Development of a Surface Magneto-Optic Kerr Effect Magnetometer. Susan Stoffer Sorensen

Transcription

1 Development of a Surface Magneto-Optic Kerr Effect Magnetometer Susan Stoffer Sorensen A senior thesis submitted to the faculty of Brigham Young University In partial fulfillment of the requirements for the degree of Bachelor of Science Dr. Karine Chesnel, Advisor Department of Physics and Astronomy Brigham Young University December 2013 Copyright 2013 Susan Stoffer Sorensen All Rights Reserved

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3 ABSTRACT Development of a Surface Magneto-Optic Kerr Effect Magnetometer Susan Stoffer Sorensen Department of Physics and Astronomy Bachelor of Science This thesis presents the development and optimization of a surface magnetooptic Kerr effect (SMOKE) magnetometer. Our magnetometer is explained in terms of its three major parts: mechanical setup, electrical connections, and LabVIEW programming. An upgrade of the electrical system is shown to double the available applied field. Studies of the deviation angle and incident polarization direction show an ideal deviation angle range of 10 to 16 from extinction and that the polarizer should be aligned completely along either the P or S polarization axis. The addition of more mirrors to the optical system gives greater choice of incident angle and allows optical components to be placed further from the magnet poles. This is shown to reduce laser intensity fluctuations caused by magnetic interference. Our data manipulation process is explained. Finally, a comparison between SMOKE and EHE hysteresis measurements suggests that our SMOKE apparatus is functioning properly. Keywords: Surface Magneto-Optic Kerr Effect, Magnetometer, Light Polarization, Ferromagnetism, Thin Films iii

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5 ACKNOWLEDGMENTS First and foremost, I would like to thank Dr. Karine Chesnel, my research mentor, for all of her support and aid on this project. She gave me a huge amount of freedom to work with the SMOKE, and I have learned so much from it and from her. I extend a huge thank you to the entire Brigham Young University Physics Department, which is the foundation of my education. Thank you to Scott Daniel and his student, Andrew Wendt, without whom I may never have gotten the Master-Slave configuration to work. I would also like to acknowledge Kyle Miller and Luke Pritchett who worked on the SMOKE before me and wrote the basic LabVIEW program for the original single BOP setup. Thank you, also, to the rest of my research group for giving me advice about the SMOKE and for helping me practice for conference presentations. Finally, thank you to my loving parents and husband for listening to me ramble on and on about the SMOKE while patiently pretending it was half as interesting to them as it was to me. v

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7 Contents Table of Contents... vii List of Figures... viii 1. The SMOKE Technique Introduction to SMOKE/MOKE Magnetic Domains and Hysteresis P and S Polarization Convention Samples Measured by our SMOKE Instrumental Setup Mathematical Analysis of SMOKE Our SMOKE Setup Mechanical Setup Electrical Setup LabVIEW programming Results Selecting Value for delta Selecting the Incident Polarization Direction Incidence Angle Adjustments SMOKE Measurement and Data Manipulation Comparison with EHE Measurement Summary Bibliography vii

8 Figures Figure 1 Kerr rotation in terms of P and S polarization...2 Figure 2 MFM image of magnetic domains...3 Figure 3 (a), (b) In and out of plane magnetic domains...4 Figure 4 Example of a hysteresis loop...5 Figure 5 A simplified diagram of a SMOKE setup...7 Figure 6 (a), (b), (c) Polarization of the beam at different points...8 Figure 7 A raw hysteresis loop measured by the SMOKE...9 Figure 8 A photograph of the electromagnet used in our SMOKE setup...12 Figure 9 Laser intensity fluctuations for the first hour after it is turned on...13 Figure 10 The mount used to hold the gaussmeter during calibration...14 Figure 11 A linear fit for a magnet calibration...14 Figure 12 A spatial profile of the magnetic field of the electromagnet...15 Figure 13 (a), (b) Magnet calibrations from before and after system upgrade...16 Figure 14 A basic diagram of the connections between power supplies...17 Figure 15 Series connections between power supplies...20 Figure 16 Parallel connections between power supplies...21 Figure 17 A full diagram of the detailed connections between power supplies...22 Figure 18 The front panel of the LabVIEW program...23 Figure 19 (a)-(h) Hysteresis loops with varying δ angles...26 Figure 20 Signal to noise ratio vs δ...27 Figure 21 Hysteresis loops measured for three different polarizer angles...28 Figure 22 Our initial SMOKE setup...29 Figure 23 Laser intensity fluctuations with magnetic interference...30 Figure 24 Our current SMOKE setup...31 Figure 25 Laser intensity fluctuations without magnetic interference...31 Figure 26 (a), (b), (c) Raw, normalizing, and normalized signals...32 Figure 27 Multiple hysteresis loops averaged together...33 Figure 28 Linear fits of the slopes at the top and bottom of a hysteresis loop...35 Figure 29 The final version of the hysteresis loop after data manipulation...36 Figure 30 Comparison between measurements made by SMOKE and EHE...37 viii

