Luận văn Study of perpendicular exchange bias mechanism in MnPd/Co multilayers

ductively to it. In the present thesis, the area compositions of Mn and Pd on the target were about 60:40, respectively. Meanwhile, a circular Co target was used to prepared ferromagnetic layers. The RF sputtering system has two power sources used for two targets. The targets were placed in its positions in the deposition chamber and after that, the deposition chamber was pumped out until the pressure inside was less than 5 × 10-6 mbar. Samples were fabricated in Ar gas. The gas flow was regulated by a mass flow controller and kept at a constant rate during the deposition. Sputtering process was carried out in the condition of the Ar pressure kept at about 5 × 10-3 mbar. No external magnetic field was applied in the deposition and substrates were at ambient temperature. The samples used in the present thesis are Si/[MnPd/Co]10 multilayer thin films. The MnPd and Co layers were deposited alternately onto single crystal Si(111) substrates (see Fig. 2-2) at the power of 150 W for the MnPd target and 300 W for the Co target. The corresponding deposition rates for MnPd and Co layers are 2.3 × 10-2 nm/s and 2.8 × 10-2 nm/s. The compositions of MnPd layer were determined using a wavelength dispersive X-ray spectrometer (WDS) and an energy dispersive X-ray spectrometer (EDS). The results showed the Mn and Pd compositions are 11: 89, respectively. - 17 - N bilayers x = 2.5 – 10 nm y = 3.5 – 30 nm N = 10 bilayers MnPd y (nm) Co x (nm) Co x (nm) Co x (nm) Co x (nm) MnPd y (nm) MnPd y (nm) MnPd y (nm) Si substrate Fig. 2-2. Schematic view of [MnPd/Co]N multilayer structure used in the present thesis. - 18 - 2.3 Experimental techniques 2.3.1 Glancing incident X-ray diffraction In order to analysis the structure of sample, θ/2θ scan X-ray diffraction was carried out using a PANalytical-Philips X’pert Pro system at Hanoi University of Technology. A Cu target is used as the X-ray source. A double- crystal monochromator is used to obtain monochromatic and collimated Cu Kα1 radiation (λ=0.154056). The incident X-ray and the sample were fixed. The incident angle of the X-ray beam was of 1 degree with respect to the sample surface. Meanwhile, the detector rotated so that the θ/2θ scan configuration was preserved during the measurements. In the present thesis, the angle 2θ was from 25 to 70 degrees. Diffracted beam Sample Incident beam Fig. 2-3. Schematic diagram of glancing incident θ/2θ scan X-ray diffraction configuration. 2.3.2 Field emission scanning electron microscope Cross-section images were observed by a field emission scanning electron microscope (FESEM). The best resolution of the system is up to 2 nm (standard mode), 3 to 5 times better than conventional SEM. Because a field emission source provides narrower probing electron beams at low temperature - 19 - and high energy with acceleration voltage from 0.5 to 30kV (variable at 0.1 kV/step). The magnification of the system is in the range of X 20 - X 800000. In present thesis, observations of cross-section were carried out by a Hitachi FE-SEM S4800 microscope system at the Institute of Materials Science, Vietnamese Academy of Science and Technology. After the sample was broken into half, they were immediately used to view. 2.3.3 Stylus-method profilemetry The stylus method consists of measuring the mechanical movement of a stylus as it is made to trace the topography of a film-substrate step. The film thickness is directly read out as the height of the resulting step-contour trace. The profilemeter used in this thesis is called Alpha-step model with the vertical resolution of about 1 Å. The Alpha-Step IQ is guaranteed step height repeatability which makes it easier to precisely determine the thickness of thin films, roughness, etch depth in a wide extending below 8 nm and tall step height up to 2 mm. The performance is due to modern ultra-low noise electronics and precision mechanical components. The stylus scanning motion provides exceptional stability for extremely repeatable measurements. To determine deposition rate for a material, a single layer with a film- substrate step was prepared in a specific time. The single layer was measured for three times in order to receive the mean thickness. Hence, one can calculate the deposition rate for the material. In this thesis, the deposition rates for MnPd and Co are respectively 2.3 × 10-2 nm/s and 2.8 × 10-2 nm/s. These thickness measurements were carried out at the Institute of Materials Science, Vietnamese Academy of Science and Technology. 