Magnetic particle biosensors 2

Chapter GMR Sensors Chapter GMR SENSORS 2.1 INTRODUCTION The discovery of the giant magnetoresistance (GMR) effect in the mid 1980s has opened up many areas of research in science and technology [1]. Although the most prominent role of the GMR is that in magnetic recording, new fields utilizing this technology such as magnetoelectronics and biological sensing have emerged in the past ten years [2, 3]. Magnetic label-based bioassays have become an area of increasing interest for the ability to screen for potential harmful diseases and viruses. Early schemes utilizing magnetic particle bioassays employed the use of bulk detection techniques such as AC susceptometry or SQUID magnetometry. Although such methods were of high sensitivity, they required expensive cryogenics and related instrumentation. With regards to ultimately achieving a portable, low cost, chip-based magnetic bioassay device, new detection methods had to be introduced [4]. GMR magnetic sensing for detecting and characterizing magnetic micro beads was first introduced in 1998 by means of a Bead Array Counter (BARC). In this sensor, the surfaces of 0.1 µm thick multilayer GMR strips (the sensors) were functionalized for the specific binding of suitably labeled magnetic particles. Absorption/binding of a particle on a GMR strip could be detected by a change in resistance (in practice, a change 22 Chapter GMR Sensors in voltage is measured) [3]. With the potential of being a highly sensitive biosensor, many groups have adopted this technique to create sensors using spin valves [5] or magnetic tunnel junctions [6] as the magnetic sensor element. These methods have lead to magnetic particle sensors with the ability of detecting single magnetic particles right down to the nanoscale [7]. For further biosensor development, one has to understand the sensing mechanism which occurs when a single magnetic particle is in the vicinity of a GMR sensor. Hence in this PHD project we have used the method of magnetic sensing to undertake systematic studies on the response of a magnetoresistive sensor to a single ferromagnetic or paramagnetic particle. This Chapter will discuss all the aspects of our GMR sensor, and the magnetic particles that have been used. 2.2 GIANT MAGNETORESISTIVE SENSOR To achieve a device able to detect single magnetic particles, the most important aspect is the sensor itself. The basic design always followed is shown in figure 2.2.1. Initially we made simple GMR devices but these proved unsuitable for single particle sensitivity, as described below. Satisfactory devices for single particle were later achieved by making spin valve sensors (see Section 2.3). 23 Chapter GMR Sensors Cr/Au electrode wire Active sensor area MR material Magnetic particle interaction MR material Connects to external meters Plan View Cr/Au electrode wire substrate Section View Fig. 2.2.1 The basic sensor concept used for both GMR and SV designs. For the GMR designs we used a Denton Discovery 18 machine to deposit Co/Cu and NiFe/Cu GMR multilayer structures of various lateral dimensions on both microscopic glass slides and silicon wafers. The highest MR ratio we could obtain was 2.9 % from a GMR structure of [Co(5nm)/Cu(2nm)]7 (active area 1.2 cm x mm) deposited on glass. To make structures of sizes more comparable to that of a single magnetic particle, GMR strips of dimensions 30 x 200 µm2 with structure [Co(3nm)/Cu(2.2nm)]7 were fabricated on a chemically cleaned microscopic glass slide. Electrical contacts were patterned and deposited to join to the GMR strip with a final active sensor area of 30 x 40 µm2. The glass slide was diced into individual chips, each with sensors, suitable for single or differential resistance sensing (Fig. 2.2.2). 