9 Chapter 1 The SMOKE Technique 1.1. Introduction to SMOKE/MOKE The magneto-optic Kerr effect (MOKE, also called simply the Kerr effect) is a physical phenomenon that describes an interaction between polarized visible light and magnetized materials. The Kerr effect can be used to measure magnetization of various magnetic materials, and therefore can be utilized to develop a magnetometer. This thesis focuses on a subset of MOKE called surface magneto-optic Kerr effect (SMOKE), which consists of measuring the magnetization at the surface of magnetic materials. In our case, the materials are very thin so the surface magnetization measured by the SMOKE is approximately the total magnetization of the film. A precursor to the Kerr effect was the Faraday effect, discovered by Michael Faraday in 1845 [1]. Both effects describe interactions between polarized light and magnetic materials. The Faraday effect is observed when polarized light is transmitted through a magnetic material. The Kerr effect, on the other hand, occurs in reflection geometry. The Kerr effect was discovered by John Kerr in 1877 [2], but its application to thin samples via SMOKE only began in 1985 [3]. According to Dr. Bader, one of the pioneers of the SMOKE method, recent use of SMOKE has been bolstered by interest in the very thin magnetic structures that SMOKE can be used to 1

10 study. In the search for smaller information storage, magnetic recording on thin films could produce high-density storage media [4]. SMOKE can also be used to study magnetic nanoparticles, which have a variety of potential applications in nano-medicine and magnetic imaging. In Kerr effect, polarized visible light reflects off of a magnetized surface and experiences a small rotation in polarization, as shown in Figure 1. This is known as the Kerr rotation, denoted Δθ. This rotation is proportional to the magnetization of the surface to a first-order approximation ( ). The SMOKE method uses this relationship to measure magnetization via a measurement of the Kerr rotation. Figure 1 Light polarization before and after Kerr rotation. The magnitude of Δθ is exaggerated. The convention of P and S polarization is explained in section Magnetic Domains and Hysteresis A single atom has its own magnetic moment, the strength and direction of which determine how it interacts magnetically with the atoms around it. Within a ferromagnetic material, the magnetic moments of neighboring atoms tend to point in the same direction. These groups form magnetic domains which can vary 2

11 in size from a few nm to several microns, typically. Figure 2 shows an example of magnetic domains in a thin Co/Pt multilayer, measured by Magnetic Force Microscopy (MFM). The light areas, called up domains, are pointing out of the plane of the page. The dark areas are down domains which are antiparallel to the up domains. The net magnetization is the vector sum of all the magnetic domains in the sample, and can vary with an applied external field (H). Since the image has approximately the same amount of up and down domains, its net magnetization is zero. Figure 2 Top-down image of the magnetic domains in a Co/Pt ferromagnetic thin film, taken using MFM. In our films, the easy magnetization axis is out-of-plane rather than inplane, as illustrated in Figure 3. Therefore, all of the magnetic domains point perpendicular to the surface of the sample. In our SMOKE apparatus, the field is perpendicular to the sample surface. This is called a polar geometry [5], [6], in 3

12 which the SMOKE only measures the out-of-plane magnetization. The out-ofplane component is a good approximation of the total magnetization because we can assume that there is no in-plane magnetization in our samples. (a) (b) Figure 3 (a) In-plane magnetization (b) Out-of-plane magnetization In my research, I use the SMOKE to characterize the magnetic response of ferromagnetic thin films and nanoparticle assemblies in the presence of varying H. The measurement from the SMOKE produces a magnetization loop. When the magnetization of a sample is path dependent, the sample is said to exhibit hysteresis, and the magnetization loop is called a hysteresis loop, an example of which is shown in Figure 4. A varying external field is applied across a magnetic material, and the net magnetization, M, of the sample is measured. At the coercive point, there are about as many up domains as do domains, so the net magnetization is zero (M = 0). As the field increases, the domains will tend to flip to align with the external field. Eventually, all of the domains will have aligned with the external field so that only one large domain remains. At this point, called 4

13 M (emu) saturation, the net magnetization does not further increase with increasing external field. When the field is then decreased, the magnetization reverses. In most ferromagnetic samples, the domains will not start reversing back at the saturation field value, but instead at a lower field value called the nucleation point. Samples that have distinct saturation and nucleation points such that the loop has some horizontal width are said to exhibit hysteresis. The same behavior is observed in the negative field direction. The full circle constitutes a major loop. A measurement which does not reach saturation in both directions is called a minor loop. These are both magnetization loops, which the SMOKE instrument is used to measure. H (Oe) Figure 4 An example of a hysteresis loop, measured by a Vibrating Sample Magnetometer (VSM). The arrows below the labels for coercive point, saturation, and nucleation show examples of domain configurations at those points. 5

