Approval Record NORTHEASTERN UNIVERSITY. Graduate School of Engineering

Approval Record NORTHEASTERN UNIVERSITY Graduate School of Engineering Thesis Title: Dynamic Magnetostrictive Response of Heterostructural Magnetoelectric Magnetic Field Sensors. Author: Scott Matthew Gillette Department: Electrical and Computer Engineering Approved for Thesis Requirement of the Master of Science Degree Thesis Adviser: Vincent Harris Thesis Reader: Carmine Vittoria Thesis Reader: Yajie Chen Thesis Reader: Anton Geiler Department Chair: Date Date Date Date Date Graduate School Notified of Acceptance: Director of the Graduate School: Yaman Yener Date

Dynamic Magnetostrictive Response of Heterostructural Magnetoelectric Magnetic Field Sensors. A Thesis Presented by Scott Matthew Gillette to The Department of Electrical and Computer Engineering in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering in the field of Electromagnetics, Plasma, and Optics Northeastern University Boston, Massachusetts April, 2011

Abstract Magnetoelectric (ME) heterostructural laminate composites have recently demonstrated high sensitivity room temperature operation in magnetic field sensing applications. Traditionally, a static (dc) magnetic field is applied to these sensors to enable peak magnetostriction. In this thesis, the non-linear nature of the magnetostrictive response of a ME heterostructure is utilized, by applying a modulation magnetic field, to demonstrate a peak improvement by a factor of 11.62x in sensitivity and by 57.43 db in 0-Hz signal-to-noise ratio of a sensor consisting of a longitudinally magnetized and transversely poled lamination of Metglas/PZT/Metglas layers in comparison with a conventional dc biased configuration. The ME sensor modulated by an AC magnetic field tuned to stimulate an electro-magneto-mechanical resonance further exhibits enhanced environmental noise immunity, 1/f noise mitigation, and does not require a dc magnetic bias field. Combined, these advantages hold promise for the development of miniature ME sensor elements for size- and weight-sensitive applications. i

Acknowledgements I begin by thanking my advisor, Professor Vince Harris, for giving me the opportunity to work at Northeastern University s Center for Microwave Magnetic Materials and Integrated Circuits for the past two years. He has generously shared his time and knowledge to guide me through a challenging, invaluably rewarding M.S. program. Thank you! I extend a thank you to Carmine Vittoria and Yajie Chen for their help and encouragement during the past two years. I thank Anton Geiler for acting as a mentor and for providing his expertise on numerous research efforts. I thank Carmine Carosella and Dwight Viehland for providing the magnetoelectric magnetic field sensors. Finally, I thank all of my colleagues, my family, friends and my fiancée, Steph, for their support and encouragement. Thank you all very much. ii

Table of Contents Abstract... i Acknowledgements... ii Table of Contents... iii Table of Figures... v Table of Tables... ix Chapter 1. Introduction... 1 1.1. Introduction to Thesis... 1 1.2. Phenomena Background... 2 1.3. The Magnetoelectric Effect... 11 1.4. Strain Coupled Magnetoelectric Composites... 14 1.5. ME Laminate Composites as Magnetic Field Sensors... 21 Chapter 2. Conventional DC Operation... 27 2.1. Introduction and Theory... 27 2.2. Experimental Setup... 29 2.2.1. DC Biasing Method Equipment List... 29 2.2.2. DC Biasing Method Block Diagram and Equipment Overview... 30 2.2.3. DC Biasing Method Experimental Procedure... 35 2.3. Results and Analysis... 37 2.3.1. Sensor 1 Results... 39 2.3.2. Sensor 2 Results... 43 2.4. Conclusion... 47 Chapter 3. Modulation Sensing Technique... 48 3.1. Introduction and Theory... 48 3.1.1. Motivation... 48 3.1.2. Relationship Between Strain and Applied Magnetic Field.... 49 3.1.3. Mathematical Theory of Modulation Sensing Technique.... 53 3.2. Experimental Setup... 59 3.2.1. Modulated Sensing Technique Equipment List... 59 iii

3.2.2. Modulated Sensing Technique Block Diagram and Equipment Overview... 61 3.2.3. Modulated Sensing Technique Experimental Procedure... 64 3.2.4. Noise Study and Resulting Experimental Setup Modifications... 68 3.3. Results and Analysis... 74 3.3.1. Sensor 1 Results... 75 3.3.2. Sensor 2 Results... 80 3.4. Conclusion... 84 Chapter 4. Conclusion... 85 4.1. Future Research Plans... 87 Appendix... 89 A.1. Example Data File... 89 A.2. Matlab Code DC Biasing Method... 90 A.3. Matlab Code Modulated Sensing Technique... 95 References... 101 iv

Table of Figures Figure 1: Magnetic field density vs. applied magnetic field hysteresis loop for a polycrystalline slab of ferromagnetic Yttrium Iron Garnet measured at room temperature using CM3IC s vibrating sample magnetometer.... 3 Figure 2: Charge, representing polarization vs. electric field hysteresis loop for a ferroelectric Rochelle salt crystal at 23º C and a relative humidity of 30%. This P-E loop 2 demonstrates the first measurement of ferroelectricity and proved the existence of the ferroelectric phenomenon... 5 Figure 3: Piezoelectric strain response as a function of applied electric field for two different aspect ratios of thin film Lead Zirconate Titanate (PZT) substrates. ε 33 indicates that both applied electric field and measured strain were in the Z-axis of the substrate.... 7 Figure 4: Magnetization and strain for TERFENOL-D as a function of applied magnetic field. The derivative of magnetostriction is plotted with the dashed line.... 8 Figure 5: a) A commercial piezoelectric microphone guitar pickup fabricated by Artec. b) A commercial piezoelectric precision actuator capable of micron resolution manufactured by Physik Instruments.... 10 Figure 6: a) A magnetostrictive audio transducer that allows a surface, such as a table, wall, or window, to act as a speaker. This commercially available device uses the magnetostrictive material TERFENOL-D and is fabricated by FeONIC. b) A commercial magnetostrictive linear position sensor, with micron resolution, produced by MTS Sensors.... 10 Figure 7: Direct interactions between stress (σ) and strain ( ), electric field (E) and polarization (P), and magnetic field (H) and magnetization (M), are illustrated with the red, yellow, and blue arrows, respectively. In a single phase multiferroic magnetoelectric material (green arrows), electric field is directly coupled to magnetic field. In many multiferroic magnetoelectric devices, strain-coupling (black arrows) between magnetostrictive and piezoelectric phases provides the magnetoelectric effect.... 11 Figure 8: a) A PZT/Metglas multiferroic magnetostrictive composite, mounted to a Mylar slab, fabricated by Bolin Hu at Northeastern University's CM3IC. This image shows the leads attached for measuring the magnetoelectric effect. b) Cross-sectional view of the PZT/Metglas composite fabricated through pulse laser deposition of a PZT target onto a polished Metglas sheet. Not drawn to scale.... 14 Figure 9: a) A Metglas/PZT/Metglas multiferroic magnetostrictive laminate provided by Carmine Carousella, mounted to a Teflon slab. The dime is provided for size reference. b) Cross-sectional view of the Metglas/PZT/Metglas heterostructure. The v

Metglas strains under an applied magnetic field causing a strain-induced electric field transverse to the PZT. Not drawn to scale.... 15 Figure 10: Magnetoelectric multilayer fabricated through epitaxial growth of NiFe 2 O 4 (NFO) on BaTiO 3 (BTO) on a SrTiO 3 (STO) substrate. The interfaces are emphasized using horizontal lines.... 16 Figure 11: ME coupling coefficient of a heterostructural Metglas/polyvinylidene-flouride magnetoelectric laminate composite magnetic field sensor.... 20 Figure 12: Metglas/PZT/Metglas laminated heterostructural composite, provided by Carmine Carousella, held by tweezers to enable resonance bending modes during testing. Length, height, and thickness dimensions are indicated.... 23 Figure 13: Metglas/Poled-PZT/Metglas laminated heterostructural composite with interdigitated electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the length) dimensions are indicated.... 24 Figure 14: D31 and D33 mode operation of piezoelectric PZT. For the D31 mode, a longitudinally applied strain results in a transversely generated voltage response. For the D33 mode, a longitudinally applied strain results in a longitudinally generated voltage response. Directions 3 and 1 are denoted on the axis.... 25 Figure 15: Example of an interdigitated electrode geometry. Interdigitated electrodes are typically used in ME laminates where the piezoelectric phase is to be operated in a D33 mode, as exemplified by Sensor 2.... 26 Figure 16: Magnetostriction of Metglas shown on +-1000 Oe scale (left) and a +-75 Oe scale (right) to exhibit a peak magnetostriction of approximately 27.5 ppm and a maximum in slope (dλ/dh) at 40 Oe.... 28 Figure 17: Slope of Metglas magnetostriction curve exhibiting a maximum at approximately 40 Oe.... 28 Figure 18: DC biasing method experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5 floppy disk, and the LakeShore Model 4060 Zero Gauss Chamber are not numbered in figure.... 30 Figure 19: Block diagram of the experimental setup for the DC biasing method.... 31 Figure 20: The sensor mounting apparatus consists of a table top vice grip and a set of tweezers fabricated from non-magnetic materials. It is shown positioning a sensor inside the dual Helmholtz coils.... 34 Figure 21: Signal-to-noise ratio as a function of applied magnetic field for Sensor 1.... 39 Figure 22: Sensitivity as a function of applied magnetic field for Sensor 1.... 39 Figure 23: 0-Hz noise floor as a function of applied magnetic field for Sensor 1.... 40 vi

