Colloidal transport on magnetic garnet films

Ferrimagnetic Tb/Co multilayers patterned by ion bombardment as substrates for magnetophoresis

Ion bombardment with 30 keV Ga+ ions can locally change the magnetic properties of perpendicular magnetic anisotropy ferrimagnetic Tb/Co based multilayers. The induced changes in the effective magnetization create high gradients of magnetic fields in the proximity of the perimeters of the bombarded areas. Superparamagnetic, micrometer-sized beads floating in an aqueous suspension over such a patterned structure respond to the ensuing magnetostatic energy landscape. This landscape, and its associated forces on the beads, can be controlled with a time varying, external, homogeneous magnetic field. It is shown that with a 3.37 kA/m (approx. 4.2 mT) field and switching the direction at 10 Hz frequencies the beads can be driven with average forward velocities reaching 40  μ m/s. This has the potential for use in lab-on-a-chip type assays.

Scalable high-throughput microfluidic separation of magnetic microparticles

Surface-engineered magnetic microparticles are used in chemical and biomedical engineering due to their ease of synthesis, high surface-to-volume ratio, selective binding, and magnetic separation. To separate them from fluid suspensions, existing methods rely on the magnetic force introduced by the local magnetic field gradient. However, this strategy has poor scalability because the magnetic field gradient decreases rapidly as one moves away from the magnets. Here, we present a scalable high-throughput magnetic separation strategy using a rotating permanent magnet and two-dimensional arrays of micromagnets. Under a dynamic magnetic field, nickel micromagnets allow the surrounding magnetic microparticles to self-assemble into large clusters and effectively propel themselves through the flow. The collective speed of the microparticle swarm reaches about two orders of magnitude higher than the gradient-based separation method over a wide range of operating frequencies and distances from a rotating magnet.

Combined Funnel, Concentrator, and Particle Valve Functional Element for Magnetophoretic Bead Transport Based on Engineered Magnetic Domain Patterns

Controlled actuation of superparamagnetic beads (SPBs) within a microfluidic environment using tailored dynamic magnetic field landscapes (MFLs) is a potent approach for the realization of point-of-care diagnostics within Lab-on-a-chip (LOC) systems. Making use of an engineered magnetic domain pattern as the MFL source, a functional LOC-element with combined magnetophoretic "funnel", concentrator, and "valve" functions for micron-sized SPBs is presented. A parallel-stripe domain pattern design with periodically decreasing/increasing stripe lengths is fabricated in a topographically flat continuous exchange biased (EB) thin film system by ion bombardment induced magnetic patterning (IBMP). It is demonstrated that, upon application of external magnetic field pulses, a fully reversible concentration of SPBs at the domain pattern's focal point occurs. In addition, it is shown that this functionality may be used as an SPB "funnel", allowing only a maximum number of particles to pass through the focal point. Adjusting the pulse time length, the focal point can be clogged up for incoming SPBs, resembling an on/off switchable particle "valve". The observations are supported by quantitative theoretical force considerations.

Magneto-Optical Indicator Films: Fabrication, Principles of Operation, Calibration, and Applications

Magneto-optical indicator films (MOIFs) are a very useful tool for direct studies of the spatial distribution of magnetic fields and the magnetization processes in magnetic materials and industrial devices such as magnetic sensors, microelectronic components, micro-electromechanical systems (MEMS), and others. The ease of application and the possibility for direct quantitative measurements in combination with a straightforward calibration approach make them an indispensable tool for a wide spectrum of magnetic measurements. The basic sensor parameters of MOIFs, such as a high spatial resolution down to below 1 μm combined with a large spatial imaging range of up to several cm and a wide dynamic range from 10 μT to over 100 mT, also foster their application in various areas of scientific research and industry. The history of MOIF development totals approximately 30 years, and only recently have the underlying physics been completely described and detailed calibration approaches been developed. The present review first summarizes the history of MOIF development and applications and then presents the recent advances in MOIF measurement techniques, including the theoretical developments and traceable calibration methods. The latter make MOIFs a quantitative tool capable of measuring the complete vectorial value of a stray field. Furthermore, various scientific and industrial application areas of MOIFs are described in detail.