14 1.3. P and S Polarization Convention Since the SMOKE apparatus reflects light off of a sample, SMOKE measurements are like scattering experiments. In scattering experiments, the convention of P and S polarization is used. These serve as a coordinate system for polarization with respect to the plane of scattering (the plane containing both the incident and scattered beams). P polarized light is linearly polarized in the plane of scattering. S polarized light is linearly polarized perpendicular to the plane of scattering (S stands for senkrecht, the German word for perpendicular). This convention will be used frequently throughout this thesis. In our SMOKE setup, P polarized light is horizontal and lies in the plane of the optical table, and S polarized light is vertical. Our setup is shown in Figure Samples Measured by our SMOKE There are currently two main types of magnetic samples that we expect to measure with our SMOKE apparatus: multilayer films and nanoparticle assemblies. Our samples are generally between 10 nm and 100 nm thick. The SMOKE measurements shown in this thesis are done on a Co/Pt ferromagnetic multilayer thin film. The film consists of a bilayer made of 4 Å of Co and 7 Å of Pt. These bilayers are repeated fifty times for a total width of 55 nm. This multilayer structure can be written [Co(4 Å) / Pt(7 Å)] 50. The SMOKE can also be used to study nanoparticle assemblies, particularly Fe 3 O 4 (magnetite). The magnetic element in the multilayer is Co, whereas the magnetic element in the nanoparticles is Fe. 6

15 1.5. Instrumental Setup The SMOKE setup and method allow us to measure the net magnetization of a sample through a measurement of light intensity via the Kerr effect. There are several components used for the SMOKE optical setup: a laser, a 50:50 beam splitter, two linear polarizers mounted in rotating stages, two photodiodes, and a sample mount. Our setup also includes four mirrors. The mirrors are not strictly necessary for a SMOKE measurement, but make beam alignment easier. Figure 5 shows a basic diagram of the optical components and beam path necessary for a SMOKE measurement, where the mirrors have been omitted for simplicity. Our actual setup is shown and explained in section 2.1. Figure 5 Top-view simplified diagram of a SMOKE magnetometer. (The incident angle shown is not to scale.) The colors of the beam represent its polarization (see Figure 6 below). During measurement, light from the laser diode passes through the first polarizer (referred to simply as the polarizer) such that the transmitted beam is 7

16 completely P polarized (Figure 6 (a)). The light then passes through the beam splitter such that a portion of the light is reflected to a normalizing photodiode (PD-1) which monitors the laser intensity fluctuations. The signal measured by PD-1 is used to remove laser intensity fluctuations from the final hysteresis loop measurement. The beam then reflects off of the sample. The sample is perpendicular to an applied field from the electromagnet and becomes magnetized. The light experiences a Kerr rotation so that the polarization now has components in both the S and P directions (Figure 6 (b)). Because the Kerr rotation is relatively small, the light is still mostly P polarized with a small S component. The light then passes through a second polarizer, which will be called the analyzer. The analyzer is set almost at extinction with the polarizer, such that its transmission axis is nearly aligned with the S polarization axis. The reason for the slight offset is explained in section 1.6. The analyzer therefore transmits the S component of the beam while blocking nearly all of the P component (Figure 6 (c)). Since the polarization was originally completely P polarized, the S component represents the rotated portion of the beam. A larger S component corresponds to a greater Kerr rotation. The intensity of the resulting signal is measured as a voltage by the detecting photodiode (PD-2). (a) (b) (c) Figure 6 Side-view diagrams of beam polarization (a) Polarization after the polarizer. (b) Kerr rotation of the beam after reflecting from the sample. (c) Polarization of the beam after the analyzer. 8

17 Raw Signal (mv) Over the course of a hysteresis loop measurement, the applied field is varied cyclically between a positive and negative value. This changes the magnetization of the sample, which in turn changes the Kerr rotation, which is measured as a change in voltage. We then record the raw PD-2 voltage as a function of applied field strength. An example of such a raw measurement is shown in Figure 7. This is the initial loop used for the full data manipulation process explained in section 3.4. H (Gauss) Figure 7 A raw hysteresis loop measured on PD-2. In summary, the SMOKE measures the intensity of the reflected light as a voltage through a photodiode. This is proportional to the Kerr rotation experienced by the reflected light. The Kerr rotation is, in turn, proportional to magnetization of the magnetic sample. This way, the SMOKE actually measures a voltage in order to calculate net magnetization. 9

