the interplay between topology and symmetry we use patterns of all possible two dimensional magnetic point group symmetries with equal lengths lattice vectors. Transport of colloids is achieved by modulating the potential with external, homogeneous but time dependent magnetic fields. The modulation loops can be classified into topologically distinct classes. All loops falling into the same class cause motion in the same direction, making the transport robust against internal and external perturbations. We show that the lattice symmetry has a profound influence on the transport modes, the accessibility of transport networks, and the individual transport directions of paramagnetic and diamagnetic colloidal particles. We show how the transport of colloidal particles above a two fold symmetric stripe pattern changes from universal adiabatic transport at large elevations via a topologically protected ratchet motion at intermediate elevations toward a non-transport regime at low elevations. Transport above four-fold symmetric patterns is closely related to the two-fold symmetric case. The three-fold symmetric case however consists of a whole family of patterns that continuously vary with a phase variable. We show how this family can be divided into two topologically distinct classes supporting different transport modes and being protected by proper and improper six fold symmetries. We discuss and experimentally demonstrate the topological transition between both classes. All three-fold symmetric patterns support independent transport directions of paramagnetic and diamagnetic particles. The similarities and the differences in the lattice symmetry protected transport of classical over-damped colloidal particles versus the topologically protected transport in quantum mechanical systems are emphasized.

Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes.

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. We design a pattern featuring a topological defect that functions as an attractor or a repeller of microparticles, as well as a pattern that directs microparticles along a prescribed complex trajectory. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently. Our findings pave the way for new avenues in transport control and dynamic self-assembly in colloidal science.

Colloidal domain lithography in multilayers with perpendicular anisotropy: an experimental study and micromagnetic simulations.

Currently, much attention is being paid to patterned multilayer systems in which there exists a perpendicular magnetic anisotropy, because of their potential applications in spintronics devices and in a new generation of magnetic storage media. To further improve their performance, different patterning techniques can be used, which render them suitable also for other applications. Here we show that He(+) 10 keV and Ar(+) 100 keV ion bombardment of (Ni(80)Fe(20)-2 nm/Au-2 nm/Co-0.6 nm/Au-2 nm)(10) multilayers through colloidal mask enables magnetic patterning of regularly arranged cylindrical magnetic domains, with perpendicular anisotropy, embedded in a non-ferromagnetic matrix or in a ferromagnetic matrix with magnetization oriented along the normal. These domains form an almost perfect two-dimensional hexagonal lattice with a submicron period and a large correlation length in a continuous and flat multilayer system. The magnetic anisotropy of these artificial domains remains unaffected by the magnetic patterning process, however the magnetization configuration of such a system depends on the magnetic properties of the matrix. The micromagnetic simulations were used to explain some of the features of the investigated patterned structures.

Magnetic patterning of Co/Ni layered systems by plasma oxidation.

We studied the structural, chemical, and magnetic properties of Ti/Au/Co/Ni layered systems subjected to plasma oxidation. The process results in the formation of NiO at the expense of metallic Ni, as clearly evidenced by X-ray photoelectron spectroscopy, while not affecting the surface roughness and grain size of the Co/Ni bilayers. Since the decrease of the thickness of the Ni layer and the formation of NiO increase the perpendicular magnetic anisotropy, oxidation may be locally applied for magnetic patterning. Using this approach, we created 2D heterostructures characterized by different combinations of magnetic properties in areas modified by plasma oxidation and in the regions protected from oxidation. As plasma oxidation is an easy to use, low cost, and commonly utilized technique in industrial applications, it may constitute an improvement over other magnetic patterning methods.

Colloidal domain lithography for regularly arranged artificial magnetic out-of-plane monodomains in Au/Co/Au layers.

Regularly arranged magnetic out-of-plane patterns in continuous and flat films are promising for applications in data storage technology (bit patterned media) or transport of individual magnetic particles. Whereas topographic magnetic structures are fabricated by standard lithographical techniques, the fabrication of regularly arranged artificial domains in topographically flat films is difficult, since the free energy minimization determines the existence, shape, and regularity of domains. Here we show that keV He(+) ion bombardment of Au/Co/Au layer systems through a colloidal mask of hexagonally arranged spherical polystyrene beads enables magnetic patterning of regularly arranged cylindrical magnetic monodomains with out-of-plane magnetization embedded in a ferromagnetic matrix with easy-plane anisotropy. This colloidal domain lithography creates artificial domains via periodic lateral anisotropy variations induced by periodic defect density modulations. Magnetization reversal of the layer system observed by magnetic force microscopy shows individual disc switching indicating monodomain states.

Strong Interfacial Perpendicular Magnetic Anisotropy in Exchange-Biased NiO/Co/Au and NiO/Co/NiO Layered Systems.