Three-dimensional close-to-substrate trajectories of magnetic microparticles in dynamically changing magnetic field landscapes

The transport of magnetic particles (MPs) by dynamic magnetic field landscapes (MFLs) using magnetically patterned substrates is promising for the development of Lab-on-a-chip (LOC) systems. The inherent close-to-substrate MP motion is sensitive to changing particle-substrate interactions. Thus, the detection of a modified particle-substrate separation distance caused by surface binding of an analyte is expected to be a promising probe in analytics and diagnostics. Here, we present an essential prerequisite for such an application, namely the label-free quantitative experimental determination of the three-dimensional trajectories of superparamagnetic particles (SPPs) transported by a dynamically changing MFL. The evaluation of defocused SPP images from optical bright-field microscopy revealed a "hopping"-like motion of the magnetic particles, previously predicted by theory, additionally allowing a quantification of maximum jump heights. As our findings pave the way towards precise determination of particle-substrate separations, they bear deep implications for future LOC detection schemes using only optical microscopy.

Hydrodynamic synchronization and clustering in ratcheting colloidal matter

Ratchet transport systems are widespread in physics and biology; however, the effect of the dispersing medium in the collective dynamics of these out-of-equilibrium systems has been often overlooked. We show that, in a traveling wave magnetic ratchet, long-range hydrodynamic interactions (HIs) produce a series of remarkable phenomena on the transport and assembly of interacting Brownian particles. We demonstrate that HIs induce the resynchronization with the traveling wave that emerges as a "speed-up" effect, characterized by a net raise of the translational speed, which doubles that of single particles. When competing with dipolar forces and the underlying substrate symmetry, HIs promote the formation of clusters that grow perpendicular to the driving direction. We support our findings both with Langevin dynamics and with a theoretical model that accounts for the fluid-mediated interactions. Our work illustrates the role of the dispersing medium on the dynamics of driven colloidal matter and unveils the growing process and cluster morphologies above a periodic substrate.

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.

Thermally active nanoparticle clusters enslaved by engineered domain wall traps

The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stiffness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiments and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential.

Magnetophoretic Decoupler for Disaggregation and Interparticle Distance Control

The manipulation of superparamagnetic beads has attracted various lab on a chip and magnetic tweezer platforms for separating, sorting, and labeling cells and bioentities, but the irreversible aggregation of beads owing to magnetic interactions has limited its actual functionality. Here, an efficient solution is developed for the disaggregation of magnetic beads and interparticle distance control with a magnetophoretic decoupler using an external rotating magnetic field. A unique magnetic potential energy distribution in the form of an asymmetric magnetic thin film around the gap is created and tuned in a controlled manner, regulated by the size ratio of the bead with a magnetic pattern. Hence, the aggregated beads are detached into single beads and transported in one direction in an array pattern. Furthermore, the simultaneous and accurate spacing control of multiple magnetic bead pairs is performed by adjusting the angle of the rotating magnetic field, which continuously changes the energy well associated with a specific shape of the magnetic patterns. This technique offers an advanced solution for the disaggregation and controlled manipulation of beads, can allow new possibilities for the enhanced functioning of lab on a chip and magnetic tweezers platforms for biological assays, intercellular interactions, and magnetic biochip systems.

Negative resistance for colloids driven over two barriers in a microchannel

When considering the flow of currents through obstacles, one core expectation is that the total resistance of sequential single resistors is additive. While this rule is most commonly applied to electronic circuits, it also applies to other transport phenomena such as the flow of colloids or nanoparticles through channels containing multiple obstacles, as long as these obstacles are sufficiently far apart. Here we explore the breakdown of this additivity for fluids of repulsive colloids driven over two energetic barriers in a microchannel, using real-space microscopy experiments, particle-resolved simulations, and dynamical density functional theory. If the barrier separation is comparable to the particle correlation length, the resistance is highly non-additive, such that the resistance added by the second barrier can be significantly higher or lower than that of the first. Surprisingly, in some cases the second barrier can even add a negative resistance, such that two identical barriers are easier to cross than a single one. We explain this counterintuitive observation in terms of the structuring of particles trapped between the barriers.

