Magnetic particle biosensors 1

Chapter Magnetoresistance Chapter MAGNETORESISTANCE 1.1 INTRODUCTION The phenomenon whereby the resistance of a material changes with the application of an external magnetic field is known as magnetoresistance (MR), which was first reported in 1857 by William Thomson [1]. His observation that the resistivity change of a ferromagnetic material depended on the relative orientation of its magnetization direction with respect to the direction of the current flow is now known as the anisotropic magnetoresistive (AMR) effect. It has since then been reported that all metals display the AMR effect, with it being more pronounced in certain semi metals such as Bismuth [2]. Following the discovery of AMR, it was not till more than a hundred years later, together with the advancement of thin film fabrication techniques, that the next type of magnetoresistance was reported – giant magnetoresistance (GMR). This effect was observed in magnetic multilayer structures and could achieve a MR ratio of more than 50% as compared to 2.5% in AMR films [3]. To date the MR effect has also been observed in various other structures such as the spin valve (SV), doped manganate oxides (colossal magnetoresistance - CMR) as well as magnetic tunnel junctions (tunneling magnetoresistance - TMR). Chapter Magnetoresistance All MR structures essentially display the same characteristic of changing its electrical resistance with respect to an external field. Due to the different mechanisms that govern the resistance change, certain MR structures exhibit higher sensitivity than others enabling them to be candidates for low field sensing applications. The most prominent area where MR is used is in the field of magnetic recording, where GMR-spin valve sensors are used as magnetic read head and storage devices [3]. The impact that GMR has on society resulted in Albert Fert and Peter Grunberg winning the joint Nobel Prize in Physics in 2007 for their discovery of giant magnetoresistance [4]. Apart from the field of magnetic recording, the MR effect has also been used in magnetometers, galvanometers, transducers, and more recently in the field of biology for the identification and detection of magnetically tagged bio-molecules [5, 6]. Two main advantages in biology of using magnetic detection methods over those of fluorescent techniques is firstly, only small sample amounts are needed in order to obtain a measurable signal. Secondly, complex microscope systems are also no longer needed [7]. Considering that biological samples are not affected by magnetic fields, the biological entity in question can be attached to magnetic particles for the manipulation and subsequent detection using magnetic sensors [8]. In view of the potential applications of magnetic sensing in the field of biology, we have in this PhD project carried out a systematic study of the response of a GMR sensor to a single magnetic particle. In this chapter, the general theory of the different types of MR will be introduced (AMR, GMR, CMR, MTJ), along with a comparison between each of their advantages and disadvantages with regards to their use as a magnetic field sensor. Chapter 1.2 Magnetoresistance ANISOTROPIC MAGNETORESISTANCE (AMR) The AMR effect is a characteristic of ferromagnetic materials; where at temperatures below that of the Curie temperature (Tc), they display a stable magnetization state. This magnetization state can be varied with the application of an external magnetic field, which results in a change in material resistivity corresponding to the direction of the magnetization state with respect to the direction of current flow [1]. A convenient way to describe AMR is by taking into account the spin orbit coupling and the anisotropic scattering mechanism of s and d electrons. In ferromagnetic materials, the 3d band is split into two different sub-bands representing the spin-up and spin-down orientations of the electron. Due to magnetic ordering, these two sub-bands are not equally filled resulting in the different resistivites of each spin channel which, according to Fermi’s Golden rule, is proportional to the densities of states at the Fermi level for elastic scattering processes [9, 10]. The AMR effect is assumed to result from the influence of the magnetic field and spin-orbit interaction (SOI), causing mixing in the d+ and d- states, which has been demonstrated to be anisotropic with the probability of sd scattering being larger for electrons traveling parallel to the magnetization direction [11]. For a structure displaying the AMR effect, its resistivity can be described by the following equation: ρ = ρ + Δρ m cos θ (1.1) where ρ is the total resistivity of the structure, ρ0 the resistivity when no spin orbit interaction occurs and ρm the component of resistivity (due to SOI) dependent on the angle of magnetization [12] (Fig. 1.2.1). Chapter Magnetoresistance Permalloy thin film y x Hy i Easy Axis x θ M i i Fig. 1.2.1 Schematic of a permalloy thin film showing the relationship