2.3.4 Energy dispersive X-ray spectrometer (EDS) - 20 - X-rays emitted from a sample under electron bombardment are collected with a liquid nitrogen-cooled solid state detector and analyzed via computer according to their energy. Typically, the computer programs used in EDS will display a real time histogram of number of X-rays detected per channel (variable, but usually 10 electron volts/channel) versus energy expressed in KeV. Using EDS, all of the energies of the characteristic X-rays incident on the detector are measured simultaneously and data acquisition is therefore very rapid across the entire spectrum. However, the resolution of an EDS detector is considerably worse than that of a WDS spectrometer. Besides, it is very difficult to determine precisely elements and its compositions if there is only a small amount of one of the overlapped elements. In practice, EDS is most often used for qualitative elemental analysis, simply to determine which elements are present and their relative abundance. Depending on the specific needs of the investigations, quantitative results may be advised to use the electron microprobe. In some instances, however, the area of interest is simply too small and must be analyzed by TEM (where EDS is the only option) or high resolution SEM (where the low beam currents used preclude WDS, making EDS the only option). In this thesis, the sample composition was analyzed by a Hitachi FESEM S4800 microscope system integrated EDS at the Institute of Materials Science, Vietnamese Academy of Science and Technology. 2.3.5 Wavelength dispersive X-ray spectrometer (WDS) WDS was the original technique developed to precisely and accurately determine chemical compositions of micro-volumes (a few cubic microns) of "thick" specimens, and the instrument used is the electron microprobe. The - 21 - key feature of the electron microprobe is a crystal-focusing spectrometer, of which there are usually 3-5 different diffracting crystals. The WDS spectrometer can acquire the high count rate of X-rays produced at high beam currents, because it measures a single wavelength at a time. This is important for trace element analysis. In practice, it is advantageous to use the speed of EDS for an initial survey of an unknown sample because major elements will be rapidly identified. However, if trace elements are present they will not be identified, and it may be difficult to interpret complex overlaps which are common in EDS analysis. Following the initial energy dispersion survey, wavelength dispersion can be used to check for overlaps and to increase sensitivity for trace elements. A Jeol JXA 8800R electron probe microanalyzer at the Institute of Geology and Minerals was used in the present study. 2.3.6 Magnetization hysteresis loops Magnetization curve provides basic magnetic properties of a magnetic material. From the curve, one can estimate the saturation magnetization MS, the coercitivity HC, the magnetic anisotropy K, the magnetization remanence MR and the exchange bias field HE. Magnetic behavior can also be understood of microscopic structural properties. In the present study, measurements of magnetization curves were performed using a DMS 880 VSM system at the ITIMS. The magnetic field used in the present study was up to 13.5 kOe along both the parallel and perpendicular directions. For these measurements, the background resulted from any source such as the sample holder and the substrate was subtracted. Before each measurement, a standard Ni sample (with total magnetic moment of 3.799 emu) was always used to calibrate the system. For the measurement of the hysteresis loops at low temperatures, a tube attached in the VSM and a thermocouple is placed inside the tube - 22 - together with the heating coil. By evaporating liquid nitrogen and simultaneously adjusting the current for the heating coil, one can control the system with the temperature accuracy of about 5 degrees. 