Layering of magnetic nanoparticles at amorphous magnetic templates with perpendicular anisotropy

We reveal the assembly of magnetite nanoparticles of sizes 5 nm, 15 nm and 25 nm from dilute water-based ferrofluids onto an amorphous magnetic template with out-of-plane anisotropy. From neutron reflectometry experiments we extract density profiles and show that the particles self-assemble into layers at the magnetic surface. The layers are extremely stable against cleaning and rinsing of the substrate. The density of the layers is determined by and increases with the remanent magnetic moment of the particles.

Dynamics and clogging of colloidal monolayers magnetically driven through a heterogeneous landscape

We combine experiments and numerical simulations to investigate the emergence of clogging in a system of interacting paramagnetic colloidal particles driven against a disordered landscape of larger obstacles. We consider a single aperture in a landscape of immobile silica particles which are irreversibly attached to the substrate. We use an external rotating magnetic field to generate a traveling wave potential which drives the magnetic particles against these obstacles at a constant and frequency tunable speed. Experimentally we find that the particles display an intermittent dynamics with power law distributions at high frequencies. We reproduce these results by using numerical simulations and show that clogging in our system arises at large frequency, when the particles desynchronize with the moving landscape. Further, we use the model to explore the hidden role of flexibility in the obstacle displacements and the effect of hydrodynamic interactions between the particles. We also consider numerically the situation of a straight wall and investigate the range of parameters where clogging emerges in such case. Our work provides a soft matter test-bed system to investigate the effect of clogging in driven microscale matter.

Emergent collective colloidal currents generated via exchange dynamics in a broken dimer state

Controlling the flow of matter down to micrometer-scale confinement is of central importance in material and environmental sciences, with direct applications in nano and microfluidics, drug delivery, and biotechnology. Currents of microparticles are usually generated with external field gradients of different nature (e.g., electric, magnetic, optical, thermal, or chemical ones), which are difficult to control over spatially extended regions and samples. Here, we demonstrate a general strategy to assemble and transport polarizable microparticles in fluid media through combination of confinement and magnetic dipolar interactions. We use a homogeneous magnetic modulation to assemble dispersed particles into rotating dimeric state and frustrated binary lattices, and generate collective currents that arise from a novel, field-synchronized particle exchange process. These dynamic states are similar to cyclotron and skipping orbits in electronic and molecular systems, thus paving the way toward understanding and engineering similar processes at different length scales across condensed matter.

Spontaneous propulsion of a water nanodroplet induced by a wettability gradient: a molecular dynamics simulation study

The directional propulsion of liquid droplets at the nanoscale is quite an interesting topic of research in the fields of micro/nano-fluidics, water filtration, precision medicine, and cooling of electronics. In this study, the unidirectional spontaneous transport of a water nanodroplet on a solid surface with a multi-gradient surface (MGS) inspired by natural species is modeled and analyzed using molecular dynamics (MD) simulations. There are three different MGSs considered in this study containing different wedge angles of the hydrophilic region of the solid surface. The MGSs contain two regions: a hydrophilic wedge-shaped region with a constant surface energy parameter equal to 50 meV and a hydrophobic region with a tuned surface energy parameter. The energy parameter of the hydrophobic region is set equal to 1, 5, 10, 20, 30, and 40 meV in order to alter the intensity of the wettability gradient of the two surfaces and its effect on the propulsion of the water nanodroplet is analyzed. Furthermore, three different sizes of water droplets containing 6000, 8000, and 10 000 water molecules are also used in this study and their effect on the transport behavior of the water nanodroplet is also measured. Moreover, two different designs on a solid surface with a continuous wettability gradient are modelled and the impact of solid surface geometry on the transport of the water droplet is calculated by means of mean square displacement (MSD) and average velocity data. In addition, the wedge-shaped surface is found to be more superior to the parallel-shaped surface for the spontaneous propulsion of the water droplet.

