University of Florida | Journal of Undergradua te Research | Volume XX Issue Y | Summer 20 ZZ 1 Implementation of a Differential Hall Element Magnetometer Matthew W. Calkins, Elisabeth S. Knowles, and Mark W. Meisel Department of Physics and the National High Magnetic Field Laboratory, University of Florida, Gainesville, Fl 32611 8440 A Differential Hall Element Magnetometer, or DHEM, offers an alternative to a SQUID magnetometer for room temperature mag netic sample characterizations. A DHEM utilizes two Hall elements to measure the Hall voltage that can then be converted to magnetic moment of a sample The first generation DHEM 1.0, provided a proof of concept and the second generation DHEM 2.0 described herein, automated the data recording process an d incorporated a passive constant current device. Using a SQUID magnetometer, the DHEM 1.0, and the DHEM 2.0, the coercive field of a 333 mg speaker magnet sample was determined to be 2800 G, 2400 G, and 2800 G, respectively. A 30 mg speaker magnet sampl e was also characterized by the DHEM 2.0 in order to determine a figure of merit or dynamic range of the device A nonlinear response was observed and may be due to magnetoresistance in the voltage leads. Future work on this project will include a new sample mount and a wire organization system to reduce this effect INTRODUCTION Motivation A Differential Hall Element Magnetometer, or DHEM, offers a novel way to characterize magnet ic materials at room temperatures. A reliable and sensitive DHEM can be used in lieu of a Superconduct ing Q U antum Interference Device SQUID, magnetometer that can m ake more precise measurements at low temperatures. For example, many interdisciplinary projects with biologists and biochemists focus on isothermal, room temperature magnetization measurements that the DHEM can perform The first generation DHEM, called DHEM 1. 0, provided proof of concept and a second ge neration DHEM 2.0, has been constructed and is described in this pape r  The attempt to use commercially available and inexpensive Hall elements was inspired by the work of others using specialized units [ 2 ] Origins and Types of Magnetization There are three main types of magnetism that a material can exhibit namely diamagnetism, paramagnetism, and ferromagnetism. Diamagnetic materials have a net magnetic moment that is antiparallel to an applied magnetic field. Paramagnetic materials have a moment that is parallel to an applied field but this moment vanishes when the applied field is removed. Ferromagnetic materials also have a net moment that is parallel to the applied field but the moment may remain aft er the applied field is removed. A ha rd ferromagnetic material requires an applied field to return to zero magnetization after being fully magnetized. This applied field is called the coercive field. The maximum magnetization of a ferromagnetic material is k nown as magnetic saturation and the magnetization at zero applied field is called the rem antent magnetization. Hall Effect The Hall effect is commonly observed in semiconductors where a current in a magnetic field induces a voltage perpendicular to the current [ 3 ] The Hall effect arises from two forces on electrons, which are equal in equilibrium. A charge moving in a magnetic field feels a Lorentz force F m where (1) and q is the charge of the particle, v is its velocity, and B is the magnetic field. In the case of an electric current, q is the charge of an electron e. F or a material of cross sectional area A and electron density n t he drift velocity v d of electrons in a current I is (2) Combining Equations (1) and (2) yields (3)
M ATTHEW W. C ALKINS E LISABETH S. K NOWLES M ARK W. M EISEL University of Florida | Journal of Undergraduate Research | Volume XX Issue YY | Summer 20 ZZ 2 A charged particle experiences an additional force by the creation of a voltage potential perpendicular to the current due to the Hall effect This force, F H can be written as (4) where w is the width of the material and V H is the Hall voltage. The Lorentz and Hall force s Equations (3) and (4), are equal in equilibrium allowing the expression of the Hall voltage to be written as (5) where t is the thickness of the semiconductor. Experimental Apparatus Overview The ex perimental apparatus shown schematically in F igure 1, consists of an Oxford 9 T superconducting magnet charged to 2 T, a Hewlett Packard 3457A digital multimeter, a differential operational amplifier two H all elements, a constant current system a stepper motor with controller, and a LabVIEW program Figure 2 shows the stepper motor system. Oxford Magnet The Oxford superconducting magnet with a room temperature bore of 90 mm diameter and a maximum field of 9 T, creates an external magnetic field by maintaining a current through a superconducting solenoid. In order to keep the wires in the superconducting state, the magnet has a n jacket of liquid nitrogen (77 K) and an inner bath of liquid helium (4 K) Figure 2. The stepper motor system. The Hall Element Probe contains the two Hall elements and is swept through the magnet bore by the lead screw and stepper motor. Figure 1. Experimental configuration to measure a differential Hall voltage. The two Hall elements are shown with the current leads horizontal and the voltage leads vertical. The Improved Howland Current Pump, IHCP, was made in PHY 4802L Advanced Electronics Lab with the help of Marc Gold, my lab partner. The stepper motor boar d was made by D. M. Pajerowski .