2.3.7 Magnetization-temperature curve Magnetization-temperature curve were carried out by a VSM system (described in the previous subsection). Temperature was controlled by evaporating liquid nitrogen (in the range of low temperature) or blowing pure nitrogen gas (in the range of high temperature), and simultaneously adjusting the current for the heating coil. In the present study, the measurement was performed in the temperature range from 120 to 320 K and the step of 5 K. 2.3.8 Magnetic force microscope & atomic force microscope Observations of magnetic domains were carried out using a NT-MDT Solver magnetic force microscope (MFM) at the College of Technology, Vietnam National University, Hanoi. The tip used in the present study was coated by CoCr alloy with the coating thickness of 40 nm, the curvature radius of 30-40 nm and the cone angle less than 30 degrees. Before each measurement, it was magnetized along the direction perpendicular to the sample surface. The same tip was used to observe the MFM and AFM images. The surface roughness was determined to be less than 2 nm. - 23 - Chapter 3 3. EXPERIMENTAL RESULTS 3.1 Introduction In this chapter, the results of crystallographic and magnetic properties of [MnPd/Co]10 multilayer thin films are presented. The crystallographic properties characterized by XRD, FESEM and AFM. Meanwhile, the magnetic properties, in particular parallel and perpendicular exchange biases and anisotropy, are characterized by VSM and MFM. The aim of the present thesis is to study the perpendicular exchange bias effect. Therefore, the investigation and comparison between parallel and perpendicular exchange biases is necessary. The perpendicular magnetic anisotropy is also important due to its contribution to the effect. Some measurements were carried out at room temperature for a better understanding of physical origin of the perpendicular anisotropy and also perpendicular exchange bias. The magnetic properties of the multilayers are discussed in the next chapter in conjunction with the structure. 3.2 Crystallographic structure 3.2.1 Glancing incident X-ray diffraction Fig. 3-1 shows the θ/2θ scan X-ray diffraction pattern of [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5 nm) as-deposited multilayers. -24- 25 30 35 40 45 50 55 60 65 70 0 200 400 600 800 1000 1200 1400 ( 2 2 0 ) ( 2 0 0 ) (b) (c) (a) ( 1 1 1 ) Fig. 3-1. X-ray diffraction spectra of [MnPd(10 nm)/Co(x nm)]10 multilayers, (a) x = 2.5 nm, (b) x = 3.5 nm, (c) x = 4.5 nm. 2θ (deg.) I n t e n s i t y ( a . u . ) - 25 - 3.2.2 Cross-section observation Shown in Fig. 3-2 is the cross-section image of [MnPd(10 nm)/Co(7.5nm)]10 as-deposited multilayer. Fig. 3-2. Cross-sectional view of [MnPd(10 nm)/Co(7.5 nm)]10 as- deposited multilayer. 3.3 Magnetic properties The magnetic properties of the present sample were characterized by using the VSM and MFM. Based on the VSM measurements with the field cooling process, one can estimate the exchange bias field as well as the anisotropy constants. The magnetic anisotropy was also investigated through the domain structure observed by MFM for some typical samples at room temperature. Some hysteresis loop measurements were carried out at room temperature in order to understand the origin of the perpendicular magnetic anisotropy. - 26 - 3.3.1 Domain observation Observation of the domains by MFM at the sample surface of [MnPd(10 nm)/Co(3.5 nm)]10 as-deposited multilayer is shown in Fig. 3-3. Fig. 3-3. MFM image of [MnPd(10 nm)/Co(3.5 nm)]10 as-deposited multilayer. 3.3.2 Magnetization hysteresis loops at low temperature Before the magnetization hysteresis loop measurements, the samples had to undergo the so-called field cooling (FC) process. First, MnPd/Co multilayer deposited onto Si(111) substrate was heated to T = 590 K and kept at that condition for 5 minutes. Then the sample was cooled down to room temperature in the presence of a magnetic field of 5 kOe - 27 - (called the cooling field HFC) applied either in the film plane (parallel direction) or normal to the plane (perpendicular direction). This process was realized in a vacuum chamber with the pressure better than 2 × 10-5 mbar. After that, the sample cooled in a field of 5 kOe between the two poles of the VSM from room temperature down to the measurement temperature. Finally, the hysteresis loops were measured with the applied field direction as the same as the cooling field at cryogenic temperature below the blocking temperature TB ~ 240 K, namely at T = 120 K (see Fig. 3-4). Samples with the different thicknesses of Co and MnPd layers were studied. Parallel and perpendicular hysteresis loops measured at 120 K were shown in Fig. 3-5 for the series of samples with tCo varied from 2.5 to 10 nm while tMnPd is fixed at 10 nm and in Fig. 3-6 for another series of samples with the variation of tMnPd from 3.5 to 30 nm while keeping tCo at 3.5 nm. HFC H HFC H Fig. 3-4. Schematic diagram of measurement configurations for samples at 120K. Here, the measurement field direction (H) is the same as the cooling field (HFC). - 28 - -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel tCo = 2.5 nm M (a .u .) H (kOe) -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo =3.