Figure 24: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of log scale.... 41 Figure 25: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of linear scale.... 42 Figure 26: Signal-to-noise ratio as a function of applied magnetic field for Sensor 2.... 43 Figure 27: Sensitivity as a function of applied magnetic field for Sensor 2.... 43 Figure 28: 0-Hz noise floor as a function of applied magnetic field for Sensor 2.... 44 Figure 29: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of log scale.... 45 Figure 30: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of linear scale.... 46 Figure 31: (a) Magnetostriction in Metglas. (b) Slope of magnetostriction (dλ/dh). (c) Overlay of Livingston's model of coherent rotation of magnetization with the magnetostriction of Metglas for low amplitudes of applied magnetic field.... 51 Figure 32: (a) 58 KHz reference modulation magnetic field as sensed by Sensor 1. (b) 200 Hz test field modulated with the 58 KHz reference modulation field as sensed by Sensor 1. Part (b) indicates that the total applied H term is indeed squared.... 52 Figure 33: Amplitude of the modulation field as a function of the detected 25 Hz test signal amplitude. This plot demonstrates that Hmod acts as a linear gain factor.... 59 Figure 34: Modulated sensing technique experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5 floppy disk, LakeShore Model 4060 Zero Gauss Chamber, and variable capacitor bank are not numbered in figure.... 61 Figure 35: Block diagram of the experimental setup for the modulated sensing technique.... 62 Figure 36: Voltage spectral density measurements captured of the lock-in amplifier output, representing the instruments electronic noise, compared with VSD measurements of Sensor 2. Numbers 1-4 represent capture number where each capture consists of 500 linearly averaged sweeps... 70 Figure 37: Voltage spectral density measurements captured of the lock-in amplifier output, representing the instruments electronic noise, compared with VSD measurements of Sensor 1. Numbers 1-4 represent capture number where each capture consists of 500 linearly averaged sweeps... 71 Figure 38: Voltage spectral density measurements of 4 configurations showing contributions to the noise floor. The output of the lock-in amplifier is transmitted to the digital spectrum analyzer for each configuration. The modulated sensing technique with a 5 vii

KHz modulation frequency and 200 Hz test signal is shown in blue. The green trace was measured from a setup with 5 KHz modulation field and no test field. The red trace was measured from a setup with no modulation field and a 200 KHz test field. The teal trace was measured from a setup with no input and represents the lock-in amplifiers instrumental electronic noise floor.... 73 Figure 39: Signal-to-noise ratio as a function of modulation frequency for Sensor 1.... 75 Figure 40: Sensitivity ratio as a function of modulation frequency for Sensor 1.... 76 Figure 41: 0-Hz noise floor as a function of modulation frequency for Sensor 1.... 76 Figure 42: Magnetic Spectral Density with respect to modulation frequency. X-axis is of log scale.... 78 Figure 43: Magnetic Spectral Density with respect to modulation frequency. X-axis is of linear scale.... 79 Figure 44: Signal-to-noise ratio as a function of modulation frequency for Sensor 2.... 80 Figure 45: Sensitivity as a function of modulation frequency for Sensor 2.... 80 Figure 46: 0-Hz noise floor as a function of modulation frequency for Sensor 2.... 81 Figure 47: Magnetic Spectral Density with respect to modulation frequency. X-axis is of log scale.... 82 Figure 48: Magnetic Spectral Density with respect to modulation frequency. X-axis is of linear scale.... 83 Figure 49: Full comparison between DC biasing method and modulation sensing technique.... 85 viii

Table of Tables Table 1: Piezoelectric Material Properties.... 18 Table 2: Magnetostrictive Material Properties.... 19 Table 3: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1... 40 Table 4: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2... 44 Table 5: Modulation Sensing Technique: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1.... 77 Table 6: Modulation Sensing Technique: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2.... 81 Table 7: Comparison of DC Biasing Method to Modulated Sensing Technique.... 86 ix

Chapter 1. Introduction 1.1. Introduction to Thesis The research presented in this thesis focuses on the use of multiferroic magnetoelectric laminates as magnetic field sensors with a strong focus on the development of a modulation sensing technique for use with these sensors. The newly developed modulation sensing technique exhibits greater signal-to-noise ratio (SNR), higher sensitivity, and a reduction in noise floor compared to measurements made using the conventional static magnetic field biasing method for experimentally identical environments. The modulated sensing technique also offers improvements over the conventional static magnetic field biasing technique, herein referred to as the DC biasing method, by providing superior noise mitigation and a reduction in lowfrequency 1/f noise. Presentation, results, analysis, and discussion of the modulated sensing technique developed at Northeastern University s Center for Microwave Magnetic Materials and Integrated Circuits (CM3IC) are the primary topics being reported. This thesis consists of four chapters that discuss the following topics. In Chapter 1 the origin, operational phenomena, fabrication techniques, and applications of multiferroic (MF) magnetoelectric (ME) devices are explained. In addition, a description of two state of the art prototypes, used for making measurements in this thesis, is provided. In Chapter 2, the conventional DC biasing method of MF ME laminates in a magnetic field sensing application is explained and presented with measurements using this method captured at CM3IC. Chapter 3 explains the modulated sensing technique designed for use with MF ME laminates in a magnetic field sensing application and presents its theory, development, and performance. Being the 1

primary focus of this thesis and offering the most value to the scientific community, Chapter 3 includes discussion of the evolution of the modulated sensing technique by detailing a noise floor study and resulting modifications made to the experimental setup. Chapter 4 concludes this thesis with a general overview of the research, its implications, and future work. 1.2. Phenomena Background The phenomenon of ferromagnetism, which is described as the ability of a material to exhibit net magnetic moment under the influence of an applied magnetic field, and its analogue phenomenon of ferroelectricity, which is described as the ability of a material to exhibit electric polarization under the influence of an applied electric field, have been widely investigated since their discoveries in ancient times 1 and in 1920 2, respectively. According to Chikazumi, ferromagnetism was first discovered when a shepherd s staff, containing iron, experienced an attractive force when placed nearby a certain type of stone. This discovery, representing mankind s initial conscious encounter with a magnetic force was believed to occur in Asia Minor, in either Magnesia, Macedonia or in Magnesia, Ionia whose location is speculated to lend its name to the origin of the word magnetism. One of the first applications utilizing magnetism came in the form of a compass where splinters of the magnetic stone, known at the time as loadstones, were used to determine direction due to the stone s ability to align itself with Earth s magnetic poles 1. In present day, the phenomenon of ferromagnetism is a widely studied topic in academia 3,4,5,6 and numerous applications utilizing ferromagnetic materials, such as electronic motors, generators, inductors, transformers, hard drives, etc. surround our daily life. 2

Ferromagnetic materials (and ferrimagnetic materials) possess long range magnetic ordering where magnetic domains are aligned in a manner such that the bulk material exhibits a net magnetic moment. Ferromagnetic materials are typically quantified in the form of a B-H loop, as shown in Figure 1, where magnetism (magnetic flux density) is plotted as a function of applied magnetic field. Figure 1: Magnetic field density vs. applied magnetic field hysteresis loop for a polycrystalline slab of ferromagnetic Yttrium Iron Garnet measured at room temperature using CM3IC s vibrating sample magnetometer. As the applied magnetic field amplitude increases, magnetic domains increasingly align until they become fully oriented resulting in saturation of the magnetic field density. The permeability of a ferromagnetic material is responsible for this nonlinear dependence to applied 3

magnetic field H. Equation (1.1) describes the relationship between magnetic field density B, permeability μ, magnetic field H, and magnetization M 7. (1.1) For materials with weak magnetic ordering, permeability will linearly relate B to H. However, for ferromagnetic materials, permeability is a complex non-linear relationship. Many ferromagnetic materials are characterized by non-linear permeability exhibiting time-dependence resulting in a B H loop with hysteretic nature as seen in Figure 1. Ferromagnetic materials may sometimes be known as hard magnetic materials where a very large applied magnetic field is required to fully magnetize or saturate the material. Hard magnetic materials exhibit high coercivity and high remanence, making them useful in permanent magnet applications, among many. Ferrimagnetic materials may be known as soft magnetic materials due to their ability to be magnetically saturated under low applied magnetic fields. Soft magnets exhibit low coercivity, and are useful in switched electromagnet applications, among many. Metglas is an example of a soft magnetic material and is used in the sensors that are investigated in this thesis due to the material s ability to become magnetically saturated under relatively low applied magnetic fields. The theorized phenomenon of ferroelectricity was proven to exist by J. Valasek at the University of Minnesota in 1920 when he demonstrated that, like the hysteretic nature of magnetization in iron, a hysteretic electric polarization exists in Rochelle salt crystals under switched values of applied electric field 2 as shown in 4