between the magnetization direction, current direction and the applied magnetic field (Hy). When the magnetization M is parallel to the current (θ = 0º), the resistivity is at a maximum: ρ = ρ + Δρ m (1.2) whereas when the magnetization M is perpendicular to the current (θ = 90º), the resistivity is at its minimum: ρ = ρ0 (1.3) where there is no contribution to the total resistivity due to the spin orbit interactions. From the above equations it can be seen that a high resistance state occurs when the magnetization and current direction are parallel to each other, while a low resistance state occurs when they are perpendicular, with the maximum change in resistivity given by ∆ρm [1]. Figure 1.2.2 shows a typical MR transfer curve (i.e. resistance change ∆R as a function of applied field H) for an AMR structure. AMR structures were introduced as read head sensors into the magnetic recording industry as they demonstrated better sensitivity, stability and lower noise levels compared to inductive read heads, allowing for a great increase in the achievable areal densities in Chapter Magnetoresistance magnetic storage devices. So effective were AMR read heads that by the early 1990s, ∆R/R (%) inductive read heads had been rendered obsolete [3]. Hy (A/m) Fig. 1.2.2 Typical AMR transfer characteristic. Magnetoresistance is plotted against applied field in the Hy (hard axis) direction. 1.3 GIANT MAGNETORESISTANCE (GMR) Shortly after the discovery of interlayer exchange coupling in ferromagnetic sandwiches [13], the first observation of the giant magnetoresistive effect was reported by Baibich (1986) in magnetic multilayer structures consisting of thin ferromagnetic films separated by a very thin non-magnetic film (spacer) [14]. The electrical resistance of such periodic structures (superlattice) was found to depend on the relative magnetization configuration of the ferromagnetic layers, which could be changed by the application of an appropriate magnetic field. As this structure displayed an MR ratio much larger than that in AMR (more than 150% at T = 4K), the effect was aptly named the giant magnetoresistance (GMR) [13-15]. Chapter Magnetoresistance A way to quantitatively describe the GMR effect is by Mott’s two current model [16, 17]. It is assumed that the probability of the spin flip scattering processes are much smaller than the probability of the scattering processes in which the spin is conserved, hence the electrical conductivity through the metal can be considered as two independent channels, corresponding to the spin up and spin down electrons. Furthermore, in ferromagnetic materials the d bands are exchange split into the spin up and spin down electrons. Due to magnetic ordering, the sub-bands are not equally filled resulting in the difference in the density of states at the Fermi energy for each electron spin type. As the scattering probability is proportional to the density of states at the Fermi energy, this implies that scattering rates are spin dependent leading to different resistivites for each of the spin channels [9, 10]. Thus, an electron transversing through a magnetic multilayer will experience different resistivites depending on the orientation of its spin relative to the local magnetization vectors. Figure 1.3.1 shows the scattering processes occurring in a multilayer with its corresponding resistor network model [16]. down spin up spin (a) (c) down spin up spin (b) R↓ R↓ R↑ R↑ (d) R↓ R↑ R↑ R↓ Chapter Magnetoresistance Fig. 1.3.1 Schematic of conduction in a GMR multilayer. (a) Magnetic layers are in a parallel alignment, and only spin down electrons scatter strongly resulting in a low resistance state. (b) Magnetic layers are in antiparallel alignment. Both spin states scatter strongly resulting in a high resistance state. (c) Corresponding two-current series resistor model for (a). (d) Corresponding two-current series resistor model for (b) [18]. Although the model is able to describe the observation of a low and high resistance state with respect to the parallel and antiparallel alignment of the magnetic layers, the model is however unable to sufficiently explain the underlying mechanisms giving rise to the GMR effect. To theoretically model GMR, many different approaches have been taken with the first ones mainly based on the free electron model. These initial models have all turned out more qualitative than quantitative as they not consider the complex spin polarized electronic structure of the magnetic multilayers [19]. The most widely accepted model with regards to electronic transport is that based on the semiclassical Boltzman theory [20], although a problem is that it does not account for quantum size effects resulting in the model breaking down when considering very thin magnetic multilayers. A more comprehensive model is the quantum mechanical theory of transport which considers the spin-dependent bulk scattering and transmission at the interfaces for the analysis of the conductivity and MR in the ferromagnetic layers [21, 