Translatory and rotatory motion of exchange-bias capped Janus particles controlled by dynamic magnetic field landscapes.

Magnetic Janus particles (MJPs), fabricated by covering a non-magnetic spherical particle with a hemispherical magnetic in-plane exchange-bias layer system cap, display an onion magnetization state for comparably large diameters of a few microns. In this work, the motion characteristics of these MJPs will be investigated when they are steered by a magnetic field landscape over prototypical parallel-stripe domains, dynamically varied by superposed external magnetic field pulse sequences, in an aqueous medium. We demonstrate, that due to the engineered magnetization state in the hemispherical cap, a comparably fast, directed particle transport and particle rotation can be induced. Additionally, by modifying the frequency of the applied pulse sequence and the strengths of the individual field components, we observe a possible separation between a combined or an individual occurrence of these two types of motion. Our findings bear importance for lab-on-a-chip systems, where particle immobilization on a surface via analyte bridges shall be used for low concentration analyte detection and a particle rotation over a defined position of a substrate may dramatically increase the immobilization (and therefore analyte detection) probability.

Transport Efficiency of Biofunctionalized Magnetic Particles Tailored by Surfactant Concentration.

Controlled transport of surface-functionalized magnetic beads in a liquid medium is a central requirement for the handling of captured biomolecular targets in microfluidic lab-on-chip biosensors. Here, the influence of the physiological liquid medium on the transport characteristics of functionalized magnetic particles and on the functionality of the coupled protein is studied. These aspects are theoretically modeled and experimentally investigated for prototype superparamagnetic beads, surface-functionalized with green fluorescent protein immersed in buffer solution with different concentrations of a surfactant. The model reports on the tunability of the steady-state particle substrate separation distance to prevent their surface sticking via the choice of surfactant concentration. Experimental and theoretical average velocities are discussed for a ratchet-like particle motion induced by a dynamic external field superposed on a static locally varying magnetic field landscape. The developed model and experiment may serve as a basis for quantitative forecasts on the functionality of magnetic particle transport-based lab-on-chip devices.

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.

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.

Size limits of magnetic-domain engineering in continuous in-plane exchange-bias prototype films.

Background: The application of superparamagnetic particles as biomolecular transporters in microfluidic systems for lab-on-a-chip applications crucially depends on the ability to control their motion. One approach for magnetic-particle motion control is the superposition of static magnetic stray field landscapes (MFLs) with dynamically varying external fields. These MFLs may emerge from magnetic domains engineered both in shape and in their local anisotropies. Motion control of smaller beads does necessarily need smaller magnetic patterns, i.e., MFLs varying on smaller lateral scales. The achievable size limit of engineered magnetic domains depends on the magnetic patterning method and on the magnetic anisotropies of the material system. Smallest patterns are expected to be in the range of the domain wall width of the particular material system. To explore these limits a patterning technology is needed with a spatial resolution significantly smaller than the domain wall width. Results: We demonstrate the application of a helium ion microscope with a beam diameter of 8 nm as a mask-less method for local domain patterning of magnetic thin-film systems. For a prototypical in-plane exchange-bias system the domain wall width has been investigated as a function of the angle between unidirectional anisotropy and domain wall. By shrinking the domain size of periodic domain stripes, we analyzed the influence of domain wall overlap on the domain stability. Finally, by changing the geometry of artificial two-dimensional domains, the influence of domain wall overlap and domain wall geometry on the ultimate domain size in the chosen system was analyzed. Conclusion: The application of a helium ion microscope for magnetic patterning has been shown. It allowed for exploring the fundamental limits of domain engineering in an in-plane exchange-bias thin film as a prototypical system. For two-dimensional domains the limit depends on the domain geometry. The relative orientation between domain wall and anisotropy axes is a crucial parameter and therefore influences the achievable minimum domain size dramatically.

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.

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.

Modification of the saturation magnetization of exchange bias thin film systems upon light-ion bombardment.