18 1.6. Mathematical Analysis of SMOKE The Kerr rotation is evaluated by taking the ratio of the S and P components of the electric field:. Since, we assume E p is constant so. In a SMOKE measurement, one attempts to measure the E s component. Unfortunately, the photodiodes measure intensity, which is proportional to. This causes us to lose information about the sign of the Kerr rotation. To circumvent this difficulty, we introduce a slight offset of the analyzer from the S polarization axis. This small angle is called the deviation angle, δ. When δ 0, the intensity measured at the photodiode is [4], where we assume δ is small enough to use a small angle approximation. At this point, we re-write our expression for the Kerr rotation to account for the possibility of ellipticity, Δϕ, upon reflection from the sample. This leaves us with. This can be used in the intensity equation above, along with the assumption that Δθ and Δϕ are very small, to get ( ) ( ) The approximation above allows us to assume a linear relationship between the intensity measured by the photodiode and the Kerr rotation. Since, a measurement of the intensity will result in a hysteresis loop, as desired. 10

19 Chapter 2 Our SMOKE Setup 2.1. Mechanical Setup Our current mechanical setup consists of a 635 nm laser, a 50:50 beam splitter, two linear polarizers mounted in rotating stages, two photodiodes, a sample mount, and four mirrors. These are fixed to an optical table, which is then mounted in between the poles of an electromagnet. The basic functions and placements of the optical components (not including the mirrors) are explained in section 1.5. Our SMOKE setup is built around a large mounted electromagnet that we already had, as shown in Figure 8. The geometry of the opening between the two poles of the magnet limits the space available for our optical components. To help make more space for components, mirrors are inserted into the beam path to allow for more flexibility in the placement of the other components. This also allows for adjustment of the incident angle, as will be discussed in section

20 Figure 8 Photograph of the electromagnet (left) and optical table (right) used for the mechanical setup for our SMOKE apparatus. The laser used for our SMOKE system is a collimated laser diode of wavelength 635 nm. This laser experiences intensity drift during the first hour of use. Figure 9 shows the intensity fluctuations of the laser measured by a photodiode during the first hour after the laser is turned on. For this reason, the laser is turned on at least an hour before measurements are taken. Even then, it has small intensity fluctuations, but these are removed from the final hysteresis loop using the signal from PD-1. 12

21 PD Intensity (mv) Time (sec) Figure 9 Laser intensity fluctuations for the first hour after the laser is turned on. For our measurements, we want to know the magnetic field strength in real time. The field produced by the electromagnet depends on the current applied to it. A calibration is therefore necessary to determine the field strength from the current. To do this calibration, a Hall probe gaussmeter is inserted between the poles of the magnet by clamping a mount (shown in Figure 10) onto the optical table. We increase the current in increments, with both the current and the field being recorded at each point. A linear fit is then performed on the data, as shown in Figure 11. The behavior of H(I) appears linear with a slope of G/Amp. The line determined by the fit is used in the LabVIEW program described in section 2.3 to convert current to applied field. 13

22 Figure 10 Mount used to hold the gaussmeter during calibration. The rod that extends horizontally is nonmagnetic. Figure 11 A linear fit is performed on the calibration data. The fit line equation is used to convert current to applied magnetic field. Using a gaussmeter, we were able to measure a spatial profile of the field strength between the poles of the magnet. For our measurement, a constant current of 20 A was applied to the magnet, and the gaussmeter was moved along a two dimensional grid in half centimeter increments, extending half a centimeter beyond the magnet poles on the left side. The resulting field profile is shown in 14

23 Figure 12. This measurement is useful for determining the profile of the magnetic field and its uniformity. It also helps us to determine where the sample should be placed. A very thin sample holder is used, which places the sample in the region at the center of the top of the field profile image. This region is uniform and also at a higher field value than the center point between the two poles. This measurement also allows us to measure the magnetic field gradient at different positions. The lowest gradient is near the center of the image, with a minimum gradient of 10 G/cm. The largest gradient is right next to the outside edges of the poles with a maximum gradient of around 250 G/cm. Figure 12 Spatial profile of the magnetic field between the poles of the electromagnet. Human error is evident at the spike just to the left of center at the bottom. 15

24 2.2. Electrical Setup Originally, the electromagnet for our SMOKE was powered by a single bipolar operational power supply (BOP). Our power supply model is a Kepco BOP 20-20M. This model has an output of ±20 Volts or ±20 Amps and can be set to either current or voltage mode. Our SMOKE has an impedance of about 1 Ω so the relationship between voltage and current is approximately one-to-one according to Ohm s law: V = IR, where V is voltage, R is resistance, and I is current. It was determined that this setup produced a maximum field of just under 5,000 G (see Figure 13 (a)), which is moderately high. In order to increase our available field, we have doubled the maximum current supplied to the electromagnet (see Figure 13 (b)). The resulting field is just under ±10,000 G, or 1 T. To do this, we added three extra BOPs to our system for a total of four power supplies. A basic understanding of circuits and Ohm s law explains the necessity of four power supplies and how they must be connected. (a) (b) Figure 13 (a) Calibration line measured with only one power supply sourcing ±20 A. (b) Calibration line with four power supplies sourcing a total of ±40 A. 16