Figure 2. Permittivity in a ferroelectric material exhibits a nonlinear dependence on applied electric field, E, and time, resulting in hysteretic behavior. Figure 2: Charge, representing polarization vs. electric field hysteresis loop for a ferroelectric Rochelle salt crystal at 23º C and a relative humidity of 30%. This P-E loop 2 demonstrates the first measurement of ferroelectricity and proved the existence of the ferroelectric phenomenon. This discovery has spurred vast new fields of research including tunable ferroelectric capacitors 8, where the permittivity of the dielectric spacing in a capacitor can be tuned by applying a DC voltage, and ferroelectric tunnel field effect transistors capable of unpowered memory state-retention up to a few minutes 9. 5

Ferroelectric materials behave in an analogous manner to ferromagnetic materials in that electric dipoles will align under the influence of an applied electric field. Ferroelectrics will also exhibit continuously increasing dipole alignment under increasing amplitudes of applied electric field until the dipoles become fully aligned, representing a state of saturation. The relationship between applied electric field E, electric flux density D, and polarization P is described through equation (1.2) 7. (1.2) Ferroelectricity and ferromagnetism enable the manipulation of polarization and magnetization, through the application of respective E and H fields. There also exist the phenomena of piezoelectricity and magnetostriction in which polarization and magnetization, respectively, are tightly coupled to the material s atomic lattice. Atomic lattice coupling with polarization and magnetization also exists in the forms of electrostriction and piezomagnetism; however, these phenomena are not discussed in this thesis. Piezoelectricity is defined as the ability of a material to exhibit coupling between polarization and strain, therefore enabling a coupling between strain and applied electric field. A piezoelectric material will undergo bulk dimensional deformation correlating to an applied electric field as demonstrated by the butterfly-shaped piezoelectric response curve of thin film lead zircon titanate (PZT) in Figure 3. 6

Figure 3: Piezoelectric strain response as a function of applied electric field for two different aspect ratios of thin film Lead Zirconate Titanate (PZT) substrates 10. ε 33 indicates that both applied electric field and measured strain were in the Z-axis of the substrate. The general constitutive equations for a piezoelectric material, (1.3) and (1.4), mathematically describe strain and electric displacement, respectively 11. (1.3) (1.4) 7

The strain, is defined as the axial change in length divided by original length. The magnetic flux density is denoted by D and E is the applied electric field. Variables, and represent the material s remnant strain and polarization, respectively. The elastic compliance tensor, the piezoelectric tensor, and the dielectric permittivity tensor are defined by the material s properties 11. Magnetostriction describes ferromagnetic materials with the ability to exhibit coupling between magnetization and strain, thus providing a coupling of strain to applied magnetic field. A magnetostrictive material will undergo bulk dimensional deformation correlating to an applied magnetic field 6 as demonstrated by the magnetostriction curve in Figure 4. Figure 4: Magnetization and strain for TERFENOL-D as a function of applied magnetic field. The derivative of magnetostriction is plotted with the dashed line 12. 8

The general constitutive equations for a magnetostrictive material, (1.5) and (1.6), mathematically describe strain and magnetization, respectively 13. (1.5) (1.6) Here, strain equals the axial change in length divided by length. The compliance tensor is denoted by. The applied stress T is in units of force per unit area. The magnetostrictive strain constant is d. The permeability tensor is denoted by. H is the applied magnetic field and B is the magnetic flux density. The strain coupling in both piezoelectric and magnetostrictive materials operates in a reverse manner such that an applied strain will generate net polarization or magnetization, respectively. The ability to manipulate the dimensions of a piezoelectric material by an applied electric field and a magnetostrictive material by an applied magnetic field, or to generate respective electric and magnetic fields by applying strain, has proven useful in numerous applications. Piezoelectric materials are currently used in commercial devices such as instrument microphone pickups or precision electrostatic actuators as shown in Figure 5. Magnetostrictive materials may be found in commercial devices such as audio transducers and linear position sensors as shown in Figure 6. 9

Figure 5: a) A commercial piezoelectric microphone guitar pickup fabricated by Artec 14. b) A commercial piezoelectric precision actuator capable of micron resolution manufactured by Physik Instruments 15. Figure 6: a) A magnetostrictive audio transducer that allows a surface, such as a table, wall, or window, to act as a speaker. This commercially available device uses the magnetostrictive material TERFENOL-D and is fabricated by FeONIC 16. b) A commercial magnetostrictive linear position sensor, with micron resolution, produced by MTS Sensors 17. 10

1.3. The Magnetoelectric Effect The magnetoelectric effect is defined as the ability to induce magnetization through an applied electric field and/or to induce polarization through an applied magnetic field 6. This effect can be enabled due to direct coupling of electric field to magnetization, magnetic field to polarization, polarization to magnetization, or indirectly via strain as illustrated in Figure 7. Figure 7: Direct interactions between stress (σ) and strain ( ), electric field (E) and polarization (P), and magnetic field (H) and magnetization (M), are illustrated with the red, yellow, and blue arrows, respectively. In a single phase multiferroic magnetoelectric material (green arrows), electric field is directly coupled to magnetic field. In many multiferroic magnetoelectric devices, strain-coupling (black arrows) between magnetostrictive and piezoelectric phases provides the magnetoelectric effect 18. 11

The direct magnetoelectric effect (DME) describes magnetic field induced polarization as shown in equation (1.7). (1.7) The converse magnetoelectric effect (CME) describes electric field induced magnetization as shown in equation (1.8) 19. (1.8) The direct magnetoelectric coupling coefficient α, defined in units of, serves as the conventional figure of merit for quantifying the magnitude of the magnetoelectric effect present in a magnetoelectric device. The magnetoelectric effect may exist in single phase multiferroic materials that can be both electrically and magnetically polarized, where the term multiferroic denotes a material that exhibits two or more combinations of ferroic orders, such as ferroelectric and ferromagnetic ordering 19. The magnetoelectric effect may also be enabled by fabricating bulk combinations of piezoelectric and magnetostrictive materials together in a strain-coupled manner, illustrated by the black arrows in Figure 7. Few single phase multiferroic magnetoelectric materials exist that exhibit useful magnitudes of magnetoelectric coupling, and if so, the coupling is typically exhibited at very low temperatures making these materials impractical for engineering problems 20. Currently, strain-coupled magnetoelectric composites consisting of a bulk single phase magnetostrictive material with a bulk single phase piezoelectric material have demonstrated direct magnetoelectric coupling coefficients on the order of 100, 12

which is several orders of magnitude higher than reported coefficients of single phase multiferroic magnetoelectrics 19. For this reason, strain-coupled magnetoelectric composites, exhibiting large magnetoelectric coupling coefficients at room temperature hold great potential for the development of applications utilizing magnetoelectric effect. In composites of magnetostrictive and piezoelectric materials the direct magnetoelectric effect is the result of the product of the respective magnetomechanical and electromechanical strain interaction as described in equation (1.9) 19. (1.9) Similarly, the converse magnetoelectric effect is the product of each phase s strain interaction as describe d in equation (1.10). 1.10 Equations (1.9) and (1.10) indicate that strain transfer is responsible for the generation of either the DME or CME. For instance, if a magnetoelectric composite is exposed to a magnetic field represented by the numerator in the first term of (1.9), the magnetostrictive phase will deform due to induced strain, represented by the denominator of the first term in (1.9). The magnetostrictively induced strain will transfer to the piezoelectric phase, causing a mechanical deformation, represented by the numerator of the second term in (1.9), and generate a separation of charge resulting in polarization, as represented by the denominator of the second term in (1.9). 13