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 4.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 5.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 7.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 10 nm Fig. 3-5. Parallel and perpendicular hysteresis loops measured at T = 120 K for [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) field cooled multilayers. - 29 - Fig. 3-6. Parallel and perpendicular hysteresis loops measured at T = 120 K for [MnPd(y nm)/Co(3.5 nm)]10 (y = 3.5, 5.5, 7.5, 10, 15.5, 30 nm) field cooled multilayers. -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tMnPd = 3.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tMnPd = 5.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tMnPd = 7.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) tMnPd = 10 nm H (kOe) -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tMnPd = 15.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tMnPd = 30 nm - 30 - 3.3.3 Magnetization hysteresis loops at room temperature Magnetization hysteresis loop measurements of the samples processed at different conditions were carried out at room temperature (see Fig. 3-7). MnPd/Co multilayer deposited onto Si(111) was heated to 590 K and kept at that condition for 5 minutes. Then, the sample was cooled down to room temperature in the presence of a magnetic field of 5 kOe applied either normal to the plane (perpendicular direction) (Fig.3-7-(a)) or in the film plane (parallel direction) (Fig. 3-7-(b)). These samples processed at the same conditions as that described in the previous subsection. Some others were annealed at 590 K for 5 minutes, and then cooled down to room temperature in zero field (so-called zero field cooling ZFC) (Fig. 3-7-(c)). Besides, as- deposited samples were also used for these measurements (Fig. 3-7-(d)) in order to investigate systematically the effect of the field cooling and also annealing process. It should be noted that hysteresis loops of each sample were carried out in both the parallel and perpendicular directions at room temperature. The hysteresis loops of different samples processed at the same conditions are depicted from Fig. 3-8 to Fig. 3-11. - 31 - d) Sample as- deposited H H c) Sample cooled in the zero field H H b) Sample cooled in the parallel field. H HFC H a) Sample cooled in the perpendicular field. HFC H H Fig. 3-7. Schematic diagram of measurement configurations at room temperature. Here, HFC denotes the cooling field direction and H denotes measurement field directions. Note that all samples were measured in two different directions. - 32 - -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 2.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 4.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 5.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 7.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 10 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 3.5 nm Fig. 3-8. Parallel and perpendicular hysteresis loops measured at room temperature for [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) multilayers cooled in the field perpendicular to the plane. - 33 - Fig. 3-9. Parallel and perpendicular hysteresis loops measured at room temperature for [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) multilayers cooled in the field parallel to the plane. -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 2.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 3.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 4.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 5.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 7.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 10 nm - 34 - Fig. 3-10. Parallel and perpendicular hysteresis loops measured at room temperature for [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) multilayers cooled in the zero field. -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 2.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 3.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 4.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 5.