25 Basics of Series and Parallel Circuits In order to increase the current across the electromagnet from ±20 A to ±40 A, we needed to have two parallel branches of power supplies sourcing ±20 A. By Kirchhoff s junction rule, these currents would add to ±40 A. The voltages in parallel branches are the same, so two power supplies in parallel would source ±20 V. However, since our magnet has an impedance of 1 Ω, Ohm s law requires ±40 V in order to supply ±40 A. In series, the voltages of the power supplies add and the current is the same throughout the branch, so two power supplies connected in series would supply ±40 V, but only ±20 A. Therefore, four power supplies are needed to supply ±40 V and ±40 A: two parallel branches, each with two series power supplies (Figure 14). Figure 14 A basic diagram of the series and parallel arrangement of the four power supplies with respect to the electromagnet. Master-Slave Power Supply Configuration In order to simplify controlling four power supplies with a LabVIEW program, a Master-Slave configuration is used. In this configuration, only one 17

26 BOP (called the Master) is controlled via a computer. The other three (called the Slaves) are connected to the Master such that they mimic either the voltage or current of the Master. Whether the Slaves should be set to mimic the voltage or current of the Master is determined by their position with respect to the Master in the circuit diagram shown in Figure 14. For reference, the Slaves are labeled S1, S2, and S3. The series branch with the Master will be referred to as the Master branch, and the other series branch will be called the Slave branch. Since S1 is in series with the Master, the two are forced to have the same current. S1 is set to mimic the voltage of the Master. The voltages add, resulting in a total voltage that is always twice as large in magnitude as the voltage set on the Master by the computer. The Master branch and Slave branch are in parallel, and therefore are forced to have the same total voltage. The currents, however, are not automatically forced to be equal, but are set to be the same. S2 is set to mimic the current of the Master, forcing the current in the Slave branch to match that of the Master branch. These currents add across the load, leading to twice the current that can be supplied by the Master alone. S2 also acts as a pseudo- Master for the Slave branch, meaning that S3 mimics the voltage of S2 rather than the Master. This maintains the parallel branch connections while still having the power supplies all sourcing the same voltage and current. Though the Master-Slave configuration allows us to control all four BOPs with only one BIT interface card, it only allows the computer to measure the current of the master without the use of extra equipment. Since we want to know 18

27 the total current driving the electromagnet, a multimeter was installed and connected to the computer through a separate GPIB cable. The multimeter is connected to the electrical setup via a shunt, so it measures the voltage and converts it to current using the rating of the shunt. Connections Between Power Supplies Each BOP has six main terminals on the back face. Four of these are used to create series and parallel connections between BOPs. They are called sense out (S+), out, common (com), and sense common (S-). Out and common act as the two source terminals for voltage and current. The sense terminals are usually used by the power supply as a feedback system to correct for discrepancies between to goal output and the actual output. There are two main ways to use the sense terminals: local sense and remote sense. In a local sense configuration, the sense terminals are connected directly to the source terminals of the power supply. In cases where there could be a significant voltage drop between the power supply and the load, remote sense connections are used. In remote sense, the sense terminals are connected with separate leads to the load input, which forces the power supply to counteract any voltage drop between the power supply and the load [7]. Our Master-Slave configuration is a complex arrangement of series and parallel power supplies, so both local and remote sense are used where appropriate. Our load is the electromagnet. 19

28 Having found no documentation of a similar power supply setup, we had to design the wiring required to achieve the series and parallel configuration shown in Figure 14. The connections were chosen by first considering how we would connect only two power supplies, either in series or in parallel. The two diagrams were then combined and the resulting connections were implemented in our actual electrical setup. In order to achieve a series connection, we want the voltages from the two power supplies to add. By Kirchhoff s voltage loop rule, we must connect the positive side of one supply to the negative side of the other, and attach the load across the remaining sides, as shown in Figure 15. Local sense is used for the short connection between power supplies, and remote sense is used for the longer leads to the load. Figure 15 Circuit diagram if two power supplies were set in series (left), and the back panel connections for the series connection (right). Our electromagnet has separate input and sense terminals. 20

29 In a parallel connection, the positive sides of two power supplies are connected together, and the two negative sides are connected. The load is connected between the positive and negative sides. Remote sense is used. This is shown in Figure 16. Figure 16 Circuit diagram if two power supplies were set in parallel (top), and the back panel connections to achieve the parallel connection (bottom). In our actual setup, the connection diagram is attained by combining the theoretical series and parallel diagrams. The connections are combined by using two series power supplies to replace each power supply in the parallel connection diagram. S1 and S3 are grounded together to ensure that there is no offset in voltage between the two parallel branches. The actual connection diagram is shown in Figure