This research presented in this thesis utilizes laminated composites that obtain the magnetoelectric effect through strain coupling between separate bulk magnetostrictive and piezoelectric materials. For more information on single phase multiferroic magnetoelectric materials that exhibit direct coupling between constituents, the reader is encouraged to seek out related literature 6, 21, 22, 23, 24. 1.4. Strain Coupled Magnetoelectric Composites Optimal strain coupling requires intimate contact between the magnetostrictive and piezoelectric phases which is typically achieved through direct deposition, lamination, or epitaxial growth fabrication techniques as shown by the examples in Figure 8, Figure 9, and Figure 10, respectively. Figure 8: a) A PZT/Metglas multiferroic magnetostrictive composite, mounted to a Mylar slab, fabricated by Bolin Hu at Northeastern University's CM3IC. This image shows the leads attached for measuring the magnetoelectric effect. b) Cross-sectional view of the PZT/Metglas composite fabricated through pulse laser deposition of a PZT target onto a polished Metglas sheet. Not drawn to scale. 14

Direct deposition magnetoelectric composite devices exhibit a distinct interface between piezoelectric and magnetostrictive phases which enables direct strain coupling. These composites are typically made through chemical vapor deposition or pulsed laser deposition of a magnetostrictive phase onto a piezoelectric phase (or vice-versa) and exhibit a thin-film on substrate topology. Figure 9: a) A Metglas/PZT/Metglas multiferroic magnetostrictive laminate provided by Carmine Carousella, mounted to a Teflon slab. The dime is provided for size reference. b) Cross-sectional view of the Metglas/PZT/Metglas heterostructure. The Metglas strains under an applied magnetic field causing a strain-induced electric field transverse to the PZT. Not drawn to scale. A magnetoelectric laminate consists of two or more magnetostrictive and piezoelectric phases bonded together using an adhesive that enables strain coupling. The adhesive plays an important role in transferring strain between ferroic phases and its mechanical properties must be considered. In addition, certain laminate topologies such as the one in Figure 9, require that the 15

adhesive is conductive, allowing the Metglas to serve the dual purposes of magnetostrictive phase and electrodes. Magnetoelectric laminate composites are abundant in literature due to ease of fabrication. Figure 10: Magnetoelectric multilayer fabricated through epitaxial growth of NiFe 2 O 4 (NFO) on BaTiO 3 (BTO) on a SrTiO 3 (STO) substrate 25. The interfaces are emphasized using horizontal lines. A magnetoelectric composite fabricated using epitaxial growth techniques exhibits atomic lattice matching of magnetostrictive and piezoelectric phases. This intimate crystallographic interface between phases results in favorable strain coupling. Epitaxially-grown magnetoelectrics are not as common as laminates due to the complex fabrication process which requires that each phase exhibits similarly sized crystal lattices. This requirement also limits the combinations of compatible magnetostrictive and piezoelectric materials. 16

Strain coupled magnetoelectric composites can be described using the following constituent equations, (1.11), (1.12), and (1.13), that relate magnetoelectric and piezoelectric phases through elastic interaction 19. (1.11) (1.12) (1.13) For equations (1.11), (1.12), and (1.13), σ, D, and B represent stress, electric displacement, and magnetic induction, respectively. S, E, and H are the strain, electric field, and magnetic field, respectively. Tensors c, e, q, ε, α, and μ, are the stiffness, piezoelectric coefficient, piezomagnetic coefficient, dielectric constant, magnetoelectric coefficient, and permeability, respectively, are determined by the choice of materials used in the composite. The superscript T denotes the transpose of the tensor 19. Properties of several common piezoelectric and magnetostrictive materials used in magnetoelectric composites are shown in Table 1, and Table 2, respectively 26. For Table 1, d 31 and d 33 represent piezoelectric constants, ε is the permittivity, T c is the Curie temperature, ρ is density, Q m is the mechanical quality factor, and k 33 is the electromechanical coupling factor. 17

The piezoelectric material PZT and magnetostrictive material Metglas have been widely investigated in a heterostructural laminate composite topology 26. PZT exhibits a relatively high piezoelectric constant, resulting in higher polarization per input strain than BTO and PVDF. In addition, PZT is abundant and inexpensive. Metglas exhibits relatively low magnetostriction, however, it is easily saturated by low amplitude applied magnetic fields due to high permeability. Unlike Terfenol-D that has a magnetostriction of 1400 parts per million and requires bias fields on the order of 2500 Oe, Metglas exhibits 40 ppm magnetostriction at less than 10 Oe applied bias magnetic field. The magnetoelectric laminate composites investigated in this thesis consist of Metglas and PZT phases. Table 1: Piezoelectric Material Properties. BaTiO 3 PZT-5 PZT-4 PZNPT PMNPT PVDF d 31 (pc/n) -90-175 -109 N/A 700 16.5 d 33 (pc/n) 191 400 300 N/A 2000-33 ε 1700 1750 1350 7200 5000 10 T c (ºC) 152 360 320 163 80 129 ρ(g/cm 3 ) 6 7.7 7.6 8.2 7.8 1.78 Q m N/A 80 500 N/A N/A 4 k 33 0.63 0.72 0.68 0.94 0.9-0.94 0.19 18

For Table 1, d 31 and d 33 represent piezoelectric constants, ε is the permittivity, T c is the Curie temperature, ρ is density, Q m is the mechanical quality factor, and k 33 is the electromechanical coupling factor. Table 2: Magnetostrictive Material Properties. NiFe 2 O 4 Terfenol-D Fe-Ga Metglas 2605 λ(ppm) 27-1400 200 40 μ 20 6-10 20 >40000 k 33 N/A 0.44 N/A 0.37 Q m N/A N/A N/A 1000 ρ(g/cm 3 ) 5.37 7.8 7.7 7.18 R(Ω-m) 1e6 5.8e-7 6e-7 1.3e-6 T c (ºC) 535 N/A N/A 395 For Table 2, λ is the saturation magnetostriction, μ is the permeability, k 33 is the electromechanical coupling factor, Q m is the mechanical quality factor, ρ is density, R is resistivity, and T c is the Curie temperature 26. Of the three methods for fabricating strain coupled magnetoelectric devices, laminate composites exhibit the largest sensitivity. Currently, Dr. Dwight Viehland, from the Department of Material Science and Engineering at Virginia Polytechnic Institute, has demonstrated the 19

highest magnetoelectric coupling coefficient in a device fabricated by laminating together thin layers of Metglas (25 microns) to polyvinylidene-flouride (28 microns) 27. This device exhibits an off-resonance ME sensitivity coefficient of approximately 7 V/cm-Oe corresponding to a 1 KHz AC input magnetic field and an 8 Oe magnetic bias field as shown in Figure 11 a). In Figure 11 b), an on-resonance ME sensitivity coefficient of 310 V/cm-Oe, corresponding to an electromagneto-mechanical mode stimulation frequency of approximately 50 KHz, is shown for an applied static magnetic field of 8 Oe. Figure 11: ME coupling coefficient of a heterostructural Metglas/polyvinylidene-flouride magnetoelectric laminate composite magnetic field sensor. Although no commercial applications utilizing the magnetoelectric effect yet exist, several proposed applications utilizing the relatively large magnetoelectric effect associated with ME laminate composites are currently in research and development phases. These applications 20

include the development of tunable microwave devices, transformers, and magnetic field sensors 19. Presented in this thesis is an investigation of the use of magnetoelectric laminate composites as magnetic field sensors. 1.5. ME Laminate Composites as Magnetic Field Sensors Strain-coupled magnetoelectric laminate composites that exhibit large ME coupling coefficients have emerged as promising candidates for the development of highly-sensitive magnetic field sensors in recent years 27. Key advantages of this technology include operation at room temperature, low cost, and simple fabrication requirements. In addition, steadily increasing magnetoelectric coefficient values potentially enable these devices to target highly-sensitive magnetometer markets that include optically pumped cesium vapor magnetometers, spinexchange relaxation-free (SERF) atomic magnetometers, and superconducting quantum interference devices (SQUID) 28. As previously described, ME laminate composite magnetic field sensors rely on a stress-mediated coupling between magnetostrictive and piezoelectric phases in order to produce an output voltage in response to an applied magnetic field. Magnetostrictive phases that have been utilized in the construction of ME sensors include Terfenol-D, Metglas, and Galfenol intermetallic alloys, as referenced in Table 2, whereas the piezoelectric phase is typically lead zirconate titanate (PZT) or lead magnesium niobate - lead titanate (PMN-PT), as referenced in Table 1. The magnetoelectric effect is obtained through laminating the aforementioned materials together such that under the influence of an applied magnetic field, the magnetic phase is then either longitudinally or transversely magnetized and the piezoelectric phase is longitudinally or transversely poled. 21