22]. With the current progress in electronic transport and band structure theory, it is now possible to develop realistic multi band models and perform first principles calculations of GMR, to obtain a quantitative description of the GMR effect [19]. In order to observe a GMR effect, two criteria have to be satisfied. The first is the thickness of the films must be less than the mean free path of an electron in a multilayer Chapter Magnetoresistance array. The second is that there has to be a way of changing the relative magnetization directions of the magnetic layers [18]. The first criterion can easily be satisfied by thin film fabrication techniques, while the second can be achieved by either using different materials of different coercivities or via the phenomenon of interlayer exchange coupling between adjacent magnetic layers separated by a spacer. Studies have shown that the GMR effect exists only for selected spacer thicknesses, with the MR ratio oscillating with a certain period of spacer thickness [23]. The period of oscillation not only strongly depends on the material of the spacer and the crystal structure, but also on the growth direction of both the ferromagnetic and spacer layers [24]. For device applications, the most important feature in GMR sensors is the dependence of the signal resistance change ∆R/R on the applied field strength (or flux density), with ∆R/R given by the difference in the resistance of the sensor in its antiparallel (Rap) and parallel (Rp) state divided by that of its parallel state. ΔR Rap − R p = R Rp (1.4) The field dependence of ∆R/R for GMR structures with antiferromagnetic exchange coupling takes on a near parabolic shape [14]. From experimental results, it was found that the resistance of the multilayer magnetic structures varies as cos(θ1 − θ ) , with (θ1-θ2) the relative angle between magnetization orientations [25]. The resistance of the multilayer can be calculated as: R( H ) = R p + ( Rap − R p ) [1 − cos(θ − θ )] (1.5) Although the MR ratio in GMR magnetic stacks is much greater than in AMR structure, GMR stacks were never considered for the use in magnetic recording devices. The main Chapter Magnetoresistance reasons were firstly, GMR stacks had lower sensitivity to magnetic fields as compared to AMR. Secondly, the applied fields (few kOe) required to overcome the antiferromagnetic coupling in the layers was too large for practical use in devices. Finally, the biasing field required to obtain a linear response in GMR would greatly complicate sensor head design [26]. 1.4 SPIN VALVE (SV) The spin valve was discovered in 1990 and can be considered as a modified version of a GMR stack, with a basic SV structure consisting of at least layers: buffer, ferromagnetic (unpinned) layer (F1), nonmagnetic (spacer) layer (NM), ferromagnetic (exchange coupled) layer (F2), antiferromagnetic biasing layer (AF) and capping layer. (Fig. 1.4.1) The two ferromagnetic layers (F1 and F2) are separated by a non-magnetic spacer (NM), with the magnetization of F2 pinned via exchange anisotropy to the adjacent antiferromagnetic layer AF. The other unpinned ferromagnetic layer F1 is allowed to rotate freely, with the relative magnetization orientations between the two ferromagnetic layers giving rise to the MR effect. The buffer layer on the other hand is mainly used to improve the texture of the subsequent layers of the sensor, while the capping layer is crucial for the protection of the structure. Tantalum is often used for both the buffer and capping layers [27, 28]. The main structure types for a SV sensor are the bottom SV, top SV and the symmetric SV, with their names basically referring to the position of the ferromagnetic (pinning) layer with respect to the free (unpinned) layer (Fig. 1.4.1). Chapter Magnetoresistance (a) (b) (c) Cap layer AF F (pinned) Cap layer Cap layer NM F (free) AF F (free) NM F (pinned) NM F (pinned) Substrate F (pinned) NM AF F (free) AF Buffer layer Buffer layer Buffer layer Substrate Substrate Fig. 1.4.1 The different layout of spin valve structures. (a) Bottom spin valve. (b) Top spin valve. (c) Symmetrical spin valve. The main characteristic of a SV structure is that it usually has at least hysteresis loops. The first is often centered in the vicinity of Oe which corresponds to the switching of the free layer, while the other occurs at a much larger field corresponding to the reversal of the magnetization of the exchange coupled magnetic layers. Due to the weak coupling between the free layer and the antiferromagnetically pinned layer at low fields, the free layer is sensitive in low fields and exhibits a sharp change in MR change, making it an ideal candidate for the use in MR heads. Compared to multilayer GMR, the spin valve is more complicated to analyze as both ferromagnetic layers work in different ways. In the simplified version of modeling for the SV structure, the component representing the coupling energy is taken as the magnetostatic Neel coupling energy, instead of the