The ability to induce and control the perpendicular magnetic anisotropy (PMA) of ferromagnetic layers has been widely investigated, especially those that offer additional functionalities (e.g., skyrmion stabilization, voltage-based magnetization switching, rapid propagation of domain walls). Out-of-plane magnetized ferromagnetic layers in direct contact with an oxide belong to this class. Nowadays, investigation of this type of system includes antiferromagnetic oxides (AFOs) because of their potential for new approaches to applied spintronics that exploit the exchange bias (EB) coupling between the ferromagnetic and the AFO layer. Here, we investigate PMA and EB effect in NiO/Co/Au and NiO/Co/NiO layered systems. We show that the coercive and EB fields increase significantly when the Co layer is coupled with two NiO layers, instead of one. Surrounding the Co layer only with NiO layers induces a strong PMA resulting in an out-of-plane magnetized system can be obtained without a heavy metal/ferromagnetic interface. The PMA arises from a significant surface contribution (0.74 mJ/m2) that can be enhanced up to 0.99 mJ/m2 by annealing at moderate temperatures (~450 K). Using field cooling processes for both systems, we demonstrate a wide-ranging control of the exchange bias field without perturbing other magnetic properties of importance.

Subsystem domination influence on magnetization reversal in designed magnetic patterns in ferrimagnetic Tb/Co multilayers.

Recent results showed that the ferrimagnetic compensation point and other characteristic features of Tb/Co ferrimagnetic multilayers can be tailored by He+ ion bombardment. With appropriate choices of the He+ ion dose, we prepared two types of lattices composed of squares with either Tb or Co domination. The magnetization reversal of the first lattice is similar to that seen in ferromagnetic heterostructures consisting of areas with different switching fields. However, in the second lattice, the creation of domains without accompanying domain walls is possible. These domain patterns are particularly stable because they simultaneously lower the demagnetizing energy and the energy associated with the presence of domain walls (exchange and anisotropy). For both lattices, studies of magnetization reversal show that this process takes place by the propagation of the domain walls. If they are not present at the onset, the reversal starts from the nucleation of reversed domains and it is followed by domain wall propagation. The magnetization reversal process does not depend significantly on the relative sign of the effective magnetization in areas separated by domain walls.

Optimization of spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers.

We present experimental data and their theoretical description on spin Hall magnetoresistance (SMR) in bilayers consisting of a heavy metal (H) coupled to in-plane magnetized ferromagnetic metal (F), and determine contributions to the magnetoresistance due to SMR and anisotropic magnetoresistance (AMR) in five different bilayer systems: [Formula: see text], [Formula: see text], [Formula: see text], W/Co, and Co/Pt. The devices used for experiments have different interfacial properties due to either amorphous or crystalline structures of constitutent layers. To determine magnetoresistance contributions and to allow for optimization, the AMR is explicitly included in the diffusion transport equations in the ferromagnets. The results allow determination of different contributions to the magnetoresistance, which can play an important role in optimizing prospective magnetic stray field sensors. They also may be useful in the determination of spin transport properties of metallic magnetic heterostructures in other experiments based on magnetoresistance measurements.

Simultaneous polydirectional transport of colloidal bipeds.

Detailed control over the motion of colloidal particles is relevant in many applications in colloidal science such as lab-on-a-chip devices. Here, we use an external magnetic field to assemble paramagnetic colloidal spheres into colloidal rods of several lengths. The rods reside above a square magnetic pattern and are transported via modulation of the direction of the external magnetic field. The rods behave like bipeds walking above the pattern. Depending on their length, the bipeds perform topologically distinct classes of protected walks. We design parallel polydirectional modulation loops of the external field that command up to six classes of bipeds to walk on distinct predesigned paths. Using such loops, we induce the collision of reactant bipeds, their polymerization addition reaction to larger bipeds, the separation of product bipeds from the educts, the sorting of different product bipeds, and also the parallel writing of a word consisting of several letters. Our ideas and methodology might be transferred to other systems for which topological protection is at work.

Magnetophoretic lensing by concentric topographic cylinders of perpendicular magnetic anisotropy multilayers.

Colloidal magnetophoretic lensing of water suspended micrometer-sized superparamagnetic beads (SPBs) above a topographically patterned magnetic thin film system with perpendicular magnetic anisotropy is demonstrated. The magnetic pattern consisting of concentric annuli of micron-sized widths has been superimposed with a rotating external magnetic field, and it is shown that the trajectories of the SPBs above this structure are similar to light rays in an optical focusing lens. SPB trajectories converge towards the central region and have divergent trajectories while passing the center. The experimental findings are corroborated by a quantitative model for the SPB trajectories. The magnetophoretic lensing effect leads to a high SPB concentration in the center of the pattern and may be useful for applications where SPBs have to approach each other in a controlled way.

Wide-range tuning of interfacial exchange coupling between ferromagnetic Au/Co and ferrimagnetic Tb/Fe(Co) multilayers.