Two magnetoelectric laminated composite magnetic field sensors were provided for the testing and comparison of conventional static applied magnetic field biasing with the novel modulated sensing technique that employs an applied time varying magnetic field. The first sensor, shown in Figure 12, is a laminated composite tri-layer heterostructure consisting of a piezoelectric PZT film bonded between two magnetostrictive Metglas ribbons in a Metglas/PZT/Metglas configuration, provided by Carmine Carousella. The Metglas/PZT/Metglas topology allows for the Metglas to act as both magnetostrictive phase and electrodes where charge can accumulate as the PZT phase undergoes strain. Leads were attached to each Metglas ribbon allowing for voltage measurements. The dimensions of this magnetoelectric laminate were measured to be 28.3 mm long by 2.0 mm wide by 0.2 mm thick. Metglas ribbons are manufactured to be 1 mil thick, equal to 0.0254 millimeters. Therefore the PZT film including the thickness of the lamination adhesive is calculated to be approximately 0.1492 mm thick, equal to 149.2 microns. This device is categorized as a longitudinally magnetized, transversely poled magnetoelectric magnetic field sensor and is designed to exhibit peak performance for sensing magnetic fields that interact parallel to its length. The magnetic field sensor, pictured in Figure 12, is herein referred to as Sensor 1. 22

Figure 12: Metglas/PZT/Metglas laminated heterostructural composite, provided by Carmine Carousella, held by tweezers to enable resonance bending modes during testing. Length, height, and thickness dimensions are indicated. The second sensor, shown in Figure 13, is a laminated composite tri-layer heterostructure consisting of a poled piezoelectric PZT film bonded between two magnetostrictive Metglas ribbons in a Metglas/Poled-PZT/Metglas topology. Instead of utilizing the Metglas phase as an electrode, this sensor exhibits internal patterned interdigitated electrodes in contact with the poled-pzt film separated by a distance of approximately 1mm. This magnetoelectric magnetic field sensor is categorized as a longitudinally magnetized, longitudinally poled device and is designed to exhibit peak performance for sensing magnetic fields that interact parallel to its length. The dimensions of this magnetoelectric laminate were measured to be 80.4 mm long by 10.4 mm wide and exhibited a thickness of 0.4mm where PZT was sandwiched between Metglas, and a thickness of 0.2 mm in the absence of a PZT layer at either end. This indicates that four layers of Metglas (two layers laminated together per side of PZT) were used in total. The approximate thickness of PZT, including lamination adhesive, is calculated to be 0.2 mm. The Metglas layers were purposefully constructed to exhibit a length longer than that of the PZT phase in order to maximize the magnetoelectric coefficient by straining the PZT in a more 23

uniform manner. Extensive optimization regarding number of Metglas layers, Metglas length, and additional factors have been investigated 29. This device was generously provided by Dwight Viehland s Materials Science group at Virginia Polytechnic Institute. The magnetic field sensor pictured in Figure 13, is herein referred to as Sensor 2. Figure 13: Metglas/Poled-PZT/Metglas laminated heterostructural composite with interdigitated electrodes, provided by Dwight Viehland. Length, height, and thickness (at two locations along the length) dimensions are indicated. Sensor 1 and Sensor 2 are constructed of similar materials in the same layered laminate topology; however, each sensor operates in a fundamentally different manner due to the directionally dependent method of harvesting the piezoelectrically generated voltage response of strained PZT. It is observed in Table 1 that the D33 piezoelectric coefficient is much greater than the D31 coefficient for PZT of similar types. A diagram demonstrating the difference between utilizing PZT in a D31 mode and a D33 mode is shown in Figure 14 30. 24

Sensor 1 was fabricated to utilize the PZT in a D31 mode where a longitudinally applied strain, coupled from magnetostrictively induced strain in the Metglas, results in a transversely generated voltage response. Conveniently, use of a D31 mode enables Sensor 1 to utilize the Metglas as electrodes on either side of the PZT film. Although the piezoelectric coefficient is lower for ME sensors utilizing the D31 mode, the complexity of sensor construction is greatly reduced. Figure 14: D31 and D33 mode operation of piezoelectric PZT. For the D31 mode, a longitudinally applied strain results in a transversely generated voltage response. For the D33 mode, a longitudinally applied strain results in a longitudinally generated voltage response. Directions 3 and 1 are denoted on the axis. Sensor 2 was fabricated to utilize the PZT in a D33 mode where a longitudinally applied strain, coupled from magnetostrictively induced strain in the Metglas, results in a longitudinally 25

generated voltage response. In order to detect this voltage response an interdigitated pair of electrodes, demonstrated by the geometry shown in Figure 15, was placed longitudinally on the PZT, underneath the Metglas. Leads were then attached to exposed portions of the interdigitated pair of electrodes for voltage measurements. By designing a ME magnetic field senor to utilize the D33 sensing mode, the device benefits from a higher piezoelectric coefficient but increases the complexity of sensor construction 29. Figure 15: Example of an interdigitated electrode geometry. Interdigitated electrodes are typically used in ME laminates where the piezoelectric phase is to be operated in a D33 mode, as exemplified by Sensor 2. The following two chapters detail the use of both magnetoelectric laminate composites, Sensor 1 and Sensor 2, in a magnetic field sensing application. In Chapter 2, each sensor is characterized using the conventional method of biasing magnetoelectric magnetic field sensors with an applied static (DC) magnetic field. In Chapter 3, each sensor is characterized using the novel modulated sensing technique where an applied time varying (AC) magnetic field is used to modulate each device. By using two sensors exhibiting different operational modes, dimensions, magnetoelectric coefficient, and constructions, it is demonstrated that the modulated sensing technique exhibits no preference to sensor type. 26

Chapter 2. Conventional DC Operation 2.1. Introduction and Theory Strain-coupled magnetoelectric laminate composites have conventionally 5,19 been biased using an applied static magnetic field which enables optimal magnetostriction properties in the magnetostrictive phase and provides a maximum output voltage in response to an input magnetic field signal, herein defined as sensitivity (Volts/Oersted). Typically, these devices exhibit peak sensitivity when the amplitude of the applied DC magnetic bias field corresponds with a maximum in the slope (dλ/dh) of the magnetostriction curve for a magnetostrictive material. When magnetically DC biased at this point, a superimposed magnetic field source signal will cause the greatest percentage change in magnetostriction, and if coupled to a piezoelectric, will induce a maximum voltage response. Static magnetic field biasing of the ME sensor can be accomplished using permanent magnets or through the use of DC current driven electromagnets. The term DC, meaning direct current, is used here to describe a static magnetic bias field. Electromagnets, in the form of dual nesting Helmholtz coils, were utilized in the experimental setup to generate all required magnetic fields. For generating a static magnetic field, direct current (DC) was applied to the coils. For generating a time varying magnetic field, alternating current (AC) was applied to the coils. This nomenclature is frequently used throughout the thesis to describe static and time varying magnetic fields. The provided ME laminate magnetic field sensors were both constructed using a Metglas magnetostrictive phase. The magnetostriction in a similar sample of Metglas, shown in Figure 16, was measured to exhibit 0 ppm strain in the absence of an applied magnetic field and to non- 27

linearly saturate at a maximum strain of 27.5 ppm under a 200 Oe magnetic bias field. The maximum dλ/dh, is observed to occur at approximately 40 Oe as demonstrated in Figure 17. Figure 16: Magnetostriction of Metglas shown on +-1000 Oe scale (left) and a +-75 Oe scale (right) to exhibit a peak magnetostriction of approximately 27.5 ppm and a maximum in slope (dλ/dh) at 40 Oe. Figure 17: Slope of Metglas magnetostriction curve exhibiting a maximum at approximately 40 Oe. 28

Metglas was chosen for use in these sensors due to its ability to be saturated using relatively low amplitude DC magnetic bias fields. Both sensors were designed for potential deployment in power-conscious applications where the generation of high amplitude magnetic fields is impractical. Although the measured sample of Metglas differs slightly from the material used in each ME laminate sensor, the notion of Metglas exhibiting magnetostrictive saturation under relatively low magnetic fields is valid. 2.2. Experimental Setup 2.2.1. DC Biasing Method Equipment List The following list of equipment was used to measure both Sensor 1 and Sensor 2 using the conventional DC biasing method and is number coordinated with Figure 18: 1) Stanford Research Systems SR770 FFT Digital Spectrum Analyzer 2) Stanford Research Systems SR830 DSP Lock-in Amplifier 3) Sorensen DCR 80-12B Power Supply 4) LakeShore 421 Gaussmeter with MNT-4E04-VH Transverse AC Hall Probe 5) Dual nesting Helmholtz coil with 9 cm uniform field capability. 6) Non-magnetic sensor mounting apparatus 7) BNC coaxial cables and clip leads 8) 3.5 Inch Floppy Disk 9) LakeShore Model 4060 Zero Gauss Chamber 29