The magnetic modification of exchange bias materials by 'ion bombardment induced magnetic patterning' has been established more than a decade ago. To understand these experimental findings several theoretical models were introduced. Few investigations, however, did focus on magnetic property modifications caused by effects of ion bombardment in the ferromagnetic layer. In the present study, the structural changes occurring under ion bombardment were investigated by Monte-Carlo simulations and in experiments. A strong reduction of the saturation magnetization scaling linearly with increasing ion doses is observed and our findings suggest that it is correlated to the swelling of the layer material based on helium implantation and vacancy creation.

Magnetically Patterned Rolled-Up Exchange Bias Tubes: A Paternoster for Superparamagnetic Beads.

We realized a deterministic transport system for superparamagnetic microbeads through micrometer-sized tubes acting as channels. Beads are moved stepwise in a paternoster-like manner through the tube and back on top of it by weak magnetic field pulses without changing the field pulse polarity and taking advantage of the magnetic stray field emerging from the tubular structures. The microtubes are engineered by rolling up exchange bias layer systems, magnetically patterned into parallel stripe magnetic domains. In this way, the tubes possess distinct azimuthally aligned magnetic domain patterns. This transport mechanism features high step velocities and remote control of not only the direction and trajectory but also the velocity of the transport without the need of fuel or catalytic material. Therefore, this approach has the potential to impact several fields of 3D applications in biotechnology, including particle transport related phenomena in lab-on-a-chip and lab-in-a-tube devices.

Manipulation of Superparamagnetic Beads on Patterned Exchange-Bias Layer Systems for Biosensing Applications.

A technology platform based on a remotely controlled and stepwise transport of an array arrangement of superparamagnetic beads (SPB) for efficient molecular uptake, delivery and accumulation in the context of highly specific and sensitive analyte molecule detection for the application in lab-on-a-chip devices is presented. The near-surface transport of SPBs is realized via the dynamic transformation of the SPBs' magnetic potential energy landscape above a magnetically stripe patterned Exchange-Bias (EB) thin film layer systems due to the application of sub-mT external magnetic field pulses. In this concept, the SPB velocity is dramatically influenced by the magnitude and gradient of the magnetic field landscape (MFL) above the magnetically stripe patterned EB substrate, the SPB to substrate distance, the magnetic properties of both the SPBs and the EB layer system, respectively, as well as by the properties of the external magnetic field pulses and the surrounding fluid. The focus of this review is laid on the specific MFL design in EB layer systems via light-ion bombardment induced magnetic patterning (IBMP). A numerical approach is introduced for the theoretical description of the MFL in comparison to experimental characterization via scanning Hall probe microscopy. The SPB transport mechanism will be outlined in terms of the dynamic interplay between the EB substrate's MFL and the pulse scheme of the external magnetic field.

Directed Magnetic Particle Transport above Artificial Magnetic Domains Due to Dynamic Magnetic Potential Energy Landscape Transformation.

An approach for a remotely controllable transport of magnetic micro- and/or nanoparticles above a topographically flat exchange-bias (EB) thin film system, magnetically patterned into parallel stripe domains, is presented where the particle manipulation is achieved by sub-mT external magnetic field pulses. Superparamagnetic core-shell particles are moved stepwise by the dynamic transformation of the particles' magnetic potential energy landscape due to the external magnetic field pulses without affecting the magnetic state of the thin film system. The magnetic particle velocity is adjustable in the range of 1-100 µm/s by the design of the substrate's magnetic field landscape (MFL), the particle-substrate distance, and the magnitude of the applied external magnetic field pulses. The agglomeration of magnetic particles is avoided by the intrinsic magnetostatic repulsion of particles due to the parallel alignment of the particles' magnetic moments perpendicular to the transport direction and parallel to the surface normal of the substrate during the particle motion. The transport mechanism is modeled by a quantitative theory based on the precise knowledge of the sample's MFL and the particle-substrate distance.