**3. Classification of magnetic materials, magnetization, and characterization of micro-objects**

One of the greatest advantages of magnetic actuation lies in the possibility to transfer powering and actuation in a wireless fashion. Remote magnetic actuation relies on the coupling, namely the creation and maintenance of a magnetic link, between two objects showing magnetic properties. Typically, an external control platform, based on permanent magnets, electromag‐ nets, or a combination of them, and a micro-object, that could be a magnetic bead, a magnetized cell, or a microrobot, constitute the key elements. Materials behavior in response to a magnetic field depends on the material atomic organization. In particular, the spatial organization of the material microscopic domains and the possible changes in this organization produced by the presence of an external magnetic field determine the material response. Indeed, the magnetization induced in a material is proportional to the ability of these domains to align or to form cooperative structures when a magnetic field is applied. This ability can be described by means of the magnetic susceptibility χ, a non-dimensional parameter defined by the ratio of the magnetization M induced in the material and the applied magnetic field H.

$$\mathbf{M} = \mathbf{\tilde{x}} \mathbf{H} \tag{8}$$

Depending on this parameter, it is possible to classify magnetic materials in three main categories: diamagnetic, paramagnetic, and ferromagnetic (**Figure 2**) [7]. Diamagnetic mate‐ rials, such as bismuth or brass, have no net atomic or molecular magnetic moment and do not retain magnetization when the external magnetic field is removed. When these materials are subjected to an applied field, atomic currents generate and produce a bulk magnetization antiparallel to the field H, thus resulting in negative and negligible susceptibility χ levels (~10−6 to ~10−3). Paramagnetic materials have a net magnetic moment at the atomic level which shows a random orientation when no magnetic field is acting. When the magnetic field H is applied, the moment tends to align with it. The susceptibility of such materials is in the range 10−6–10−1. Ferromagnetic materials, such as iron, nickel, and cobalt, on the other hand, have a net magnetic moment at the atomic level, but unlike paramagnetic materials, they show a strong coupling between neighboring moments as they align all in the same direction and parallel to each other to produce a larger magnetization state. This coupling gives rise to a spontaneous alignment of the moments over macroscopic regions, called domains, which undergo further alignment when the material is subjected to an applied field. Ferromagnetic materials can be permanently magnetized since they are able to retain residual magnetization after the removal of the applied magnetic field. They can be furtherly classified as soft or hard materials: The first ones are featured by a high permeability and a low coercivity Hc (the coercivity is defined as the magnetic field intensity needed to reduce the magnetization of a ferromagnetic material from its complete saturation to zero). This makes them easy to be magnetized and demagnetized. The second ones have a relatively low permeability and high coercivity which make them more suitable for the fabrication of permanent magnets [8, 9].

**Figure 2.** Schematic representation of diamagnetic, paramagnetic, and ferromagnetic materials microscopic structures at rest and in the presence of a magnetic field H.

To enable magnetic field-mediated task execution in a LOC, it is necessary to provide the objects to be manipulated with magnetic properties. In some cases, magnetic manipulation relies on the intrinsic magnetic properties of the sample, as in the case of red blood cells [10]. More frequently, labeling and internalization of magnetic material, or fabrication of magnetic microcarriers, are required. To this aim, magnetic micro- and nanoparticles have gained growing attention in LOC systems and in microrobotics in general. Usually, polymeric or silica microparticles with embedded iron oxide nanoparticles are used. Simple iron oxide nanopar‐ ticles are also used, mainly magnetite (Fe3O4) and maghemite (γ-Fe2O3) ones. Due to the reduced dimensions of the magnetic core (diameter <1 μm), these particles usually consist of single magnetic domains showing a superparamagnetic behavior. The main advantages of using magnetic particles are that they have a large surface-to-volume ratio; they can be conveniently biofunctionalized, thus favoring their coating or enabling labeling molecules. To provide a micro-object with magnetic properties, two main strategies can be employed: (1) labeling with magnetic particles or (2) particle internalization. In both cases, sample incubation in the presence of a relatively high concentration of particles is required.

rials, such as bismuth or brass, have no net atomic or molecular magnetic moment and do not retain magnetization when the external magnetic field is removed. When these materials are subjected to an applied field, atomic currents generate and produce a bulk magnetization antiparallel to the field H, thus resulting in negative and negligible susceptibility χ levels (~10−6 to ~10−3). Paramagnetic materials have a net magnetic moment at the atomic level which shows a random orientation when no magnetic field is acting. When the magnetic field H is applied, the moment tends to align with it. The susceptibility of such materials is in the range 10−6–10−1. Ferromagnetic materials, such as iron, nickel, and cobalt, on the other hand, have a net magnetic moment at the atomic level, but unlike paramagnetic materials, they show a strong coupling between neighboring moments as they align all in the same direction and parallel to each other to produce a larger magnetization state. This coupling gives rise to a spontaneous alignment of the moments over macroscopic regions, called domains, which undergo further alignment when the material is subjected to an applied field. Ferromagnetic materials can be permanently magnetized since they are able to retain residual magnetization after the removal of the applied magnetic field. They can be furtherly classified as soft or hard materials: The first ones are featured by a high permeability and a low coercivity Hc (the coercivity is defined as the magnetic field intensity needed to reduce the magnetization of a ferromagnetic material from its complete saturation to zero). This makes them easy to be magnetized and demagnetized. The second ones have a relatively low permeability and high coercivity which make them more suitable for the fabrication of permanent magnets [8, 9].