24 Chapter (a) GMR Sensors (b) Cr/Au contacts x y [Co(3)/Cu(2.2)]7 Fig. 2.2.2 (a) Sensor chip with GMR multilayer structure of [Co(3)/Cu(2.2)]7 fabricated on a microscopic glass slide. (b) Microscope image of the 30 x 40 µm2 sensor structure connected to Cr/Au contact pads. To obtain the transfer characteristic of the GMR sensor, a chip was mounted onto a small Veroboard connected to external measurement circuits in a two point contact configuration (Fig. 2.2.3) using silver conductive adhesive (12683-15, EMS). A constant current of 1mA was supplied by a Keithley 2400 SourceMeter and a dipole electromagnet (Electronic Measurements Inc.) used to sweep a field along the y-axis of the sensor. The corresponding voltage change was measured by a Nanovoltmeter (Keithley 2182). The transfer characteristic of a 30 x 40 µm2 GMR sensor is shown in Figure 2.2.4. 25 Chapter GMR Sensors (a) Variable magnetic field (b) Active area of sensor Constant current source Voltage measurement Dipole magnet Power supply Fig. 2.2.3 (a) Experimental layout to measure the resistance vs. field transfer function. This was used for both GMR and SV designs. (b) Dipole magnet used in measuring the GMR response. 2.25 2.00 1.75 ∆R/R (%) 1.50 1.25 1.00 0.75 0.50 0.25 0.00 -0.25 -3000 -2000 -1000 1000 2000 3000 H (Oe) Fig. 2.2.4 Transfer characteristic of a 30 x 40 µm2 GMR sensor of structure [Co(3)/Cu(2.2)]7 fabricated on a microscopic glass slide. External field was swept along the y axis direction. A maximum MR ratio of 2% was obtained. The two peaks observed were due magnetic hysteresis. 26 Chapter GMR Sensors A major problem faced was the low MR ratio of these GMR structures. Figure 2.2.4 shows a change of only % for a typical 30 x 40 µm2 structure. This is much smaller than the MR ratios reported in literature (> 30 %) [8, 9]. We believe this was due to two main reasons. Firstly, the manual control of the sputtering system can give rise to errors in the thicknesses of the multilayers. Secondly, the number of layers in our GMR structure is less than those reported in the literature. Both of these factors can contribute to the low MR ratio [10]. We also faced adhesion problems between the GMR and (Cr/Au) contacts, and degradation of the GMR sensor material with time. Due to the limitations of the sputtering system (only targets), we were unable to fabricate in-house more complicated structures like the spin valve. Hence we collaborated with the Data Storage Institute, Singapore [11] and obtained high quality material that allowed us to fabricate GMR spin valves. These SV structures were used for all the results generated in Chapters 3, and 5. 2.3 SPIN VALVE SENSOR (a) Fabrication of 12 x µm2 active area structures (for AFM experiments) Spin Valve (SV) structures were fabricated from a inch wafer with the thin film multilayer material Ta3/NiFe2/IrMn8/CoFe2/Ru0.8/CoFe3/Cu2.3/CoFe2.6/Cu1/Ta5 (with thickness shown in nanometer) deposited using an ultrahigh vacuum system (ULVAC Japan). The wafer was then magnetically annealed at 235ºC for hours at a field of ~1 T in a commercial magnetic vacuum annealing oven at a pressure of 1.0 x 10-6 Torr, giving a bulk resistance of ~9 %, with sheet resistance of 18.3 Ω/□ [12]. Using standard photolithography techniques, sensors were fabricated from the wafer by wet 27 Chapter GMR Sensors etching with HF + HNO3 (1:1) to form isolated lines of SV material of width 12 µm [13], with four pairs of sensors fabricated on each chip to allow for single or differential measurement. Electrical contacts were deposited by DC magnetron sputtering (Denton Discovery 18) of Cr followed by Au. The Cr/Au contacts were deposited over the SV lines to effectively short the SV, except for a small gap which defined the active area and resistance of the sensor. The wafer was finally diced into chips of mm x 5mm. (Fig. 2.3.1) The difficulties faced with this method were firstly, the edges of the SV sensor were not well defined due to the isotropic nature of wet etching (see Fig. 2.3.1(b)). Secondly, adhesion problems between the Cr/Au contacts and the SV sensor surface still persisted, causing certain areas of the contacts to peel off during the lift off process. (a) (b) Cr/Au contact SV active area x y Contact pads Fig. 2.3.1 (a) Layout of a mm x mm sensor chip, with pairs of SV sensors. (b) Optical micrograph of a single 12 x µm2 SV sensor. Using the methodology described in section 2.2, the transfer characteristics of a typical 12 x µm2 sensor is shown in figure 2.3.2. The SV structure showed a