30 Figure 17 Full diagram of the back terminal connections between the four power supplies and the load. Curved segments represent wires that cross, but do not connect. Each power supply also has a rear programming connector, Kepco model PC-12. These PC-12 circuit connectors can be wired for either local control (manually adjusting the front panel knobs) or remote control (computer input). Our PC-12s are wired for remote control. Two control terminals on the PC-12s for each of the Slaves are connected to the Master unit s PC LabVIEW Programming Measurements with the SMOKE are taken via a LabVIEW program. The program has two primary functions. First, controlling the Master BOP. Second, collecting and manipulating the data from the photodiodes and multimeter. 22

31 Controlling the Master BOP In this Master-Slave configuration, the LabVIEW program needs only to control the Master. Before the program is run to measure a magnetization loop, the user inputs the parameters of the loop, such as desired maximum and minimum voltages, initial voltage (generally zero), voltage step size, number of consecutively measured loops, and rate of data collection on the front panel (see Figure 18). For each loop, the Master voltage is increased steadily from the initial voltage to the maximum voltage (generally positive), then decreased to the minimum voltage (generally negative), and then increased back to the initial voltage. The voltage is varied in increments given by the user. This is repeated as many times as the user desires in order to get multiple loops. Figure 18 Front panel of the LabVIEW program for the SMOKE system. The white boxes prompt user input. (The top box for polarization deviation is only for the purpose of record keeping.) 23

32 Collecting and Manipulating the Data At each step in voltage, data is collected from the photodiodes and from the multimeter. The reading from the multimeter is converted to applied magnetic field via a previously determined calibration. This is plotted against the voltage measured by PD-2. This makes a raw hysteresis loop. The signal from PD-1 is used to normalize the signal. The raw, noise, and normalized signals are displayed on the front panel of the LabVIEW program. The LabVIEW program also performs many small calculations and conversions that are invisible to the user. The user can choose to export data files and images for the raw PD-2 signal, the PD-1 signal, and the normalized signal. The program can also export data files and images of multiple loops averaged together for both the raw and normalized signals. An example of this averaging can be seen in section

33 Chapter 3 Results In this chapter, I will present the results of several studies performed to optimize the performance of the SMOKE setup and evaluate the reliability of its measurements. These include studies of the ideal deviation (δ), polarizer (α), and incident (β) angles. I will also show the data manipulation process used to clean the measurements made by the SMOKE and compare a SMOKE measurement to a magnetization loop measured by an Extraordinary Hall Effect (EHE) magnetometer Selecting Value for delta As mentioned in section1.6, the analyzer is not set exactly at extinction with the polarizer. Instead, it is set at a small deviation angle, δ, from extinction. This is necessary for two primary reasons. The first reason is to allow us to approximate a linear relationship between the Kerr rotation and the measured light intensity, as explained in section 1.6. The second reason is to optimize the signal-to-noise ratio. The ideal δ for our sample was determined experimentally by measuring hysteresis loops over a range of deviation angles. All of the normalized hysteresis loops in Figure 19 were measured with the polarizer at the same fixed angle, but the analyzer was set for a different δ for each image. When δ changes sign, the loop also changes sign. 25

34 Normalized Signal Normalized Signal Normalized Signal H (G) H (G) H (G) H (G) H (G) H (G) H (G) H (G) Figure 19 Hysteresis loops measured with the polarizer fixed along the P polarization axis with varying δ angles. From the images above, we can estimate where δ becomes too small or too large. Near extinction at δ = 0 (Figure 19 (a)), very little light reaches PD-2, and the signal to noise ratio is weak. Consequently, the normalized signal is mostly flat. As δ increases, the signal begins to tilt (Figure 19 (b)), and starts to show a recognizable loop around δ = 6 (Figure 19 (c)). At δ = 10 (Figure 19 (d)), the signal starts to show the expected loop shape and features, and the noise can be significantly reduced through averaging. The signal becomes cleaner as δ is increased to 16, as shown in Figure 19 (e). When δ is increased further (Figures 19 (f) and (g)), a discrepancy arises between the saturation slopes for 26

35 Signal to Noise Ratio positive or negative field values, which prevents us from straightening the loop during later data manipulation. When delta is increased even further, loop becomes highly asymmetrical, as seen in Figure 19 (h). The ideal δ corresponds to a strong signal to noise ratio and a loop which is symmetric at the saturation slopes. The images above suggest that the ideal δ for our SMOKE system is between 10 and 16. This range of acceptable deviation angles is supported by an analysis of the signal to noise ratio for varying δ, as shown in Figure 20. As δ increases from 0, the signal to noise ratio increases overall, with a local maximum between 12 and 16. It then dips back below one. Oscillations are likely due to an asymmetrical distortion effect in the shape of the loop. The ratio then increases further as the two polarizers get further from extinction, reaching a higher peak between 25 and 40. However, an analysis of the loops at these higher δ angles shows that they are asymmetrical. Therefore, only the peak between 12 and 16 represents a desirable range of δ angles. 2.5 Signal to Noise Ratio vs δ Deviation Angle (degrees) Figure 20 Signal to noise ratio for varying δ, with the peak of the ideal range (δ = 0 ) circled in red. 27