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 7.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 10 nm - 35 - Fig. 3-11. Parallel and perpendicular hysteresis loops measured at room temperature for [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5, 5.5, 7.5, 10 nm) as-deposited multilayers. -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 2.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 4.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 5.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 3.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 7.5 nm -15 -10 -5 0 5 10 15 -1.0 -0.5 0.0 0.5 1.0 Perpendicular Parallel M (a .u .) H (kOe) tCo = 10 nm - 36 - 3.3.4 Temperature dependence of magnetization in MnPd/Co multilayers The multilayer of [MnPd(10 nm)/Co(3.5 nm)]10 was heated up to 590 K and kept at that condition for 5 minutes. After that, the sample was cooled down to room temperature in the zero field. This process was carried out in a vacuum chamber with the pressure better than 2×10-5 mbar. The magnetization – temperature curve of this multilayer was recorded by first cooling the sample from room temperature to 120 K in the zero magnetic field, then applying the magnetic field of 2500 Oe and warming the sample up to 320 K in the presence of the field and recording the moment in this warming cycle (Forward). Next, keeping the field while the sample is cooled from 320 K down to 120 K and recording the moment (Backward). It is noted that the applied field is perpendicular to the plane. The obtained curve is shown in Fig. 3-12. 120 150 180 210 240 270 300 330 0 50 100 150 200 250 300 Forward Backward M (e m u/ cm 3 ) T (K) ZFC H = 2500 Oe Fig. 3-12. Magnetization – temperature curve of [MnPd(10 nm)/Co(3.5 nm)]10 multilayer in the presence of a field of 2500 Oe. - 37 - Chapter 4 4. DISCUSSIONS 4.1 Introduction This chapter is to discuss the results of crystallographic and magnetic properties of [MnPd/Co]10 multilayers presented in the previous chapter. The behaviors of exchange bias in both the parallel and perpendicular directions and magnetic anisotropy will be studied. After that, based on the results of parallel and perpendicular exchange biases and the magnetic anisotropy, we propose a phenomenological picture to qualitatively explain the perpendicular exchange bias coupling mechanism. 4.2 Crystallographic structure Crystallographic properties are obtained from XRD patterns and cross- section observation using a FESEM. They are discussed here due to their relation to the magnetic properties of the multilayers. 4.2.1 Glancing incident X-ray diffraction Fig. 3-1 shows the θ/2θ scan X-ray diffraction patterns for as-deposited [MnPd(10 nm)/Co(x nm)]10 (x = 2.5, 3.5, 4.5) multilayers grown onto Si(111) substrates held at ambient temperature. It is observed that in the samples, MnPd is polycrystalline with fcc structure. Apart from the peak (111), other peaks of MnPd are also observed as (200) and (220) for the sample with the smallest tCo (tCo = 2.5 nm). However, they are found to be very weak and unobservable with increasing tCo. Meanwhile, almost no peak for Co can be observed showing that Co layer may be formed with low crystallinity. - 38 - 4.2.2 Cross-section observation Shown in Fig. 3-2 is cross-sectional view observed by FESEM microscope on the fresh broken pieces of the as-deposited [MnPd(10 nm)/Co(3.5nm)]10 multilayer thin film. One can see that there are 20 layers corresponding to alternate MnPd and Co through the dark and bright contrast (as shown in Fig. 2-2). From the bottom to top, cumulative waviness increases gradually. The effect is usually observed in multilayer thin films, especially in metallic ones [63]. 4.3 Magnetic properties The magnetic properties are discussed based on the magnetic measurements. From the hysteresis loops, one can estimate the exchange bias field as well as the anisotropy constants. Besides, the anisotropy property can be also qualitatively estimated through domain structure observed by MFM. As shown in Fig. 3-5 and Fig. 3-6, the negative shifts of the hysteresis loops show that the exchange bias effect is found in the [MnPd/Co]10 multilayers in both the parallel and perpendicular directions. From the hysteresis loops, the exchange bias field (HE) and the coercivity (HC) can be extracted by using definitions: HE = |HSU + HSD|/2 (Eq. 4-1) HC = (HSU - HSD)/2 (Eq. 4-2) Where, HSU and HSD are the switching fields in the up