Collective Directional Locking of Colloidal Monolayers on a Periodic Substrate

We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred.

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.

Mixed-order phase transition in a colloidal crystal

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid-solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field [Formula: see text] At the transition field [Formula: see text], the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length [Formula: see text] Mean-field critical exponents are predicted, since the upper critical dimension of the transition is [Formula: see text] Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

Resonant reshaping of colloidal clusters on a current carrying wire

Colloids in confined geometries promise a path towards tailored microscopic superstructures. Yet, a major roadblock is posed by kinetically trapped states that prevent the assemblies from reaching their anticipated shapes. We investigate magnetic colloids trapped on a cylindrical surface of a current carrying wire. If kinetic traps could be avoided the wire's surface would act as an ideal mold for colloidal rings and helical fibers. We devise here a way to dynamically shake down the clusters and avoid kinetic traps in their energy landscape. A low frequency magnetic modulation wave around the wire axis effectively eliminates defects from the clusters and stretches them into slender rings and helical filaments. A theoretical model is developed that qualitatively explains the observed resonant reshaping response of clusters.

Micromagnet arrays enable precise manipulation of individual biological analyte-superparamagnetic bead complexes for separation and sensing

In this article, we review lab on a chip (LOC) devices that have been developed for processing magnetically labelled biological analytes, e.g., proteins, nucleic acids, viruses and cells, based on micromagnetic structures and a time-varying magnetic field. We describe the methods that have been developed for fabricating micromagnetic arrays and the bioprocessing operations that have been demonstrated using superparamagnetic (SPM) beads, i.e., programmed transport, switching, separation of specific analytes, and pumping and mixing of fluids in microchannels. The primary advantage of micromagnet devices is that they make it possible to develop systems that control individual SPM beads, enabling high-efficiency separation and analysis. These devices do not require hydrodynamic control and lend themselves to parallel processing of large arrays of SPM beads with modest levels of power consumption. Micromagnet devices are well suited for bioanalytical applications that require high-resolution separation, e.g., detection of rare cell types such as circulating tumour cells, or biosensor applications that require multiple magnetic bioprocessing operations on a single chip.

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.

A Tunable Magnetic Domain Wall Conduit Regulating Nanoparticle Diffusion

We demonstrate a general and robust method to confine on a plane strongly diffusing nanoparticles in water by using size tunable magnetic channels. These virtual conduits are realized with pairs of movable Bloch walls located within an epitaxially grown ferrite garnet film. We show that once inside the magnetic conduit the particles experience an effective local parabolic potential in the transverse direction, while freely diffusing along the conduit. The stiffness of the magnetic potential is determined as a function of field amplitude that varies the width of the magnetic channel. Precise control of the degree of confinement is demonstrated by tuning the applied field. The magnetic conduit is then used to realize single files of nonpassing particles and to induce periodic condensation of an ensemble of particles into parallel stripes in a completely controllable and reversible manner.

Magnetophoretic Conductors and Diodes in a 3D Magnetic Field

We demonstrate magnetophoretic conductor tracks that can transport single magnetized beads and magnetically labeled single cells in a 3-dimensional time-varying magnetic field. The vertical field bias, in addition to the in-plane rotating field, has the advantage of reducing the attraction between particles, which inhibits the formation of particle clusters. However, the inclusion of a vertical field requires the re-design of magnetic track geometries which can transport magnetized objects across the substrate. Following insights from magnetic bubble technology, we found that successful magnetic conductor geometries defined in soft magnetic materials must be composed of alternating sections of positive and negative curvature. In addition to the previously studied magnetic tracks taken from the magnetic bubble literature, a drop-shape pattern was found to be even more adept at transporting small magnetic beads and single cells. Symmetric patterns are shown to achieve bi-directional conduction, whereas asymmetric patterns achieve unidirectional conduction. These designs represent the electrical circuit corollaries of the conductor and diode, respectively. Finally, we demonstrate biological applications in transporting single cells and in the size based separation of magnetic particles.