Figure 18: DC biasing method experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5 floppy disk, and the LakeShore Model 4060 Zero Gauss Chamber are not numbered in figure. 2.2.2. DC Biasing Method Block Diagram and Equipment Overview A block diagram of the experimental setup used to take DC biased measurements of Sensor 1 and Sensor 2 is shown below in Figure 19. Signal flow direction is demonstrated using red arrows. 30

Figure 19: Block diagram of the experimental setup for the DC biasing method. The magnetoelectric sensors were connected to the input of a Stanford Research Systems SR770 FFT digital spectrum analyzer which was configured to capture voltage spectral density measurements (Vrms/ Hz) of sensor response to an applied magnetic test field. The magnetic test field was generated by passing a 25 Hz alternating current signal from the SR770 source output through Helmholtz coil set 1. The amplitude of the 25 Hz magnetic field was measured using the MNT-4E04-VH transverse AC hall probe, which exhibits AC bandwidth from 10 Hz to 400 Hz, in conjunction with the LakeShore 421 gaussmeter set in AC Gauss RMS mode. The 31

AC magnetic test field was set to 25 Hz at 0.10 Gauss RMS, equal to 10-5 Tesla RMS in air, and was held constant for the remainder of all measurements. Generation of the DC biasing magnetic field was accomplished by passing a direct current, generated by a Sorensen DCR 80-12B, through Helmholtz coil set 2. For precise, constant control of the current, strapping of the Sorensen DCR 80-12B was reconfigured to enable signal programming voltage mode as described in section 3.2.4 of the instrument user manual. In this mode, the full-scale voltage output of the Sorensen DCR 80-12B can be programmed using a 0-10VDC input signal capable of sourcing at least 1 ma. The Aux output 1 of the SR830 DSP lock-in amplifier, which can provide -10.5 VDC to +10.5 VDC at an output current up to 10 ma, was used to control the voltage output of the Sorensen DCR 80-12B with high precision. The dual nesting set of Helmholtz coils was fabricated specifically for use in these experiments. Two non-magnetic ring-shaped coil housings, fabricated from aluminum and plastic, were wrapped with two differing sets of coil windings. The first coil set consisted of 1500 turns of 30 AWG insulated magnet wire which accommodated the low alternating current output of the SR770 signal generator source. This coil was used in conjunction with the SR770 source output to generate the AC magnetic test field signal. The second coil consisted of 200 turns of 18 AWG insulated magnet wire and accommodated the high direct current output of the Sorensen DCR 80-12B power supply. This coil was used to generate a DC biasing magnetic field from 0 Gauss up to 50 Gauss. A Helmholtz coil is defined as a pair of symmetrical electromagnet coils that are separated by a distance equal to the radius of each coil. When current is passed through both 32

coils, separated by their radius, a uniform magnetic field is produced along a length between the coils approximately equal to the distance of separation. A key design aspect in fabricating the Helmholtz coil was the ability to generate uniform magnetic fields over the length of the largest sensor. Therefore, the uniform field length was required to be at least as long as the active element area in Sensor 2 of 40 mm, and preferably the entire length of Sensor 2 of 80.4 mm. The dual Helmholtz coils constructed for this investigation were fabricated to exhibit a 90 mm radius, therefore providing an approximate 90 mm uniform field length. The Helmholtz equation (2.1) calculates magnetic flux density along a line centered through each coil as a function of permeability, number of turns, current, and coil radius. (2.1) Both coils were secured to Plexiglas frames and mounted on a wood platform to provide a stable electromagnetic Helmholtz coil test fixture promoting repeatable measurements. Two sets of banana connectors were mounted to the wood platform where leads from both sets of Helmholtz coils were tied. This method of interfacing with the dual Helmholtz coil provided robust repeatable connectivity. During testing, each ME sensor was mounted into plastic tweezers as shown in Figure 12, and suspended by a table top vice grip fabricated from aluminum and plastic. Supporting each sensor on either end using a clamp, instead of on a dielectric slab as shown in Figure 9a, is theorized to promote the generation of bending modes, resulting in higher sensitivity, and to reduce mechanical damping effects associated with attaching a sensor to a dielectric slab. However, no study was performed to analyze the different sensor mounting methods due to the 33

scope of this thesis. For consistency, both sensors were mounted in an identical manner for testing. As shown in Figure 20, the mounting apparatus simply positions a ME sensor inside the dual Helmholtz coil. The use of clip leads and tweezers enable quick switching between sensors. Clip leads were attached to the electrode leads on the sensor and connected via BNC coaxial cables to the SR770 for measurements. Figure 20: The sensor mounting apparatus consists of a table top vice grip and a set of tweezers fabricated from non-magnetic materials. It is shown positioning a sensor inside the dual Helmholtz coils. 34

2.2.3. DC Biasing Method Experimental Procedure The following experimental procedure will enable a reader to accurately reproduce the DC biasing test method used to capture measurements presented in this thesis: 1) Configure the Sorensen DCR 80-12B strapping for signal programming voltage mode: a. Remove all strapping from current configuration. b. Connect nodes 7 to 8. c. Connect node 1 to + Output. d. Connect node 2 to Output. e. On Front Panel, connect + Output to Ground. f. Set Current knobs fully clockwise. 2) Configure SR830 Aux Out 1 to provide voltage programming of the DCR 80-12B: a. Press Aux Out and set to 0.000 VDC. b. Connect Aux Out 1 + Voltage signal to node 3 on Sorensen DCR. c. Connect Aux Out 1 Ground to node 1 on Sorensen DCR. 3) Connect the Sorensen DCR 80-12B DC output to coil set 2. 4) Setup the SR770 using the following steps: a. Set frequency scale from 0 to 50 Hz. b. Set Window to BMH. c. Set Measure to PSD. d. Set Display to Log Mag. e. Set Units to Volts RMS. f. Set Input to A. g. Set Grounding to Ground. 35

h. Set Coupling to AC. i. Set Trigger to Continuous. j. Set Source to Sine. k. Configure Source to generate a 25 Hz 780 mv AC RMS signal. l. Press Auto Scale. m. Set Auto-Ranging On. n. Set Averaging On. o. Set Number Averages to 500. p. Set Average Type to RMS. q. Set Average Mode to Linear. 5) Connect the SR770 source out to coil set 1. 6) Place the MNT-4E04-VH Transverse AC Hall Probe inside the LakeShore Model 4060 Zero Gauss chamber. 7) On the LakeShore 421 Gauss meter press the Zero Probe button to calibrate the hall probe in a zero gauss environment. 8) Place the MNT-4E04-VH Transverse AC Hall Probe along the central axis inside the Helmholtz coils and confirm the LakeShore 421is measuring 0.1 Gauss RMS. 9) Connect the sensor leads to input A on the SR770 and position sensor along the central axis inside the Helmholtz coils. 10) Set LakeShore 421 to measure DC magnetic field and verify the DC field is 0 Gauss. 11) Insert a 3.5 floppy disk into the SR770. 12) Press Store/Recall then press Format Disk on the SR770. 36

13) Press the Start key on the SR770 to begin collecting 500 linearly averaged sweeps for 0 Gauss applied field. 14) When data collection has completed, press Store/Recall, Save Data, enter a file name, then press Save ASCII Data to write a two column (frequency, power spectral density) text data file do the floppy disk. An example data file is provided in Appendix A.1. 15) Increment the Aux Out 1 output voltage using the rotary knob on the SR830, causing the Sorensen to increasingly pass direct current through Coil Set 2, generating a DC magnetic field, until the LakeShore 421 measures 1 Gauss. 16) Press the Start key on the SR770 to begin collecting 500 linearly averaged sweeps for 1 Gauss applied field. 17) Using a unique filename, save the data in ASCII format to floppy disk. 18) Repeat steps 15, 16, and 17 for all desired increments of DC bias magnetic field for both magnetoelectric sensors. 2.3. Results and Analysis The conventional DC biasing method was used, by following the previously described procedure, to collect Sensor 1 and Sensor 2 frequency domain voltage response data, consisting of 500 linearly averaged sweeps from 0 to 50 Hz, of a 25 Hz 0.1 Gauss RMS test field for varying DC bias magnetic fields. DC bias magnetic field values of 0, 1, 2.5, 5, 7.5, 10, 15, 20, 30, and 50 Gauss were chosen because both sensors exhibit peak performance within that range. Signal-to-noise ratio (SNR), sensitivity, 0-Hz noise floor, and magnetic spectral density measurements are presented in section 2.3.1 for Sensor 1 and section 2.3.2 for Sensor 1. 37