resistance of R ~ 66 Ω, with a MR ratio of 3.7%. Compared to the GMR multilayer structure, the SV sensor demonstrated a higher MR ratio, even for a smaller structure size. The 12 x 28 Chapter GMR Sensors µm2 devices were used in the AFM experiments (Chapter 3) for the detection of a single ferromagnetic particle of diameter µm. ∆R/R (%) 17 Oe -200 -100 100 200 H Field (G) Fig. 2.3.2 Transfer characteristic of a SV sensor (12 x µm2 active area) to an external field applied along the y-axis direction. Magnetoresistance = 3.7 %. In AFM experiments the SV were biased at a field of 17 Oe so the SV operated linearly and at maximum sensitivity. (b) Fabrication of x µm2 active area structures (for optical tweezers experiments) To detect single paramagnetic particles of µm in diameter, we required much smaller SV sensor structures, of dimensions comparable to the size of the particle [14]. This could no longer be fabricated by wet etching. In this case, in addition to the fabrication of the SV wafer described in 2.3(a), we added standard electron-beam lithography techniques (JEOL-5000 LS) to define SV strips of dimension ~2 x 24 µm2 and then ion milled (Veeco, RF-350) ~50 nm of all surrounding material. This created 29 Chapter GMR Sensors strips of ~ x 24 µm2 (Fig. 2.3.3(a)). This structure was then further ion milled ~17 nm deep at the two ends of the SV strips to remove the pinning layer. Rectangular contact pads of Ta/Au of thickness 100 nm were sputtered over the ends of the SV strips, and subsequently larger Cu/Au contact pads of thickness ~ 100 nm were then patterned and sputtered (Denton Discovery-18) over the bridging pads. This method enabled us to overcome the problem of contact adhesion to the sensor structure, which had previously resulted in many faulty SV structures. A 30 nm Al2O3 layer was finally put down over the entire wafer using pulsed sputter deposition, except for the contact pads, to prevent short circuiting when working in a liquid medium. The wafer was diced into individual chips (9.5 x 10 mm2), each with sensors (Fig 2.3.3(f)). (b) 24 µm (a) (c) (d) (e) (f) µm Contact pads µm Fig. 2.3.3 Schematic of the SV fabrication process. A SV wire (a) was ion-milled to obtain a x 24 µm2 structure (indicated in grey), (b). The two edges were ion milled to remove the pinning layer (~ 17 nm) of the SV. (shown as dotted region) leaving intact a x µm2 structure. (c), Bridging contacts of Ta/Au (indicated in yellow) were deposited over the milled regions. (d), Regular Cr/Au contacts were deposited over the bridging contacts. (e) Optical micrograph of a completed SV structure. (f) Layout of a completed chip with SV sensors. Electrical connections are made to contact pads. 30 Chapter GMR Sensors Figure 2.3.4 shows the transfer characteristics of a typical x µm2 spin valve sensor. The maximum MR ratio is 4.2%. This structure was used for the detection of a single superparamagnetic particle of diameter µm, which will be described in detail in Chapter 4. ∆R/R (%) -200 -100 100 200 H Field (G) Fig. 2.3.4 Transfer function of a SV sensor (2 x µm2 active area) to an external field applied along the y-axis direction. Magnetoresistance = 4.2 %. (c) Spin valve sensor response Spin valve sensors are most sensitive to planar fields along the y-axis direction (see Fig. 2.3.5), while highly insensitive to fields in the z-axis direction due to the strong magnetostatic energy which results from the in-plane magnetization of the magnetic domains [15]. 31 Chapter GMR Sensors (a) Cr/Au contact SV active area (b) x y x Spin valve material Cr/Au electrode Mfree z y Mpinned Isense Fig. 2.3.5 (a) Optical micrograph of a 12 x µm2 SV sensor. (b) Schematic of the SV sensor with corresponding co-ordinate system. Mpinned is the magnetization direction of the pinned magnetic layer, while Mfree is the easy axis of the free layer. Isense is the direction of current flow through the sensor. (a) 2.5 ∆R/R (%) 2.0 (b) 1.5 1.0 0.5 (c) 0.0 -200 -100 100 200 H Field (Oe) Fig. 2.3.6 Transfer characteristic for a 12 x µm2 SV sensor in response to (a) H field applied in y, (b) H field applied in x, (c) H field applied in z directions. To