Transport and selective chaining of bidisperse particles in a travelling wave potential

We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe-patterned magnetic garnet film. The substrate generates a one-dimensional periodic energy landscape above its surface. The application of an elliptically polarized rotating magnetic field causes the landscape to translate, inducing direct transport of paramagnetic particles placed above the film. The ellipticity of the applied field can be used to control and tune the interparticle interactions, from net repulsive to net attractive. When considering particles of two distinct sizes, we find that, depending on their elevation above the surface of the magnetic substrate, the particles feel effectively different potentials, resulting in different mobilities. We exploit this feature to induce selective chaining for certain values of the applied field parameters. In particular, when driving two types of particles, we force only one type to condense into travelling parallel chains. These chains confine the movement of the other non-chaining particles within narrow colloidal channels. This phenomenon is explained by considering the balance of pairwise magnetic forces between the particles and their individual coupling with the travelling landscape.

Enhanced diffusion and anomalous transport of magnetic colloids driven above a two-state flashing potential

We combine experiments and theory to investigate the diffusive and the subdiffusive dynamics of paramagnetic colloids driven above a two-state flashing potential. The magnetic potential was realized by periodically modulating the stray field of a magnetic bubble lattice in a uniaxial ferrite garnet film. At large amplitudes H0 of the driving field, the dynamics of the particle resemble an ordinary random walk with a frequency-dependent diffusion coefficient. However, subdiffusive and oscillatory dynamics at short time scales are observed when decreasing H0. We present a persistent random walk model to elucidate the underlying mechanism of motion, and perform numerical simulations to demonstrate that the anomalous motion originates from the dynamic disorder in the structure of the magnetic lattice, induced by the slightly irregular shape of bubbles.

Regulating wave front dynamics from the strongly discrete to the continuum limit in magnetically driven colloidal systems

The emergence of wave fronts in dissipative driven systems is a fascinating phenomenon which can be found in a broad range of physical and biological disciplines. Here we report the direct experimental observation of discrete fronts propagating along chains of paramagnetic colloidal particles, the latter propelled above a traveling wave potential generated by a structured magnetic substrate. We develop a rigorously reduced theoretical framework and describe the dynamics of the system in terms of a generalized one-dimensional dissipative Frenkel-Kontorova model. The front dynamics is explored in a wide range of field parameters close to and far from depinning, where the discrete and continuum limits apply. We show how symmetry breaking and finite size of chains are used to control the direction of front propagation, a universal feature relevant to different systems and important for real applications.

Geometric Frustration of Colloidal Dimers on a Honeycomb Magnetic Lattice

We study the phase behavior and the collective dynamics of interacting paramagnetic colloids assembled above a honeycomb lattice of triangular shaped magnetic minima. A frustrated colloidal molecular crystal is realized when filling these potential minima with exactly two particles per pinning site. External in-plane rotating fields are used to anneal the system into different phases, including long range ordered stripes, random fully packed loops, labyrinth and disordered states. At a higher amplitude of the annealing field, the dimer lattice displays a two-step melting transition where the initially immobile dimers perform first localized rotations and later break up by exchanging particles across consecutive lattice minima.

Bidirectional particle transport and size selective sorting of Brownian particles in a flashing spatially periodic energy landscape

Precise bidirectional transport and size fractionation of microscopic colloidal particles is demonstratedviasquare-wave modulation of a magnetic landscape.

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.

Micromagnet arrays for on-chip focusing, switching, and separation of superparamagnetic beads and single cells

Nonlinear magnetophoresis (NLM) is a novel approach for on-chip transport and separation of superparamagnetic (SPM) beads, based on a travelling magnetic field wave generated by the combination of a micromagnet array (MMA) and an applied rotating magnetic field. Here, we present two novel MMA designs that allow SPM beads to be focused, sorted, and separated on-chip. Converging MMAs were used to rapidly collect the SPM beads from a large region of the chip and focus them into synchronised lines. We characterise the collection efficiency of the devices and demonstrate that they can facilitate on-chip analysis of populations of SPM beads using a single-point optical detector. The diverging MMAs were used to control the transport of the beads and to separate them based on their size. The separation efficiency of these devices was determined by the orientation of the magnetisation of the micromagnets relative to the external magnetic field and the size of the beads and relative to that of micromagnets. By controlling these parameters and the rotation of the external magnetic field we demonstrated the controlled transport of SPM bead-labelled single MDA-MB-231 cells. The use of these novel MMAs promises to allow magnetically-labelled cells to be efficiently isolated and then manipulated on-chip for analysis with high-resolution chemical and physical techniques.