Ruderman-Kittel-Kasuya-Yosida (RKKY) like exchange energy found in multilayered MR [29]. This simple approach is however not particularly accurate as the SV structures are more complex, with the pinned and free layers often having different thicknesses. More rigorous treatments have been 10 Chapter Magnetoresistance undertaken by many groups to exactly describe the transfer characteristics of the SV sensor [30, 31], with Parker and co-workers developing an analytical model for accurate study of switching conditions in SVs for memory applications. Their approach of considering the energy densities of free and pinned layers separately was able to analyze the switching characteristics of SV sensors under different biasing field conditions [32]. With the ever increasing demand for areal densities in the 1990s, the recording industry turned towards GMR-SV read heads for high sensitivity and low field switching properties. The first ever GMR-SV head was introduced in 1998 and as GMR-SV heads are able to produce much larger signals than that of AMR, the number of sensors required per device decreased, resulting in lower cost and higher reliability. These advantages eventually lead to the total replacement of AMR heads in the field of magnetic recording [20]. 1.5 CPP STRUCTURES In all MR structures previously mentioned, the current flow is in the plane of the magnetic stack (current in plane – CIP). Another form of GMR structure exists (Fig. 1.5.1), where the current is made to pass perpendicular to the plane of the film (CPP), where all electrons in the current are made to undergo scattering at each interface resulting in a larger MR effect as compared to CIP methods. Experimental data for CPP GMR structures have produced MR ratios as large as 170% at 4.2K [21]. 11 Chapter Magnetoresistance (a) (b) I I CIP Multilayer MR stack Leads CPP Multilayer MR stack Fig. 1.5.1 Schematic showing the current flow geometry through GMR structures. (a) Current in plane (CIP). (b) Current perpendicular to plane (CPP). Although CPP structures are able to avoid complications such as shunting of the capping, biasing and buffer layers, the resistance of a CPP structure is extremely small, in the order of nano ohms for a 1mm2 sample at 4.2K [33]. A possible way to overcome this is to use superconducting contacts, but such measurements can only be done at low temperatures [21]. Although the small resistances make it impractical for the use of CPP GMR structures in realistic devices, it has enabled theorists to better understand the scattering mechanisms that occur in bulk and at the interfaces of the magnetic structures [34]. 1.6 COLOSSAL MAGNETORESISTANCE (CMR) Colossal MR (CMR) discovered in 1993 by von Helmolt et.al., can be observed in doped manganate oxides with perovskite-type structures, which display enormous MR at temperatures about the Curie point Tc (transition temperature) [35, 36]. MR ratios as high 12 Chapter Magnetoresistance as 108 % have been reported in La-Y-Ca-Mn-O type thin films, a huge increase when compared to multilayer GMR. In doped oxides of lanthanum manganite LaMnO3, 2+ valence ions such as Ba, Ca, Cd, Sr, Pb are believed to replace the La3+ ions resulting in a change in the material structure. This gives rise to the material having both ferromagnetism and metallic behavior, with a marked decrease in resistance. Though many ideas have been proposed, the true mechanism behind CMR is still unknown. One of the suggested models is that of the double exchange interaction, with the mixing of Mn3+/Mn4+ valence creating mobile charge carriers which increase conductivity. Competing interactions between ferromagnetic double exchange and antiferromagnetic superexchange at T < Tc lead to a perturbed spin lattice, which can in turn lead to partial localization of magnetic impurities which constitute magnetic polarons. The conduction of these polarons coupled with the increase of ferromagnetic ordering of the lattice at T ~ Tc in an external applied field leads to the CMR effect [37, 38]. With double exchange interactions found to be insufficient in explaining CMR [39], subsequent models have taken into account the possibilities of electron-lattice coupling resulting in conduction via polarons [40], spindependent electronic transport across local magnetic clusters [41], the formation of immobile polarons leading to current density collapse [42] as well as the effect of intergrain tunneling in the attempt to better explain CMR [43]. The major disadvantages of using CMR structures for device applications is that most transition temperatures are much lower than room temperature, and high fields have to be applied in order to observe the CMR effect. Although certain CMR structures have 13 Chapter Magnetoresistance been observed to have transition temperatures up to 380K, the requirement for a large field still persists [44]. 