ABSTRACT PHASE TRANSITIONS AND ASSOCIATED MAGNETIC AND TRANSPORT PROPERTIES IN SELECTED NI-MN-GA BASED HEUSLER ALLOYS by Sunday Arome Agbo The phase transitions and associated magnetic and transport properties of Ni2Mn0.70Cu0.30Ga, Ni2Mn0.70Cu0.25Cr0.05Ga and Ni2Mn0.70Cu0.30Ga0.95In0.05 have been investigated via x-ray diffraction, scanning electron microscopy, magnetic, calorimetric, and electrical resistivity measurements. While Ni2Mn0.70Cu0.30Ga exhibited a tetragonal structure at room temperature, cubic and orthorhombic phases coexisted in the other two samples. The scanning electron microscope micrographs indicated that no impurity phases existed in the samples. All three samples exhibited the first order martensitic phase transformation upon cooling and heating. The phase transitions were accompanied by large magnetic entropy changes and anomalies in the electrical resistivity data. For a field change of 50 kOe, peak magnetic entropy changes of -17 J kg-1K-1, -39 J kg-1K-1, -1 -1 and -26 J kg K were observed for Ni2Mn0.70Cu0.30Ga, Ni2Mn0.70Cu0.25Cr0.05Ga and Ni2Mn0.70Cu0.30Ga0.95In0.05 respectively, when the measurements were done while heating. When the measurements were done while cooling from 400 K to lower temperatures, the -1 -1 -1 -1 -1 -1 peak values were -33 Jkg K , -17 Jkg K , and -15 Jkg K for Ni2Mn0.70Cu0.30Ga, Ni2Mn0.70Cu0.25Cr0.05Ga and Ni2Mn0.70Cu0.30Ga0.95In0.05 respectively. The experimental results are discussed taking the decoupling and coupling of the phase transitions into consideration. PHASE TRANSITIONS AND ASSOCIATED MAGNETIC AND TRANSPORT PROPERTIES IN SELECTED NI-MN-GA BASED HEUSLER ALLOYS A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science by Sunday Arome Agbo Miami University Oxford, Ohio 2020 Advisor: Dr. Mahmud Khan Reader: Dr. Herbert Jaeger Reader: Dr. Stephen Alexander ©2020 Sunday Arome Agbo This Thesis titled PHASE TRANSITIONS AND ASSOCIATED MAGNETIC AND TRANSPORT PROPERTIES IN SELECTED NI-MN-GA BASED HEUSLER ALLOYS by Sunday Arome Agbo has been approved for publication by The College of Arts and Science and Department of Physics ____________________________________________________ Dr. Mahmud Khan ______________________________________________________ Dr. Herbert Jaeger _______________________________________________________ Dr. Stephen Alexander Table of Contents Chapter 1: Introduction ……………………………………………………....1 Chapter 2: Theoretical Background……………………………………….….5 2.1 Basics of Magnetism……………………………………….……..5 2.2 Classification of Magnetic Materials……………………………..6 2.2.1 Diamagnetism…………………………………………………..…7 2.2.2 Paramagnetism………………………………………………….....9 2.2.3 Ferromagnetism………………………………………………….11 2.2.4 Antiferromagnetism……………………………………………...15 2.2.5 Ferrimagnetism………………………………………………......15 2.3 Exchange Interactions…………….………………..…………….15 2.3.1 Direct Exchange Interaction……………………………………..16 2.3.2 Indirect Exchange Interaction……………………………………17 2.3.3 Superexchange Interaction……………….……………….……...17 2.3.4 Double Exchange Interaction……………………………………18 2.4 The Magnetocaloric Effect…………….…….……………….….18 2.4.1 Magnetocaloric Effect Thermodynamics………….………….….19 2.5 Phase Transition…………….…….……………….………….….23 2.5.1 The Martensitic Phase Transition ……………………………….23 Chapter 3: Experimental Methods……………………………………….......26 3.1 Sample Fabrication…………………………………….…….…..26 3.2 Structural Characterization………………………………….…...27 3.2.1 Theory and Principle of X-Ray Diffraction Methods…….….…..27 3.2.2 X-Ray Diffraction Measurements..................................................28 3.2.3 Analysis of X-Ray Diffraction Data……………………….…….30 3.3 Compositional Characterization………………………………....31 3.3.1 Scanning Electron Microscope………………………………..…31 3.3.2 Energy Dispersive X-Ray Spectroscopy………………………...34 3.4 Electrical and Magnetic Characterization…………………….…34 3.4.1 The Physical Property Measurement…………………………….36 iii 3.4.2 Vibrating Sample Magnetometer (VSM)…………………….....39 3.5 Calorimetric Characterization…………………………………..41 Chapter 4: Results and Discussion………………………………………….43 4.1 Temperature dependence of magnetization……………….….....43 4.2 Structural Analysis……………………….……………….….....47 4.3 Compositional Analysis……………………….………………..48 4.4 Electronic Transport Property Analysis……………...…………50 4.5 Field dependence of magnetization …………………………….54 Chapter 5: Summary and Conclusion………………………………………67 References …………………………………………………………………..68 iv List of Figures Figure 1.1 The X, Y, and Z elements that constitute that constitute a Heusler Alloy are highlighted in the periodic table…………………………………………………….…1 Figure 2.1 Schematic diagram of the magnetic dipole moment………………………6 Figure 2.2 Pictorial representations of a diamagnetic material displaying, a) the alignment of net magnetic moments vs. external field H, b) magnetization vs. external field, and c) magnetization vs. temperature T…………………………………………..