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.

Functional colloidal micro-sieves assembled and guided above a channel-free magnetic striped film

Colloidal inclusions in lab-on-a-chip devices can be used to perform analytic operations in a non-invasive fashion. We demonstrate here a novel approach to realize fast and reversible micro-sieving operations by manipulating and transporting colloidal chains via mobile domain walls in a magnetic structured substrate. We show that this technique allows one to precisely move and sieve non-magnetic particles, to tweeze microscopic cargos or to mechanically compress highly dense colloidal monolayers.

Fully alternating, triaxial electric or magnetic fields offer new routes to fluid vorticity

Noncontact methods of generating strong fluid vorticity are important to problems involving heat and mass transfer, fluid mixing, active wetting, and droplet transport. Furthermore, because zero or even negative shear viscosities can be induced, vorticity can greatly extend the control range of the smart fluids used in magnetorheological devices. In recent work we have shown that a particular class of ac/ac/dc triaxial fields (symmetry-breaking rational fields) can create strong vorticity in magnetic particle suspensions and have presented a theory of the vorticity that is based on the symmetry of the 2-d Lissajous trajectories of the field and its converse. In this paper we demonstrate that there are three countably infinite sets of fully alternating ac/ac/ac triaxial fields whose frequencies form rational triads that have the symmetry required to drive fluid vorticity. The symmetry of the 3-d Lissajous trajectories of the field and its converse can be derived and from this the direction of the vorticity axis can be predicted, as can the dependence of the sign of the vorticity on the phase relations between the three field components. Experimental results are presented that validate the symmetry theory. These discoveries significantly broaden the class of triaxial fields that can be exploited to produce strong noncontact flow.

Landscape-inversion phase transition in dipolar colloids: tuning the structure and dynamics of 2D crystals

We study the 2D crystalline phases of paramagnetic colloidal particles with dipolar interactions and constrained on a periodic substrate. Combining theory, simulation, and experiments, we demonstrate a new scenario of first-order phase transitions that occurs via a complete inversion of the energy landscape, featuring nonconventional properties that allow for (i) tuning of crystal symmetry, (ii) control of dynamical properties of different crystalline orders via tuning of their relative stability with an external magnetic field, (iii) an equivalent but independent control of the same dynamic properties via temporal modulations of that field, and (iv) nonstandard phase-ordering kinetics involving spontaneous formation of transient metastable domains.

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.

Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential

We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.

Manipulation of micro- and nanostructure motion with magnetic fields

In this review we will focus on how magnetic fields can be used to manipulate the motion of various micro- and nanostructures in solution. We will distinguish between ferromagnetic, paramagnetic and diamagnetic materials. Furthermore, the use of various kinds of magnetic fields, such as homogeneous, inhomogeneous and rotating magnetic fields, is discussed. To date most research has focused on the use of ferro- and paramagnetic materials, but here we also describe the possibilities of magnetic manipulation of diamagnetic materials. Since the vast majority of soft matter is diamagnetic, this paves the way for many new applications to manipulate the motion of micro- and nanostructures.

Unconventional dynamic hysteresis in a periodic assembly of paramagnetic colloids

Dynamic hysteresis phenomena are widespread in physical sciences and describe the complex behavior of systems driven out of equilibrium by a periodic forcing. We use here paramagnetic colloids above a stripe-patterned garnet film as the model system to study dynamic hysteresis, the latter induced when the particles are periodically translated by an oscillating magnetic field. In contrast to the expected behavior for a bistable system, we observe that the area of the hysteresis loop decreases by increasing the driving frequency and reduces to zero for frequencies higher than 5-7s(-1). To explain the experimental results, we develop a simple model based on an overdamped Brownian particle driven by a periodic potential with an oscillating amplitude.