**Figure 2.** Schematic representation of diamagnetic, paramagnetic, and ferromagnetic materials microscopic structures

To enable magnetic field-mediated task execution in a LOC, it is necessary to provide the objects to be manipulated with magnetic properties. In some cases, magnetic manipulation relies on the intrinsic magnetic properties of the sample, as in the case of red blood cells [10]. More frequently, labeling and internalization of magnetic material, or fabrication of magnetic microcarriers, are required. To this aim, magnetic micro- and nanoparticles have gained growing attention in LOC systems and in microrobotics in general. Usually, polymeric or silica microparticles with embedded iron oxide nanoparticles are used. Simple iron oxide nanopar‐ ticles are also used, mainly magnetite (Fe3O4) and maghemite (γ-Fe2O3) ones. Due to the reduced dimensions of the magnetic core (diameter <1 μm), these particles usually consist of single magnetic domains showing a superparamagnetic behavior. The main advantages of using magnetic particles are that they have a large surface-to-volume ratio; they can be

at rest and in the presence of a magnetic field H.

40 Lab-on-a-Chip Fabrication and Application

Sample magnetic labeling relies on the possibility to properly functionalize particle surface to enable the binding with functional groups exposed on sample surface. This applies, for example, for cell labeling: functional micro- or nanoparticles are conjugated with antibodies corresponding to specific cell surface antigens [11].

In the case of internalization, the magnetic particles are included in the sample structure itself by embedding the magnetic material during the micro-object fabrication process or exploiting transfection and magnetofection techniques in the case of biological samples. In this case, superparamagnetic iron oxide nanoparticles (SPIONs), usually properly modified to promote internalization, for example, through polystyrene or dextran coatings, or exploiting other transfection agents, such as peptides or antibodies [12], are widely employed.

An alternative to sample magnetization through labeling or internalization is the exploitation of magnetic carriers or manipulation systems that avoid a direct contact between sample and magnetic material.

In this case, magnetic properties can be imparted to a carrier, by simply including magnetic materials in its structure. To this aim, not only SPIONs have been employed: the integration of ferromagnetic materials, for example, in the form of powder, has been investigated in applications in which high magnetic responsivity and residual magnetization were required. Ferromagnetic materials, such as Ni, have been employed also in the form of surface coating, obtained through sputtering or evaporation techniques, with the aim to provide micro-objects showing complex geometries, fabricated, for example, through 2D or 3D lithography techni‐ ques, with magnetic properties [13].

Once identified the methods allowing to magnetize the samples to be manipulated, it can be useful to briefly describe some techniques allowing to properly characterize a magnetic microobject. When designing the hardware for a magnetic manipulation or separation platform, it is useful (in some cases even mandatory) to precisely know the magnetic properties of the beads or structures to be manipulated. Particularly, interesting parameters, most commonly evaluated, are the magnetic susceptibility χ, the saturation magnetization Ms and the coercivity field Hc. Considering that small entities usually show weak magnetic properties, traditional technologies employed at the macroscale, such as Hall sensor-based probes, do not result suitable for their characterization. Microstructured magnetic materials can be properly characterized through both inductive- and force-based techniques. Inductive methods, such as the vibrating sample magnetometry (VSM) and the superconducting quantum interference device (SQUID) magnetometry, are usually employed for magnetic characterization at the micro-/nanoscale. In both cases, the measurement can be carried out at variable temperature and by applying different magnetic fields, thus allowing to obtain the typical material magnetization curves in a specific range of temperatures. In VSM, a magnetic sample is vibrated within a uniform magnetic field: sample vibration induces a current in dedicated sensing coils; by measuring the resulting voltage induced into the coil, it is possible to obtain sample magnetic moment and to magnetically characterize it. The sensitivity of this kind of technique can reach 10−6 emu. When the samples are really diluted or show really weak magnetic properties, thus claiming for higher sensitivities, SQUID-based magnetometry can be a suitable solution, enabling to reach sensitivities up to 10−8–10−12 emu. The magnetic properties of the material are measured by detecting quantum mechanical effects in conjunc‐ tion with superconducting detection coils. In both VSM and SQUID magnetometry, however, the duration of a single measurement is in the order of some hours. This obviously represents a strong limitation for all cases in which the characterization of a large number of samples is needed. On the other hand, force-based methods, such as Gouy and Faraday balances, rely on the change in weight of a magnetic material when it is subjected to a uniform magnetic field. Commercial systems based on the Faraday method, such as the alternating gradient magne‐ tometer (AGM), provide sensitivities in the 10−8–10−9 emu range with really fast measurement procedures [14, 15].