investigate the SV response to an external field, a magnetic field was swept along each of the x, y, z axes of the SV sensor with the corresponding resistance 32 Chapter GMR Sensors changes recorded (Fig. 2.3.6). The maximum MR ratio was obtained from a field applied in the y axis, corresponding to the magnetization directions of the ferromagnetic layers switching from the parallel to antiparallel alignment (Fig. 2.3.6(a)). For fields applied in the x-axis direction (Fig. 2.3.6(b)), a minimum was obtained at H = Oe, with an increase in resistance resulting from the rotation of the magnetization of the free layer toward the ± x direction. Further increase of the applied field along the ± x axis, caused the pinned layer to rotate as well, leading to a slight decrease in the total resistance. For a field applied along the z axis (out of plane), although the MR ratio should remain unchanged due to the magnetic anisotropy of thin films, we observed a slight shift in the MR. This could be due to the sensor chip not placed entirely perpendicular to the field, which resulted in the SV responding to small field components in the x and y directions. In general, the SV sensor was most sensitive to fields applied in the y-axis direction. In the experiments described in the following chapters, an external field was applied along the y-axis direction in order for the SV sensor to work in its linear region where sensitivity is a maximum. (d) SIMS depth profile of a spin valve sensor The structure of the SV sensor Ta3/NiFe2/IrMn8/CoFe2/Ru0.8/CoFe3/Cu2.3/CoFe2.6/Cu1/Ta5 material (with thickness is in nanometer). Given that the magnetic annealing step may cause the atoms of certain metals to migrate, we investigated the structure of the SV sensor after annealing using a Time-Of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS, Ion-Tof Gmbh). A depth profile of a spin valve was done using a Cs ion source of 1keV to sputter an area of 300 33 Chapter GMR Sensors µm2, with the secondary ions subsequently collected and analyzed. Figure 2.3.7 shows the intensity profile of each primary element with respect to the sputtering time (t). The entire SV structure was etched through in a time of ~ 1900s corresponding to a depth of ~ 30 nm. From the figure, we can see the correspondence in certain metals to the as deposited structure. For example, the intensity of the Ta layer is high for t = 200s and 1800s corresponding to the position of the capping and buffer layers respectively. The maximum intensity of Mn (from IrMn clusters) is noted to occur from t ≈ 1200 – 1600 s corresponding to the nm thick as deposited IrMn layer. 34 Chapter GMR Sensors Fig. 2.3.7 TOF-SIMS depth profile of the SV thin film material Ta3/NiFe2/IrMn8/CoFe2/Ru0.8/CoFe3/Cu2.3/CoFe2.6/Cu1/Ta5 (with thickness in nanometer). Ion count intensity is plotted against acquisition time. From the depth profile we can observe that the SV is a complicated structure with no clear interface between each layer. Presumably there is considerable diffusion arising from the annealing step. Such structural complexity can also be found in other GMR structures [16], a reason which makes MR so difficult to theoretically model. 35 Chapter 2.4 GMR Sensors MAGNETIC PARTICLES We have used spin valve sensors as the detection method for single ferromagnetic and superparamagnetic particles. The properties and characteristics of each particle will be highlighted in the following sections. (a) µm ferromagnetic particles In our AFM and twisting experiments (Chapters and respectively), we used µm diameter SpheroTM ferromagnetic particles (CFM-80-5, Spherotech Inc.), which are prepared using chromium dioxide coated onto uniform polystyrene particles (Fig. 2.4.1). These particles are ferromagnetic, retaining magnetism once exposed to an external field and can be de-magnetized and magnetized repeatedly and reproducibly [17]. These particles can also be easily functionalized for various biological experiments. Fig. 2.4.1 Optical micrograph of µm diameter Spherotech particles at 20x magnification. 