…9 Figure 2.3 Pictorial representations of a paramagnetic material displaying a) the alignment of magnetic dipole moments for zero and positive field strength, b) magnetization as a function of H and c) magnetization as a function of T……………..11 Figure 2.4 Schematic diagram showing Magnetic domains in a ferromagnetic material in the absence of external magnetic field…………………………………….…12 Figure 2.5 Pictorial representation of a magnetic hysteresis loop for a generic ferromagnetic material showing the basic parameters…………………………………...14 Figure 2.6 Schematic depiction of superexchange for MnO………………………...18 Figure 2.7 Schematic diagram showing isothermal and adiabatic processes of the MCE on the application and removal of magnetic field in a system………………….…21 Figure 2.8 Schematic diagram of L21 and C1b cubic structures…………….……….24 Figure 2.9 Schematic diagram showing the cubic, tetragonal, and orthorhombic crystal structures of Ni2MnGa …………………………………………………..………25 Figure 3.1 Schematic representation of Bragg’s condition………………………….28 Figure 3.2 Pictorial representation of an X-ray diffractometer ……………….…….29 Figure 3.3 Schematic diagram of an X-ray diffractometer………………………….30 Figure 3.4 Schematic diagram of SEM showing the main components…………….32 Figure 3.5 A depiction of a resistivity puck …………………………………….…..35 Figure 3.6 schematic diagram of the main components in the PPMS system……….36 Figure 3.7 Schematic diagram of the PPMS probe assembly showing the major components………………………………………………………………………...…….38 Figure 3.8 A depiction of a VSM-PPMS system showing its components………….40 v Figure 3.9 Schematic diagram of a heat flux DSC………………………………......41 Figure 4.1 Temperature dependence of magnetization for Ni2Mn0.70Cu0.30Ga measured at H = 1 kOe…………………………………………………………………..44 Figure 4.2 Temperature dependence of magnetization for Ni2Mn0.70Cu0.25Cr0.05Ga measured at H = 1 kOe…………………………………………………………….…….45 Figure 4.3 Temperature dependence of magnetization for Ni2Mn0.70Cu0.30Ga0.95In0.05 measured at H = 1 kOe…………………………………………………………….…….46 Figure 4.4 Room temperature XRD pattern for Ni2Mn0.70Cu0.30Ga, Ni2Mn0.70Cu0.25Cr0.05Ga and Ni2Mn0.70Cu0.30Ga0.95In0.05 ……………….........................48 Figure 4.5 Room temperature SEM micrographs of Ni2Mn0.70Cu0.30Ga, Ni2Mn0.70Cu0.25Cr0.05Ga and Ni2Mn0.70Cu0.30Ga0.95In0.05 ……………………………….49 Figure 4.6 Temperature dependence of normalized resistance for Ni2Mn0.70Cu0.30Ga measured at zero magnetic field…………………………………………………………51 Figure 4.7 Temperature dependence of normalized resistance for Ni2Mn0.70Cu0.25Cr0.05Ga measured at zero magnetic field……………………………….52 Figure 4.8 Temperature dependence of normalized resistance for Ni2Mn0.70Cu0.30Ga0.95In0.05 measured at zero magnetic field……………………………53 Figure 4.9 Field dependence of magnetization, M(H), for Ni2Mn0.70Cu0.30Ga measured isothermally (warming and cooling) at temperatures near the martensitic phase transition............................................................................................................................55 Figure 4.10 Field dependence of magnetization, M(H), for Ni2Mn0.70Cu0.25Cr0.05Ga measured isothermally (warming and cooling) at temperatures near the martensitic phase transition…………………………………………………………………………………56 Figure 4.11 Field dependence of magnetization, M(H), for Ni2Mn0.70Cu0.30Ga0.95In0.05 measured isothermally (warming and cooling) at temperatures near the martensitic phase transition……………………………………………………………………………...….57 Figure 4.12 Temperature dependence of magnetic entropy changes, ΔSM(T), for Ni2Mn0.70Cu0.30Ga measured while (a) warming and (b) cooling………………………..58 Figure 4.13 Temperature dependence of magnetic entropy changes, ΔSM(T), for Ni2Mn0.70Cu0.25Cr0.05Ga measured while (a) warming and (b) cooling………………….59 Figure 4.14 Temperature dependence of magnetic entropy changes, ΔSM(T), for Ni2Mn0.70Cu0.30Ga0.95In0.05 measured while (a) warming and (b) cooling……………….60 vi Figure 4.15 Field dependence of magnetization, M(H), for Ni2Mn0.70Cu0.30Ga measured while warming and cooling at T = 345 K……………………………………..61 Figure 4.16 The Arrott plot, M2 versus H/M in the vicinity of phase transition temperature for Ni2Mn0.70Cu0.30Ga………………………………………………….…...62 Figure 4.17 The Arrott plot, M2 versus H/M in the vicinity of phase transition temperature for Ni2Mn0.70Cu0.25Cr0.05Ga…………………………………….…………..63 Figure 4.18 The Arrott plot, M2 versus H/M in the vicinity of phase transition temperature for Ni2Mn0.70Cu0.30Ga0.95In0.05………………………………………………63 Figure 4.19 DSC heat flow curves upon heating and cooling for Ni2Mn0.70Cu0.30Ga...64 Figure 4.20 DSC heat flow curves upon heating and cooling for Ni2Mn0.70Cu0.25Cr0.05Ga………………………………………………………………….65