36 Normalized Signal 3.2. Selecting the Incident Polarization Direction If the polarizer, rather than the analyzer, is offset, we notice that it introduces a slope in the hysteresis loop. This is particularly noticeable at extinction (δ = 0 ). Figure 21 shows SMOKE measurements for three different values of the polarizer angle (α), where the analyzer is adjusted to maintain a δ of zero. When the polarizer is set to only transmit P polarized light, the measurement is flat at extinction. When the light is no longer purely P polarized, the signal at extinction is not completely flat. Instead, the shape of the hysteresis loop is slanted. When the polarizer is set even further from the P axis, the slant in the hysteresis loop at extinction becomes much more pronounced. This result suggests that P and S polarized light experience different phase shifts upon reflection [8]. A combination of P and S polarized light would result in an elliptically polarized reflected beam, which can significantly distort the measurement. It is therefore important that the polarizer be aligned completely along either the P or S axis if one desires a loop that is not slanted. In my work, I have chosen to align the initial polarization along the P axis. H (G) H (G) H (G) Figure 21 Hysteresis loops measured for three different polarizer angles (α). The analyzer was adjusted to maintain δ=0. 28

37 3.3. Incident Angle Adjustments Initially, only one mirror was used in the mechanical setup, as shown in Figure 22. We also had a large sample holder which extended into the cavity between the magnet poles. This configuration limited our choices for the angle of incidence, β, of the beam on the sample. Our incidence angle for this setup was around β = 20 from the sample surface. Figure 22 Our initial SMOKE setup, using only one mirror and a thick sample holder. Beam path is shown. This setup also had limited space for the optical components. In order to achieve beam alignment, the components had to be within about 15 cm of the magnet poles. A measurement of the field at that point with a gaussmeter shows that, when 20 A are applied to the magnet, the laser experiences a significant magnetic field of kg. Indeed, we found that our laser intensity fluctuations 29

38 Normalizing Signal (mv) were dependent upon the magnetic field strength, resulting in a U shape in the PD-1 signal in Figure 23. Figure 23 Measurement of laser intensity fluctuations when the laser was close to a changing magnetic field. Our upgraded SMOKE setup uses four mirrors, and a very thin sample holder mounted directly on the pole of one of the magnets, as seen in Figure 24. This allows us much greater flexibility in our choice of incident angle. Our current angle is around β = 68 from the sample surface. This also allows us to mount the laser and other optical components much further from the magnet poles. The laser, mounted about 35 cm away from the magnet poles, experiences a reduced field of about 35 G when 20 A is applied to the magnet. This causes negligible field interference, as shown by the lack of a U shape in measurements of laser intensity fluctuations such as Figure

39 Figure 24 A photograph of our current mechanical setup for the SMOKE apparatus, which uses four mirrors and a thin sample holder. Inset image (upper right) shows close-up of the beam path at the sample. Figure 25 Laser intensity noise after the laser has been moved far away from the electromagnet poles. 31

40 3.4. SMOKE Measurement and Data Manipulation The recorded SMOKE data is cleaned via several steps: normalization, averaging multiple loops, straightening, and magnitude normalization, which are described in detail below. Normalization The signal from PD-1 (see Figure 26 (a)) is used to remove noise from laser intensity fluctuations from the raw detected signal (see Figure 26 (b)). This is done according to the equation - -, where the multiplication factor 1000 is used to artificially amplify the signal. Figure 26 (c) shows an example of a normalized signal. (a) (b) IPD-2 / IPD-1 *1000 PD-2 Signal (mv) PD-1 Signal (mv) Figure 26 (a) Raw signal measured by PD-2. (b) Noise from laser intensity drift measured by PD-1. (c) Loop after normalizing to remove laser intensity noise. 32 (c)

41 Averaged Signal Averaging Laser instability is the primary source of noise in our system, but other sources may also cause noise. Though experiments are run with the lights off, light in the room from the hallway and computer monitors may be present. Noise can also come from stray reflections of the laser beam, electrical interference from the magnetic field, or small motion of the sample due to the magnetic field. In order to minimize the effects of this noise, several hysteresis loops are recorded in succession and then, after normalization, they are averaged together. An example of an averaged signal is shown in Figure 27. Figure 27 The hysteresis loop after averaging two loops together. 33