The SR770 digital FFT spectrum analyzer has the ability to measure from DC to 100 KHz with a dynamic range of 90 db. This instrument enabled accurate measurements from 0 Hz to 50 Hz and provided magnetoelectric response data corresponding to the magnetic test field, environmental noise factors, and internal device noise factors. The convention for describing the noise floor of magnetoelectric laminate composites involves converting voltage spectral density measurements to magnetic spectral density in Tesla/ Hertz through the equation 2.2. (2.2) This calculation requires the value of inverse sensitivity where sensitivity is defined as Volts per Oersted. Sensitivity is calculated by converting the voltage spectral density measurement at 25 Hz to Volts RMS. The single point noise floor value of magnetoelectric laminate composites is typically quantified by the amplitude of the 0-Hz peak 28. The 0-Hz peak has typically exhibited the largest non-signal noise floor in ME composites where the output viewed in the time domain exhibits the largest DC noise effects. Recently, several methods of mediating the 0-Hz noise peak associated with 1/f noise have been developed, as exhibited in Sensor 2, however, single-point noise floor measurements continue to be taken with respect to the 0-Hz noise floor. The noise floor and signal-to-noise plots are calculated using the single 0-Hz noise floor data point. Dynamic magnetic spectral density noise floor data is also presented in logarithmic and linear scales to exhibit the environmental noise floor frequency content. 38

2.3.1. Sensor 1 Results Data was imported and analyzed using the Matlab code shown in Appendix section A.2. 5 SNR Vs. Applied DC H-Field 0 SNR (db) -5-10 -15-20 0 10 20 30 40 50 Applied DC H-Field (Oe) Figure 21: Signal-to-noise ratio as a function of applied magnetic field for Sensor 1. 10-2 Sensitivity Vs. Applied DC H-Field Sensitivity (V/Oe) 10-3 10-4 0 10 20 30 40 50 Applied DC H-Field (Oe) Figure 22: Sensitivity as a function of applied magnetic field for Sensor 1. 39

0-Hz Noise Floor (T/ Hz) 10-3 0-Hz Noise Floor Vs. Applied DC H-Field 10-4 10-5 0 10 20 30 40 50 Applied DC H-Field (Oe) Figure 23: 0-Hz noise floor as a function of applied magnetic field for Sensor 1. Peak values of SNR, sensitivity, and noise floor from Figure 21, Figure 22, and Figure 23, respectively, are provided in Table 3 below. Table 3: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 1. Property Sensor 1 Peak SNR Peak Sensitivity Lowest Noise Floor 1.858 db 2.713*10-3 V/Oe 1.632*10-5 T/ Hz 40

10-3 MSD of Sensor 1 for 25 Hz 0.1 Oe Test Field 10-4 X: 25.02 Y: 2.021e-005 Magnetic Spectral Density (T/ Hz) 10-5 10-6 10-7 10-8 0 Oe 1 Oe 2.5 Oe 5 Oe 7.5 Oe 10 Oe 15 Oe 20 Oe 30 Oe 50 Oe 10-9 10 0 10 1 Frequency (Hz) Figure 24: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of log scale. 41

10-3 MSD of Sensor 1 for 25 Hz 0.1 Oe Test Field Magnetic Spectral Density (T/ Hz) 10-4 10-5 10-6 10-7 X: 25.02 Y: 2.021e-005 0 Oe 1 Oe 2.5 Oe 5 Oe 7.5 Oe 10 Oe 15 Oe 20 Oe 30 Oe 50 Oe 10-8 10-9 0 10 20 30 40 50 Frequency (Hz) Figure 25: Magnetic Spectral Density with respect to applied field for Sensor 1. X-axis is of linear scale. 42

2.3.2. Sensor 2 Results 60 SNR Vs. Applied DC H-Field 50 SNR (db) 40 30 20 10 0 10 20 30 40 50 Applied DC H-Field (Oe) Figure 26: Signal-to-noise ratio as a function of applied magnetic field for Sensor 2. 10 0 Sensitivity Vs. Applied DC H-Field Sensitivity (V/Oe) 10-1 10-2 10-3 0 10 20 30 40 50 Applied DC H-Field (Oe) Figure 27: Sensitivity as a function of applied magnetic field for Sensor 2. 43

60 SNR Vs. Applied DC H-Field 50 SNR (db) 40 30 20 10 0 10 20 30 40 50 Applied DC H-Field (Oe) Figure 28: 0-Hz noise floor as a function of applied magnetic field for Sensor 2. Peak values of SNR, sensitivity, and noise floor from Figure 26, Figure 27, and Figure 28, respectively, are provided in Table 4 below. Table 4: DC Biasing Method: Peak Values of SNR, Sensitivity and Noise Floor for Sensor 2. Property Sensor 2 Peak SNR Peak Sensitivity Lowest Noise Floor 58.8 db 2.583*10-1 V/Oe 2.404*10-8 T/ Hz 44

10-4 MSD of Sensor 2 for 25 Hz 0.1 Oe Test Field Magnetic Spectral Density (T/ Hz) 10-5 10-6 10-7 0 Oe 1 Oe 2.5 Oe 5 Oe 7.5 Oe 10 Oe 15 Oe 20 Oe 30 Oe 50 Oe X: 25.02 Y: 2.021e-005 10-8 10-9 10-1 10 0 10 1 10 2 Frequency (Hz) Figure 29: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of log scale. 45

10-4 MSD of Sensor 2 for 25 Hz 0.1 Oe Test Field Magnetic Spectral Density (T/ Hz) 10-5 10-6 10-7 X: 25.02 Y: 2.021e-005 0 Oe 1 Oe 2.5 Oe 5 Oe 7.5 Oe 10 Oe 15 Oe 20 Oe 30 Oe 50 Oe 10-8 10-9 0 10 20 30 40 50 Frequency (Hz) Figure 30: Magnetic Spectral Density with respect to applied field for Sensor 2. X-axis is of linear scale. 46

2.4. Conclusion Sensor 1 is shown to exhibit a 1.858 db peak signal-to-noise ratio, a 2.713*10.3 V/Oe sensitivity and a lowest 1.632*10-5 T/ Hz 0-Hz noise floor. Sensor 2 exhibits a much higher peak SNR of 58.8 db, peak sensitivity of 2.583*10-1 V/Oe and lowest 0 Hz noise floor of 2.404*10-8 T/ Hz. The differences between both sensors are to be expected due to Sensor 1 utilizing PZT in a D31 mode and Sensor 2 utilizing PZT in a D33 mode. In addition, the Sensor 2 exhibits an approximate 7x larger active surface area and an approximate 14.7x larger total surface area than Sensor 1 enabling Sensor 2 to exhibit greater sensitivity. The magnetic spectral density plots for Sensor 1 exhibit a significant 1/f noise contribution in addition to several harmonic peaks resulting from the 25 Hz magnetic test field signal. The MSD plots for Sensor 2 exhibit a unique dip in 1/f noise contribution at approximately 1 Hz which comes as an intentional result of Virginia Tech s design. Several harmonic peaks resulting from the 25 Hz magnetic test field signal are exhibited. The X and Y coordinate marker indicated on each Matlab MSD plot shows that each trace has been normalized to a 25 Hz, 0.10 Oe magnetic test field. 2.021*10-5 corresponds to the magnetic spectral density in Tesla/ Hz and is equal to 1*10-5 Tesla. The data presented in this chapter represents the conventional way of biasing a magnetoelectric laminate composite sensor to exhibit peak performance by optimizing the amplitude of a DC magnetic bias field. The following chapter details a new sensing technique for ME laminate composites that requires no DC magnetic field bias. 47

Chapter 3. Modulation Sensing Technique 3.1. Introduction and Theory 3.1.1. Motivation Sensitivity enhancement and noise floor reduction in ME magnetic field sensors has been pursued through several different approaches. The role of laminate assembly configurations and respective magnetic/electric poling directions on the vibrational and thermal noise rejection capability has been investigated 29. Device scaling effects and their influence on the output noise level and signal-to-noise ratio (SNR) have also been reported. The role of Metglas/PZT thickness ratio has been studied and optimized to achieve further sensitivity improvement compared to single layer Metglas/PZT/Metglas heterostructures 29. In these and other experiments, it was observed that the sensitivity of the ME sensor can be enhanced and the noise floor reduced by increasing the volume or the surface area of the active region of the device. However, from a practical point of view, miniature, low profile, and lightweight sensing elements that can be integrated into compact gradiometric arrays and other magnetometer configurations are needed. There exists a strong need for methods of increasing the sensitivity and mitigating external noise sources, especially low frequency 1/f noise, without significantly increasing the size and weight of sensors. Anticipated applications include the deployment of magnetoelectric sensors in a variety of payload-sensitive platforms, such as unmanned autonomous systems, including aircraft vehicles, that can reap the full benefits of the ME sensor technology without sacrificing the current characteristics of these systems. 48