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.

Depinning and collective dynamics of magnetically driven colloidal monolayers

We study the collective dynamics of interacting paramagnetic colloids transported via a magnetic ratchet effect above a modulated periodic potential. Upon increasing the modulation frequency, the particles undergo a series of dynamic transitions, from a continuous smectic flow to a disorder flow, and later enter into a two phase flow regime, ending in a complete pinned state. In the disordered phase, the system organizes into density waves due to traffic jams, as in granular systems, while the two phase flow regime shows strong similarities with plastic flow in vortex matter. Finally, it is shown that induced attractive interactions between the moving colloids lead to enhancement of the particle current due to formation of condensed chains traveling along the modulated landscape.

Antipersistent random walk in a two state flashing magnetic potential

We reveal the subdiffusive dynamics of paramagnetic colloids subjected to a two state flashing potential generated by periodic modulation of a magnetic bubble lattice. The particles perform a random walklike motion with antipersistent nature, showing for certain field parameters a crossover from subdiffusive to an enhanced diffusive behavior. We elucidate the stationary nature (no aging) of the subdiffusive process and stress its similarity with the random walk on a random walk model.

Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

Origin of multiplexing capabilities of multifrequency magnetic ratchets

Through a combination of theory, numerical simulation, and experiment, we investigate the motion of magnetic beads on the surface of a magnetic ratchet driven by multifrequency fields. Here, we focus on the influence of static forcing terms, which were not included in previous models, and we derive analytical models that show why the static forcing terms are responsible for inducing beads of two different sizes to move in opposite directions on the same ratchet potential. We begin our analysis with the simplest possible forcing model, and we show that the main effect of the static forcing terms is to delay the phase of flux reversal. From there, we move onto the full analysis and theoretically derive the phase range for which opposite motion among two different bead types is achieved. Based on these theoretical results, we conduct experimental investigations that explore the effects of bead size and static forcing coefficient on the direction of bead motion, which confirm most of the expected trends. These results shed light both on past experimental work both by ourselves and others, as well as elucidate the more general multiplexing capabilities of ratchets.

Multiplexing superparamagnetic beads driven by multi-frequency ratchets

Here, we explore the single particle dynamics of superparamagnetic beads exposed to multifrequency ratchets. Through a combination of theory, simulation, and experiment, we determine the important tuning parameters that can be used to implement multiplexed separation of polydisperse colloidal mixtures. In particular, our results demonstrate that the ratio of driving frequencies controls the transition between open and closed trajectories that allow particles to be transported across a substrate. We also demonstrate that the phase difference between the two frequencies controls not only the direction of motion but also which particles are allowed to move within a polydisperse mixture. These results represent a fundamentally different approach to colloidal separation than the previous methods which are based on controlling transitions between phase-locked and phase-slipping regimes, and have a higher degree of multiplexing capabilities that can benefit the fields of biological separation and sensing as well as provide crucial insights into general ratchet behavior.

Asymmetric magnetization reversal of stripe-patterned exchange bias layer systems for controlled magnetic particle transport

Domain wall movement assisted transport of particles: exchange-biased samples with designed stripe-domains show strong stray fields and an asymmetric magnetization reversal. Using these characteristics superparamagnetic particles can be trapped and transported directly on the sample over large-scale areas. High particle velocities, small external fields, and automatically reduced particle clustering allow broad applicability of this transport method.

Transport of superparamagnetic beads through a two-dimensional potential energy landscape

The nonlinear dynamic behavior of superparamagnetic beads transported through a two-dimensional potential energy landscape is explored empirically and through numerical simulation. The beads are driven through a periodic array of micromagnets by an external rotating field oriented at an angle θ relative to the magnetization direction of the substrate. The bead's motion was highly sensitive to the angle of the driving field near critical angles and to various system parameters, including bead size, rotation frequency, and substrate pole density. Our results suggest the possibility of using this behavior in a highly discriminative colloidal separation system, in which two different bead types can be tuned to move in orthogonal directions.

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.