I MPLEMENTATION OF A D IFFERENTIAL H ALL E LEMENT M AGNETOMETER University of Florida | Journal of Undergraduate Research | Volume XX Issue YY | Summer 20 ZZ 3 The magnet has two modes of operation charging and persistent which are toggled by means of a heater in intimate contact with a superconducting shunt When the heater is activated, the ch arging state is achieved, and t he current through the solenoid can be manipulated thereby resulting in a change of the magnetic field When the heater is deactivated, the magnet is in persistent current mode, and the current and field are stable. In this mode, the current leads, which are used to access the solenoid, can be removed. In the persistent state the current in the solenoid and the magnetic field remain as long as th e wires remain superconducting. The magnet boils off approximately 1% of the helium volume per day in the persistent state while the boil off rate is approximately 5 times higher in the charging state Thus, moving a probe through the magnetic field itself rather than charging the magnetic field saves time on helium transf ers and money on helium consumption Differential Hall Elements A Hall element is a four lead semiconductor unit that converts a magnetic field to a voltage by the Hall effect [ 4 ] The DHEM utilizes two Hall elements to measure the magnetization of a material. The Hall elements sit on top of a Bakelite p latform that holds the sample and con nects to the bottom of the lead screw The first Hall element is directly under the sample and outputs a voltage that is prop ortional to the strength of the external magnetic field supplied by the Oxford magnet, 0 H, and the field from the magnetization M, from the sample, or V H 1 0 H + M ( 6 ) The second Hall element only measures the external magnetic field and provides a voltage V H 2 0 H ( 7 ) The difference between these two voltages is taken by a differential op erational amp lifier circuit with no gain so ideally, its output is V H 1 V H 2 0 H + M 0 H = M ( 8 ) This differe ntial Hall voltage is read by a digital multimeter and recorded by LabVIEW. As seen in Eq uation 5 a constant input current to the Hall elements is required in order to make the output voltage of the Hall elements only proportional to the measured magnetic field. The constant current system consists of a constant voltage power supply and a n Improved Howland Current Pump or IHCP. Specifically, the IHCP, util izes an op erational amp lifier and resistors to convert a constant input volta ge from an Agilent E3614A power supply to a constant output current The resistors were chosen in such a way that a 1 V input would be converted to a 1 mA output. The Hall eleme nts are wired in series so the current through each element is equal Automation A linear stepper motor, stepper motor controller, and LabView provide a completely autonomous data acquisition proces s. The stepper motor is held 15 cm above the magnet by an aluminum framework and a 40 inch lead screw allows for sweeps to approximately 60 cm into the magnet. The stepper motor and controller board system has a resolution of 0.05 mm per step [ 6 ] Sample Characterization A sample was loaded into a gel cap and the gel cap was subsequently placed into a plastic straw. The plastic st raw was then inserted into the Hall element probe located at the end of the lead screw The sample was swept through the magnetic field to fully magnetize t he sample in one direction. The lead screw was then retracted and the sample was flipped 180 with respect to the axis of the magnetic field. The data acquisition run began with the digital multimeter reading the output voltage of the differential op erational amp lifier which was then recorded by LabVIEW. When the voltage readings were completed, LabVIEW moved the probe a specified distance via the controller board and stepper motor. The voltage was subsequently recorded at the new position and this process continue d until the probe was in the maximum field of the Oxford magnet, which is 55 cm into the magnet. The process was then reversed to sweep the probe out of the magnetic field and to 10 cm above the magnet which is essentially the zero appli ed field region Results and Analysis The magnetic field must be characterized in order to convert distance into the magnet to field strength. The Hall voltage of a single H all element was recorded during a sweep through the magnetic field. Then, the H a ll probe was kept at the point of maximum magnetic field of the magnet. The magnetic field was then charged from 0 to 2 T while recording the Hall voltage of the Hall element. The strength of the magnetic field as a function of distance into the magnet was calculated from these two data sets. Hall elements that are not perfectly matched will have slightly different H all voltages in the same field. This effect increases in highe r fields and produces a background that must be subtracted from sample characterizations. Additions to this background also come from nonzero Hall voltages in zero field and offsets in the differential