Presented in this chapter is a sensing technique that provides a dramatic improvement in sensitivity, an enhancement in signal-to-noise ratio, and an enhancement in noise floor over peak values obtained using the conventional DC biasing method for magnetoelectric laminate composite magnetic field sensors. Sensitivity enhancement is due, in part, by the use of a modulation magnetic field that is capable of stimulating an electro-magneto-mechanical resonance mode. It has been demonstrated 26 that magnetoelectric laminate composites exhibit a significant enhancement in sensitivity when exposed to an AC magnetic field that stimulates a resonance mode. Here, we take advantage of provoking a resonance mode and through the use of a lock-in demodulation scheme are able to detect off resonance magnetic field signals. 3.1.2. Relationship Between Strain and Applied Magnetic Field. This technique, herein referred to as the modulated sensing technique, employs an AC magnetic modulation field, instead of a DC magnetic bias field, to take advantage of the nonlinear nature of the magnetostriction constant dependence on an externally applied magnetic field, exhibited in Metglas magnetostrictive phase of both sensors. For small amplitudes of applied magnetic field, the magnetostrictive response can be defined using Livingston s model of coherent rotation of magnetization 31 shown in equation (3.1): (3.1) Where the saturation magnetostriction constant is, H A is the magnetic anisotropy field, and H is the applied magnetic field. For simplification, the strain can be related to an applied 49

magnetic field using equation (3.2), where C is the magnetostrictive coefficient parameter, thus indicating that strain is linearly proportional to C. (3.2) Figure 31 (a) illustrates the magnetostriction in Metglas, (b) the slope of the magnetostriction, and (c) strong agreement of Livingston s model of coherent rotation with magnetostriction for low amplitudes of applied magnetic field. The modulation sensing technique operates in the ds/dh realm as shown in Figure 31 (b) where the slope maximum is exhibited at an applied DC magnetic field of 0 Oe. Consequently, a superimposed signal field will cause the greatest percentage change in magnetostriction at 0 Oe, indicating that this sensing technique requires no DC bias field. 50

Figure 31: (a) Magnetostriction in Metglas. (b) Slope of magnetostriction (dλ/dh). (c) Overlay of Livingston's model of coherent rotation of magnetization with the magnetostriction of Metglas for low amplitudes of applied magnetic field. The H 2 term shown in equation (3.2) is critical for operation of the modulated sensing technique because it squares the applied field term which consists of the superposition of the applied magnetic test field signal with the applied magnetic modulation field signal, resulting in modulated frequency terms, and enables the lock-in amplifier to provide phase-locked demodulation. Proof that the strain term squares the superposition of two applied fields is 51

demonstrated in Figure 32, where a 200 Hz test H-field and 58KHz modulation H-field are simultaneously applied to Sensor 1. The voltage output waveform of Sensor 1 was captured using the Tektronix TDS 520A 2 channel digitizing oscilloscope to demonstrate the multiplication of both signals. Due to practical interest in lower frequency test signals, dynamic range limitations in the experimental setup, and maintaining consistency between DC biasing method and modulation sensing techniques, the test field was set to 25Hz. Figure 32: (a) 58 KHz reference modulation magnetic field as sensed by Sensor 1. (b) 200 Hz test field modulated with the 58 KHz reference modulation field as sensed by Sensor 1. Part (b) indicates that the total applied H term is indeed squared. 52

3.1.3. Mathematical Theory of Modulation Sensing Technique. Livingston has defined the strain in a magnetostrictive material, under low amplitudes of applied magnetic field H to be: 3 2 Which can be simplifi ed by using C as th e magnetostrictive coefficient parameter to: Indicating that: The modulation sensing technique utilizes the simultaneous application of two magnetic fields H sig, which can be an AC or DC magnetic test field signal, and H mod, which is the modulation magnetic field generated by using the reference channel of a lock in amplifier and thus sharing the same frequency. H mod : H from (3.2) is the applied magnetic field consisting of the superposition of H sig with Calculating for H 2 yields: 53

2 Where it can be now shown that strain is proportional to the expanded H 2 term: 2 For the modulation sensing technique, the voltage output generated by a magnetoelectric magnetic field sensor, which is proportional to strain and thus proportional to, is passed through a lock-in amplifier. The lock-in amplifier digitally multiplies an input signal by an internal reference signal to perform phase sensitive detection 32. The resulting signal V psd is the product of an input signal V test with the internal reference signal V LI wn low: ref as sho be Expanding yields: 2 54

Traditionally, it is observed that for phase-locked detection of a test frequency equal to the LIref frequency that the first cosine term goes to unity, yielding a DC result, and the second cosine term goes to twice the test frequency, which can be rejected using a lowpass filter. However, for the modulation sensing technique, V test consists of two modulated signals, and use of the lock-in amplifier produces several mixing terms described in the following. It is important to note that for this modulation sensing technique:. The voltage response output generated by a magnetoelectric magnetic field sensor will be proportional to the strain: Therefore the signal after phase sensitive detection V psd is proportional to the square of the applied magnetic field mu ltiplied by the lo ck-in reference signal V LIref : 2 55

Expanding yields: 2 The output of the SR830 lock-in amplifier contains at least an internal gain factor of 10x, which may be compounded with user defined gain. However, these gain terms can be placed in the proportionality constant, and the output of the lock-in amplifier V LIout can be described as: 2 56

Where further expanding yields: 2 1 2 Proper setting of the time constant on the SR830 provides rejection of all the higher order mixing terms and reduces the output to: 57

Using the SR830 lock-in amplifier reference output to modulate the coil, the internal reference frequency and modulation field frequency exhibit the same value and through phase sensitive detection can be cancelled out to yield: 1 The first cosine term goes to unity and the second cosine term goes to a frequency twice. Due to being much greater than the test frequency, this term is removed by properly setting the low pass filter time constant. Additionally, the term is placed in the proportionality. The output voltage of the lock in amplifier is shown to be linearly proportional to multiplied by : Here, may be an AC or DC magnetic signal field and the resulting expression, indicating that H mod and H sig act as linear gain terms, is shown below: cos The amplitude of Hmod was varied to prove that it linearly scales the amplitude of the output signal, therefore acting as a gain term as shown in Figure 33. 58

25 Hz Signal vs. Hmod Amplitude 1.8 1.6 Vdetected (mvrms) 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Hmod (Oe) Figure 33: Amplitude of the modulation field as a function of the detected 25 Hz test signal amplitude. This plot demonstrates that Hmod acts as a linear gain factor. 3.2. Experimental Setup 3.2.1. Modulated Sensing Technique Equipment List The following list of equipment was used to measure both Sensor 1 and Sensor 2 using the modulated sensing technique and is numerically coordinated with Figure 34: 59

1) Stanford Research Systems SR770 FFT Digital Spectrum Analyzer 2) Stanford Research Systems SR830 DSP Lock-in Amplifier 3) Tektronix TDS 520A 2 Channel Digitizing Oscilloscope 4) LakeShore 421 Gaussmeter with MNT-4E04-VH Transverse AC Hall Probe 5) Keithley 199 Digital Multimeter 6) Dual nesting Helmholtz coil with 9 cm uniform field capability. 7) BNC coaxial cables and clip leads 8) Non-magnetic sensor mounting apparatus 9) 3.5 Inch Floppy Disk 10) LakeShore Model 4060 Zero Gauss Chamber 11) Variable capacitor bank 12) AC amplifier with bandwidth from at least 10KHz through 70KHz 13) 1 Ohm Sense Resistor 14) Stanford Research Systems SR552 BJT Input Voltage Preamplifier 60

Figure 34: Modulated sensing technique experimental setup. The numbers correspond to the numbered items in the equipment list. The BNC coaxial cables, clip leads, 3.5 floppy disk, LakeShore Model 4060 Zero Gauss Chamber, and variable capacitor bank are not numbered in figure. 3.2.2. Modulated Sensing Technique Block Diagram and Equipment Overview A block diagram of the experimental setup used to take DC biased measurements of Sensor 1 and Sensor 2 is shown below in Figure 35. Signal flow direction is demonstrated using red arrows. 61

Figure 35: Block diagram of the experimental setup for the modulated sensing technique. The magnetoelectric sensors were connected to the input of a Stanford Research Systems SR830 DSP lock-in amplifier. The SR830 provides phase sensitive detection and demodulation of the signal field from the modulation reference field as described in section 3.2.1, low-pass filtering of higher ordered frequency terms, and passes the output signal, via X output, to the 62