36 Chapter GMR Sensors To calculate the magnetization of a single µm magnetic particle, vibrating sample magnetometry (VSM 7407, LakeShore) was done on a sample of 0.1 mg of dried magnetic particles. The magnetic moment of the sample was measured with respect to an applied field, with the hysteresis loop shown in figure 2.4.2. -4 2x10 -4 Moment (emu) 1x10 -4 -1x10 -4 -2x10 -1.0 -0.5 0.0 0.5 1.0 H Field (T) Fig. 2.4.2 Hysteresis loop of 0.1mg of dried µm beads measured by VSM. Based on the specifications from the supplier for particle density and magnetic content (%), together with the VSM experiments, the magnetic dipole moment of a single µm ferromagnetic particle was calculated to be ~ 3.6 x 10-10 emu. (b) µm superparamagnetic particles For our optical tweezers experiments (Chapter 4), we used superparamagnetic particles of µm diameter (Micromer®-M, Micromod), which are monodisperse iron oxide particles (15%) encapsulated in an organic matrix of a styrene-maleic acid 37 Chapter GMR Sensors copolymer. (Fig. 2.4.3) The key characteristic of superparamagnetic particles is that the particles have an induced magnetization only in the presence of an externally applied field, which makes them ideal for magnetic tagging and separation applications. The polymer shell also allows for surface functionalization. Fig. 2.4.3 Optical micrograph of µm superparamagnetic particles at 50x magnification. diameter Micromod The magnetic susceptibility of the µm microspheres have been measured to be 3.3 x 10-13 emu/Oe [18], leading to a magnetic dipole moment of ~ 3.33 x 10-12 emu for an applied magnetic field of 10 Oe. 2.5 CONCLUSION In this chapter we have described and shown the fabrication techniques and magnetic field response of our GMR and spin valve sensors. In particular, a fabrication process was developed to created SV sensors with active area as small as x µm2. The 38 Chapter GMR Sensors key properties of the magnetic particles used for subsequent AFM, optical tweezers, and twisting experiments were also introduced. 39 Chapter GMR Sensors REFERENCES [1] B. Dieny, in Magnetoelectronics, edited by M. Johnson (Academic, New York, 2004) [2] M. Johnson, in Magnetoelectronics, edited by M. Johnson (Academic, New York, 2004) [3] D. R. Baselt, G. U. Lee, M. Natesan, S. W. Metzger, P. E. Sheehan, R. J. Colton, Biosens. Bioelectron. 13, 731 (1998) [4] M. M. Miller, P. E. Sheehan, R. L. Edelstein, C. R. Tamanaha, L. Zhong, S. Bounnak, L. J. Whitman, R. J. Colton, J. Mag. Mag. Mat. 225, 138 (2001) [5] D. L. Graham, H. Ferreira, J. Bernardo, P. P. Freitas, J. M. S. Cabral, J. Appl. Phys. 91(10), 7786 (2002) [6] D. L. Graham, H. A. Ferreira, P. P. Freitas, Trends in Biotech. 22(9), 455 (2004) [7] G. Li, S. Sun, S. X. Wang, J. Appl. Phys. 99, 08P107 (2006) [8] K. I. Min, S. K. Joo, K.H. Shin, J. Mag. Mag. Mat. 156, 375 (1996) [9] S. Tumanski, Thin Film Magnetoresistive Sensors, (IOP 2001) [10] S. S. P. Parkin, Z. G. Li, D. J. Smith, Appl. Phys. Lett. 58, 2710 (1991) [11] A*Star Data Storage Institute, Singapore [12] K. B. Li, Y. H. Wu, J. J. Qiu, G. C. Han, Z. B. Guo, H. Xie and T. C. Chong, Appl. Phys. Lett. 79, 3663 (2001) [13] S. Franssila, in Introduction To Microfabrication, (J. Wiley, 2004) [14] M. Tondra, M. Porter, R. J. Lipert, J. Vac. Sci. Technol. A 18(4), 1125 (2000) [15] R. C. O’Handley, Modern Magnetic Materials Principles and Applications (Wiley, 2000) 40 Chapter GMR Sensors [16] J. Windeln, C. Bram, H-L Eckes, D. Hammel, J. Huth, J. Marien, H. Rohl, C. Schug, M. Wahl, A. Wienss, Appl. Surface Sci. 179(1-4), 167 (2001) [17] www.spherotech.com (technical notes) [18] D. L. Graham, H. A. Ferreira, P. P. Freitas, J. M. S. Cabral, Biosensors and Bioelectronics 18, 483 (2003) 41 [...]