M ATTHEW W. C ALKINS E LISABETH S. K NOWLES M ARK W. M EISEL University of Florida | Journal of Undergraduate Research | Volume XX Issue YY | Summer 20 ZZ 4 Figure 4. Characterizations of the 333 mg speaker magnet sample by a SQUID, DHEM 1.0 and DHEM 2.0 with measured coercive fields of 2800 G, 2400 G, and 2800 G, respectively. The differential Hall voltage was converted to moment by setting the values of the remnant H all voltage of the DHEM and remnant magnetization from the SQUID equal to each other. op erational amp lifier circuit. This background signal shown in F igure 3 was measured by sweeping both Hall elements through the field with no sample and was subtracted from the sample characterizations A 333 mg speaker magnet was characterized by a SQUID magnetometer, the DHEM 1.0, and the DHEM 2.0, and these data sets are shown in Figure 4. The remnant magnetization measured by the SQUID and the remnant Hall voltage from the DHEM were used to convert differential Hall voltage to the cgs units of magnetization, emu G. The coercive field measured by the SQUID, the DHEM 1.0, and the DHEM 2.0 were 2800 G, 2400 G, and 2800 G, respectively. A 30 mg sample was also charact erized in order to find the smallest magnetization that the DHEM 2.0 system can measure and is shown in Figure 5 The measured coercive field was 2900 G. C onclusion s The addition of a stepper motor decreased the experimenter time required to complete a run from an hour to approximately five minutes. The stepper motor also allows a much higher density of data points than the DHEM 1.0, which could only take data every 1.0 cm. A decrease in fluctuations can be seen when comparing data sets from the two versions of the DHEM. For example, the high field region of the 333 mg speaker magnet data set for the DHEM 1.0 has 10 mV fluctuations while the DHEM 2.0 data set is smooth at this level The constant current source for the DHEM 1.0 was a power supply and digital multimeter that were controlled by LabV IEW. The multimeter would measure the voltage drop over a resistor and LabVIEW would adjust the output voltage of the power supply to keep the current through the resistor constant. This negative feedback loop created these fluctuations because the resol ution of the power supply was not sufficient to keep a constant 2 mA through the resistor and, thus, the Hall elements The IHCP that is part of the DHEM 2.0 system is does not display this Figure 5. DHEM 2.0 characterization of the 30 mg speaker sample. The nonlinear response may be due to magnetoresistance of the voltage leads in the magnetic field. Figure 3. The differential background of the DHEM 2.0 system.
I MPLEMENTATION OF A D IFFERENTIAL H ALL E LEMENT M AGNETOMETER University of Florida | Journal of Undergraduate Research | Volume XX Issue YY | Summer 20 ZZ 5 phenomenon The coercive fields measured by the SQUID and DHEM 2.0 of the 333 mg speaker magnet agreed to two significant digits and were both 2800 G. The coercive field of the 30 mg sample was 2900 G. Smaller samples were run but they shifted with respect to the Hall elements during the sweep through the magne tic field. The nonlinear response observed in the differential background and sample data is most likely due to magneoresistance in the voltage wires of the Hall elements. The differential background cannot be used to subtract this effect because it depe nds on how the wires move in the magnetic field, which is different for every run. The DHEM 1.0 did not have this problem because the wires were always kept parallel to the magnetic field. Future work will involve designing and implementing a new sample mount that is able to hold smaller samples. The figure of merit can be further improved by eliminating magetoresistance in the voltage leads via organizing the wires to stay parallel to the magnet field Acknowledgements This research was supported by the National Science Foundation (NSF) via DMR 1202033 (MWM), DMR 1157490 (NHMFL), and the UF University Scholars Program. Early contributions by Alex M. Sincore and Yitzi M. Calm are recognized, and the decisive assistance from the UF Physics Cryogenics, Electronics, and Instrument Manufacturing Shops are gratefully acknowledged. REFERENCES  A. Sincore, P. A. Quientero Cabra, S. M. Gilbert, E. S. Knowles, and M. W. Meisel, Differential Ha ll Element Magnetometer for Room Temperature Magnetization Measurements ,(2010, unpublished) available at http://www.magnet.fsu.edu/education/reu/program/2010/posters/ Alex% 20SinSinc_2010%20REU_Poster.ppt  G Xiong, S von Molnr, K Ohtani, H Ohno, M Field, and G Sullivan Detection of single magnetic bead for biological applications using an InAs quantum well micro Hall sensor Appl. Phys. Lett. 87, 112502 (2005); http://dx.doi.org/10.1063/1.2043238 (3 pag es)  H. Young and R. Freedman, University Physics 12 th Ed. ( Pearson, San Francisco, CA, 2008) pp. 943 944. [ 4 ] HQ 0111 Hall Element Datasheet [ 5 ] D. M. Pajerowski, Photoinduced magnetism in nanostructures of prussian blue analogues (Univers ity of Florida, Gainesville, Fl ., 2010) available at http://www.phys.ufl.edu/~dpaj/THESIS.pdf, specifically see Ch.2, p. 70 [ 6 ] Size 17 Linear Non Captive Stepper Motor see: http://www.haydonkerk com/ inearActuatorProducts/StepperMotorLinearActuators/LinearActuators Hybrid/Size17LinearActuator/tabid/79/Default.aspx#Stepper_Motor_Linear _Actuator_noncaptive>