1.7 TUNNELING MAGNETORESISTANCE (TMR) Tunneling magnetoresistance is a phenomenon that can be observed when current flows through a magnetic tunnel junction (MTJ), which in its simplest form comprises two ferromagnetic layers separated by an insulator thin film. Classical physics states that it is not possible for a current flow though such a structure, but exceptions occur in a MTJ when the insulator film is reduced to the nanometric scale (1-2 nm), leading to a tunneling effect with the aid of an external magnetic field. Tunneling conductance was first described in 1975 by Julliere to be dependent on the angle θ between two magnetic layers according to the equation: G = G0 (1 + ε cos θ ) (1.6) where G is the tunneling conductance, while G0 and ε are constants. Miyazaki in 1995 was able to achieve a very high magnetoresistance (30% at 4.2K) in an MTJ of structure Fe/Al2O3/Fe, at the same time experimentally determining the values of G0 and ε to be 96 Ω-1 and 0.09 respectively [45, 46]. Since then the achievable MTJ MR ratio has been steadily increasing with current MTJ sensors featuring a MR range of more than 200% [47, 48]. The tunneling current through the insulator in a MTJ is dependent on the density of states (DOS) of the adjacent ferromagnetic layers. When both ferromagnetic layers are in a parallel alignment, a matching of the DOS occurs, leading to a larger tunneling probability where resistance is at a minimum. In an antiparallel alignment, the opposite 14 Chapter Magnetoresistance happens and resistance is at a maximum (Fig. 1.7.1). A MTJ structure is often fabricated by deposition on the ferromagnetic layer, a ~1-2 nm thick film of Al or Mg. This film is then oxidized to obtain the Al2O3 or MgO insulating layer (tunnel barrier), after which the other ferromagnetic layer is deposited. The two ferromagnetic layers have to be uncoupled in order to obtain switching between them, which can be achieved by either using ferromagnetic layers of different coercivites, or by means of exchange biasing just one ferromagnetic layer. The uncoupled magnetic layers results in the MTJ having a very small switching field range and hence high sensitivity to small magnetic fields. (a) V Low resistance high current state (b) FM barrier FM FM barrier FM V High resistance low current state Fig. 1.7.1 Schematic of a magnetic tunnel junction. Ferromagnetic layers are biased with a fixed voltage. (a) Ferromagnetic layers are aligned in parallel, resulting in lower resistance and higher current flow. (b) Ferromagnetic layers are aligned antiparallel resulting in higher resistance and low current flow. As MTJs demonstrate very sharp resistance changes for sensor structures of small area, it makes them ideal candidates for use in non-volatile magnetic storage devices (MRAM) as well as magnetic field sensors [49]. With respect to use in biology, the advantage of MTJs over spin valves is that the MTJ can display MR ratios more than five 15 Chapter Magnetoresistance times higher than SV, as well as obtain resistances that are tunable with the thickness of the spacer layer leading to higher output voltages. These properties make MTJ more sensitive than SV sensors. 1.8 CONCLUSION We have briefly introduced the main ideas and mechanisms behind the various types of magnetoresistive sensors. Table 1.8.1 shows a comparison between the different types of MR structures, with tunneling MR structures displaying the highest sensitivity, followed by that of the spin valve. GMR structure MR [%] Saturation Field [Oe] Sensitivity MR%/Oe AMR 2.2 – 20 0.4 Exchange Coupled multilayer 10 - 80 100 - 2000 0.1 Spin Valve - 10 – 50 1.0 Colossal 100 1000 0.1 Tunneling 10 - 25 – 25 2.0 Table 1.8.1: Comparison between various types of GMR structures [50]. In the past decade, apart from applications in the recording industry, there has been an increased interest in GMR for the development of magnetoresistive biochips and biosensors [51]. A GMR sensor was first introduced in 1998 for the detection of magnetic microbeads, by means of a Bead Array Counter (BARC) where GMR multilayers were used as a sensor structure to detect the presence of magnetic micro particles [5]. In view 16 Chapter Magnetoresistance of their potential applications in biological tagging and identification, recent reports have also seen groups turn to using the more sensitive structures such as spin valve and magnetic tunnel junctions for the sensing and detection of single magnetic particles [6, 7]. The main application of magnetic sensing for use in biology is the detection of single magnetic ‘tagging’ particles. In order to create a reliable detection system, one has to first understand the sensing mechanisms which occur when a bead is in the vicinity of a sensor. In view of this, we have in this PhD project used GMR sensing to investigate the response of the sensor to single ferromagnetic and superparamagnetic particles, which will be described in the chapters that follow. 17 Chapter Magnetoresistance REFERENCES [1] W. Thomson, Proc. Roy. Soc. 8, 546 [2] J. P. Jan, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1957) [3] M. 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