The ability to perform wide-range tuning of the magnetic field required to switch the magnetization of ferromagnetic layers with perpendicular magnetic anisotropy is of great importance for many applications. We show that, for (Au/Co)2(3) multilayers, this field can be changed from minus several kOe to plus several kOe because of changes to the coupling with a ferrimagnetic multilayer [either (Tb/Fe)6 or (Tb/Co)6] across a Au spacer (either homogeneous 1 nm thick or wedge-shaped). The adjustable parameters are the ratio of sublayer thicknesses of the ferrimagnet and the sequence of layers around the Au spacer. The change of the sequence from Co/Au/Co to Tb/Au/Co is accompanied by both the reduction of the interaction energy and the change of the magnetic field sign necessary to switch the magnetization of ferromagnetic multilayers. For a 1 nm thick Au spacer this fields change from positive (negative) to negative (positive) if the ferrimagnet is dominated by the transition metal (rare earth) as a result of its composition. The characteristic oscillatory behavior of RKKY-like coupling is demonstrated using a system with a wedge-shaped Au spacer.

Tailoring Perpendicular Exchange Bias Coupling in Au/Co/NiO Systems by Ion Bombardment.

Here, we systematically investigated the influence of ion bombardment with different fluences on the strength and direction of the exchange bias coupling in Au/Co/NiO systems with perpendicular magnetic anisotropy of the Co layer. We found that the direction of the exchange bias coupling can be reversed as a result of ion bombardment performed in an external magnetic field which is in the opposite direction to the magnetic field applied during film deposition. Moreover, the strength of the exchange bias coupling can be tailored by varying the ion fluence. These results show behaviors similar to the results found for systems of ferromagnetic layers with in-plane anisotropy. Our experimental work, supported by a two-energy-level model, demonstrates that exchange bias coupling can be tuned in a layered system with perpendicular magnetic anisotropy using ion bombardment.

Anchoring Fe3O4 nanoparticles in a reduced graphene oxide aerogel matrix via polydopamine coating.

Reduced graphene oxide-magnetite hybrid aerogels attract great interest thanks to their potential applications, e.g., as magnetic actuators. However, the tendency of magnetite particles to migrate within the matrix and, ultimately, escape from the aerogel structure, remains a technological challenge. In this article we show that coating magnetite particles with polydopamine anchors them on graphene oxide defects, immobilizing the particles in the matrix and, at the same time, improving the aerogel structure. Polydopamine coating does not affect the magnetic properties of magnetite particles, making the fabricated materials promising for industrial applications.

Perpendicularly magnetized Co20Fe60B20 layer sandwiched between Au with low Gilbert damping.

Nowadays, the CoFeB thin layered film is intensively studied because of its potential applications in spintronic devices, especially devices based on spin-transfer torque phenomena. Hitherto, it has been shown that CoFeB may possess perpendicular magnetic anisotropy (PMA) when it is sandwiched between different layers (e.g. MgO, Pt, Pd, Ta, W). However, there is no experimental evidence that CoFeB, sandwiched between Au layers, has strong PMA. Moreover, in comparison with other noble metals, Au-based film systems exhibit the smallest spin pumping effect, which provides the main contribution to the damping in thin films in contact with heavy metals. Therefore, Au/CoFeB/Au may be a good candidate for future applications, where perpendicular magnetic anisotropy and low damping are required. Here, we show that PMA and low damping can be achieved in a Au/CoFeB/Au system without annealing.

Second Harmonic Generation Response in Thermally reconstructed Multiferroic ß'- Gd2(MoO4)3 Thin Films.

Gd2(MoO4)3 (GMO) is a well-studied multiferroic material that exhibits full ferroelectric and ferroelastic behavior at room temperature. However, its difficult stabilization in thin films has prevented the study and exploitation of its multiferroic properties in different architectures. Here, we report on the study of GMO thin films deposited on Si(001) substrates by Pulsed Laser Deposition (PLD). The physicochemical properties of the films are discussed and studied. Results obtained by X-ray diffraction, X-ray photoelectron spectroscopy, high resolution transmission microscopy and second harmonic generation show that the orthorhombic (ß'-GMO) multiferroic phase can be stabilized and homogenized by post deposition thermal reconstruction. Finally, the reconstruction process takes place via a complex surface mechanism with a clear leaf-like behavior.

Tailoring magnetic anisotropy gradients by ion bombardment for domain wall positioning in magnetic multilayers with perpendicular anisotropy.

Graded anisotropy magnetic materials possess a coercive field changing laterally with position. A simple fabrication procedure to produce such an anisotropy gradient in a polycrystalline Au/Co layer system without lateral thickness variation and with perpendicular magnetic anisotropy, prototypical for a large variety of thin film systems, is shown. The procedure uses light-ion bombardment without the use of a mask. Magnetization reversal in this polycrystalline layer system takes place by unidirectional movement of a single domain wall only in regions with larger anisotropies and anisotropy gradients. In this anisotropy/anisotropy gradient regime, the domain wall is oriented perpendicular to the coercive field gradient, and it can be positioned along the gradient by an appropriate magnetic field pulse. For smaller anisotropies/anisotropy gradients, the natural anisotropy fluctuations of the polycrystalline layer system induce magnetization reversal dominated by domain nucleation. PACS: 75.30.Gw; 75.70.Cn; 75.60.Ch.