... Chapter 2 2.4 GMR Sensors MAGNETIC PARTICLES We have used spin valve sensors as the detection method for single ferromagnetic and superparamagnetic particles The properties and characteristics of each particle will be highlighted in the following sections (a) 8 µm ferromagnetic particles In our AFM and twisting experiments (Chapters 3 and 5 respectively), we used 8 µm diameter SpheroTM ferromagnetic particles... supplier for particle density and magnetic content (%), together with the VSM experiments, the magnetic dipole moment of a single 8 µm ferromagnetic particle was calculated to be ~ 3.6 x 10-10 emu (b) 2 µm superparamagnetic particles For our optical tweezers experiments (Chapter 4), we used superparamagnetic particles of 2 µm diameter (Micromer®-M, Micromod), which are monodisperse iron oxide particles... magnetization of a single 8 µm magnetic particle, vibrating sample magnetometry (VSM 7407, LakeShore) was done on a sample of 0.1 mg of dried magnetic particles The magnetic moment of the sample was measured with respect to an applied field, with the hysteresis loop shown in figure 2. 4 .2 -4 2x10 -4 Moment (emu) 1x10 0 -4 -1x10 -4 -2x10 -1.0 -0.5 0.0 0.5 1.0 H Field (T) Fig 2. 4 .2 Hysteresis loop of 0.1mg... 37 Chapter 2 GMR Sensors copolymer (Fig 2. 4.3) The key characteristic of superparamagnetic particles is that the particles have an induced magnetization only in the presence of an externally applied field, which makes them ideal for magnetic tagging and separation applications The polymer shell also allows for surface functionalization Fig 2. 4.3 Optical micrograph of 2 µm superparamagnetic particles... Colton, J Mag Mag Mat 22 5, 138 (20 01) [5] D L Graham, H Ferreira, J Bernardo, P P Freitas, J M S Cabral, J Appl Phys 91(10), 7786 (20 02) [6] D L Graham, H A Ferreira, P P Freitas, Trends in Biotech 22 (9), 455 (20 04) [7] G Li, S Sun, S X Wang, J Appl Phys 99, 08P107 (20 06) [8] K I Min, S K Joo, K.H Shin, J Mag Mag Mat 156, 375 (1996) [9] S Tumanski, Thin Film Magnetoresistive Sensors, (IOP 20 01) [10] S S P... area as small as 2 x 4 µm2 The 38 Chapter 2 GMR Sensors key properties of the magnetic particles used for subsequent AFM, optical tweezers, and twisting experiments were also introduced 39 Chapter 2 GMR Sensors REFERENCES [1] B Dieny, in Magnetoelectronics, edited by M Johnson (Academic, New York, 20 04) [2] M Johnson, in Magnetoelectronics, edited by M Johnson (Academic, New York, 20 04) [3] D R Baselt,... uniform polystyrene particles (Fig 2. 4.1) These particles are ferromagnetic, retaining magnetism once exposed to an external field and can be de-magnetized and magnetized repeatedly and reproducibly [17] These particles can also be easily functionalized for various biological experiments Fig 2. 4.1 Optical micrograph of 8 µm diameter Spherotech particles at 20 x magnification 36 Chapter 2 GMR Sensors To... is high for t = 20 0s and 1800s corresponding to the position of the capping and buffer layers respectively The maximum intensity of Mn (from IrMn clusters) is noted to occur from t ≈ 120 0 – 1600 s corresponding to the 8 nm thick as deposited IrMn layer 34 Chapter 2 GMR Sensors Fig 2. 3.7 TOF-SIMS depth profile of the SV thin film material Ta3/NiFe2/IrMn8/CoFe2/Ru0.8/CoFe3/Cu2.3/CoFe2.6/Cu1/Ta5 (with... is the direction of current flow through the sensor (a) 2. 5 ∆R/R (%) 2. 0 (b) 1.5 1.0 0.5 (c) 0.0 -20 0 -100 0 100 20 0 H Field (Oe) Fig 2. 3.6 Transfer characteristic for a 12 x 8 µm2 SV sensor in response to (a) H field applied in y, (b) H field applied in x, (c) H field applied in z directions To investigate the SV response to an external field, a magnetic field was swept along each of the x, y, z axes... Lett 58, 27 10 (1991) [11] A*Star Data Storage Institute, Singapore [ 12] K B Li, Y H Wu, J J Qiu, G C Han, Z B Guo, H Xie and T C Chong, Appl Phys Lett 79, 3663 (20 01) [13] S Franssila, in Introduction To Microfabrication, (J Wiley, 20 04) [14] M Tondra, M Porter, R J Lipert, J Vac Sci Technol A 18(4), 1 125 (20 00) [15] R C O’Handley, Modern Magnetic Materials Principles and Applications (Wiley, 20 00) 40 . maximum MR ratio of 2% was obtained. The two peaks observed were due magnetic hysteresis. -3000 -20 00 -1000 0 1000 20 00 3000 -0 .25 0.00 0 .25 0.50 0.75 1.00 1 .25 1.50 1.75 2. 00 2. 25 H (Oe) ∆R/R. measured by a Nanovoltmeter (Keithley 21 82) . The transfer characteristic of a 30 x 40 µm 2 GMR sensor is shown in Figure 2. 2.4. 25 Chapter 2 GMR Sensors Fig. 2. 2.3 (a) Experimental layout to. View Section View 24 Chapter 2 GMR Sensors x y [Co(3)/Cu (2. 2)] 7 (a) (b) Cr/Au contacts Fig. 2. 2 .2 (a) Sensor chip with GMR multilayer structure of [Co(3)/Cu (2. 2)] 7 fabricated on