42 Straightening The SMOKE is used to measure the magnetic response of magnetic samples to an external applied field. However, the measured hysteresis loops may also include unwanted diamagnetic signals, coming from the sample environment (sample holder, substrate, etc.). In diamagnetic materials, the magnetic moments of the domains tend to align antiparallel to the applied field. Therefore, diamagnetic signals introduce a negative slope. Compared to ferromagnetism, diamagnetism is a relatively weak effect, and it does not contribute to hysteresis. The diamagnetic component of the net magnetization is linear with applied field. This means that diamagnetic materials are expressed in our data as a negative linear signal added to the ferromagnetic hysteresis loop. This slope is most recognizable at the top and bottom of the loop, beyond saturation (see Figure 28). To remove the diamagnetic signal, we first perform a linear fit on the straight segments at the top and bottom of the loop. If the slopes match, we can assume that the slope is strictly a result of diamagnetism. We then subtract a line with the fitted slope from the entire hysteresis loop. This removes the diamagnetic signal, and leaves a pure ferromagnetic signal (see Figure 29). It also centers the loop around zero on the y-axis. We refer to this process as straightening the loop. 34

43 Figure 28 Linear fits are performed on the slopes of the straight segments near the two saturation points, one at a positive field value (top right) and one at a negative field value (bottom left). In this case, the slopes are equal. Height Normalization In the process of data manipulation, we lose our initial units (mv) and are left with arbitrary units (a.u.). Therefore, we normalize the height of the hysteresis loop to ±1 (see Figure 29). This allows us to compare the loop with measurements made by other magnetometers on the same sample. An example of such a comparison is given in Figure

44 Figure 29 Averaged, normalized, and straightened hysteresis loop Comparison to EHE Measurement The accuracy of the SMOKE measurement can be evaluated by comparing it to a measurement performed by a different magnetometer, such as VSM or EHE. Here, I will compare the SMOKE measurement to one performed via EHE. Both loops have been normalized to a height of ±1, and therefore the features of the loop can be compared directly. This comparison is shown in Figure

45 Figure 30 A comparison between measurements made on the same sample by SMOKE (left) and EHE (right). Grid lines are present to emphasize similar features. In the figure above, we can see that the basic shapes of the two hysteresis loops match. The SMOKE measurement scanned a larger field range than the EHE measurement, and therefore has longer straight segments above saturation. On both loops, saturation occurs around ±3000 G and nucleation is around ±1700 G. Though the SMOKE measurement still has some noticeable noise, we believe these could be eliminated by averaging more loops and taking more data points and using a smaller field step size. The matching features of the two loops lead us to an important conclusion for this thesis: the SMOKE is producing reliable measurements. These measurements are supported by those taken by other magnetometers. It appears that we have achieved a successfully functioning SMOKE apparatus. 37

46 Advantages of SMOKE Though the SMOKE and EHE loops in Figure 30 are comparable, SMOKE has an advantage over EHE. EHE is based on conduction and requires conducting samples. SMOKE, on the other hand, is based on magneto-optical effects and can be used to measure both conducting and non-conducting samples. This is important for my research group especially, as we have been studying Fe 3 O 4 (magnetite) nanoparticles. The SMOKE magnetometer has several other advantages. It allows relatively quick measurements, with a full loop taking about a minute and a half. It also does not need expensive liquid helium cooling, which is required by some other magnetometers such as the Vibrating Sample Magnetometer (VSM). Aside from the power supplies and electromagnet, the components that are used in the SMOKE assembly are relatively inexpensive Summary Using the basic principles outlined in chapter 1, we have developed a SMOKE magnetometer. The magnetometer apparatus consists of three major components: the mechanical setup, the electrical connections, and the LabVIEW programming, as explained in chapter 2. Through an analysis of hysteresis loops measured with various polarizer and analyzer angles, we can conclude that our ideal δ is between 10 and 16 and that our incident polarization should be entirely along either the P or S axis in order to minimize the distortion of the hysteresis loop. Our new optical setup has been shown to reduce magnetic 38

47 effects on laser intensity. A final comparison between SMOKE and EHE measurements suggests that we have successfully produced a functioning SMOKE magnetometer. 39

48 Bibliography [1] Faraday, Michael. Faraday's Diary. Volume IV, Nov. 12, June 26, 1847 (Thomas Martin ed.). London: George Bell and Sons, Ltd. ISBN (1933). [2] Kerr, John. "On Rotation of the Plane of the Polarization by Reflection from the Pole of a Magnet". Philosophical Magazine 3: 321 (1877). [3] Moog, E. R. and Bader, S. D., Superlattices Microstruct. 1, 543 (1985). [4] Qiu, Z. Q. and Bader, S. D., Surface magneto-optic Kerr effect. Rev. of Sci. Instrum. 71:3, (2000). [5] Bjørn, R. and Pedersen, K. B. Development of a Surface Magneto-Optic Kerr Effect Setup. Master s Thesis. Aalborg University: Denmark. (2011) [6] Landolt, G. COPHEE and SMOKE. Master s Thesis. Institute of Physics University of Zurich: Germany. (2010) [7] National Instruments, Local and remote sense. (2009, August). Retrieved from 01/ni_dc_power_supplies_help/local_and_remote_sense/ [8] Azzam, R. M. A. (1994). Ellipsometry, Handbook of optics. 1,16.2 (1994). 40