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  • Anisotropic behaviour of magneto-electric

    coupling in multiferroic composites

    by

    Steven Bourn

    A thesis submitted in partial fulfilment for the requirements for the degree of Doctor of Philosophy at the University of Central Lancashire

    April 2018

  • i

    STUDENT DECLARATION FORM

    Type of Award Doctor of Philosophy

    School School of Physical Sciences & Computing

    1. Concurrent registration for two or more academic awards

    I declare that while registered as a candidate for the research degree, I

    have not been a registered candidate or enrolled student for another

    award of the University or other academic or professional institution

    2. Material submitted for another award

    I declare that no material contained in the thesis has been used in any

    other submission for an academic award and is solely my own work

    3. Collaboration

    I declare that this research programme was not part of a collaborative

    project.

    4. Use of a Proof-reader

    No proof-reading service was used in the compilation of this thesis.

    Signature of Candidate ______________________________________________________

    Print name: ________________________________________________________________

  • ii

    Abstract

    The anisotropy of the direct magnetoelectric effect in textured nickel ferrite/lead

    zirconate titanate strain mediated bilayer composites has been studied. The

    magnetic layers of these samples have been crystallographically textured in

    planes of the form {100}, {110} and {111}.

    In this study, it is shown that the optimum bias field and the maximum

    magnetoelectric coupling signal can be controlled by changing the alignment of

    the applied magnetic field with respect to the magnetocrystalline anisotropy

    directions. It is also shown that the product of the optimum bias field and the

    maximum magnetoelectric coupling signal are proportional to the theoretical

    saturation magnetostriction.

    The samples have been magnetically characterised using a recommissioned and

    developed biaxial vibrating sample magnetometer, capable of detecting the

    component of a sample’s magnetic moment in 2 perpendicular directions and

    thus determining the net magnetic moment vector of the sample. Coupled with

    sample rotation this allows insight into the magnetic anisotropy of the sample,

    which has been compared with a micromagnetic model.

    A specialist magnetoelectric coupling rig has also been developed to allow

    application of DC and AC magnetic fields to a sample simultaneously.

    As part of the magnetic anisotropy study, a modified torque magnetometry

    method has been developed to enhance the identification of the anisotropy

    directions in magnetically soft samples, as well as a method by which torque

  • iii

    magnetometry can be approximated using the in-field direction component of

    magnetisation as measured using a standard vibrating sample magnetometer.

  • iv

    Contents

    1. Introduction ........................................................................................................................... 1

    1.1. Nickel Ferrite ................................................................................................................. 3

    1.2. Magnetic Anisotropy in Nickel Ferrite ................................................................. 4

    1.3. Magnetostriction of Nickel Ferrite ........................................................................ 6

    1.3.1. NFO_100 ................................................................................................................ 11

    1.3.2. NFO_110 ................................................................................................................ 12

    1.3.3. NFO_111 ................................................................................................................ 13

    1.4. Piezoelectricity ............................................................................................................ 14

    1.5. Multiferroic composites and the magnetoelectric effect. ........................... 16

    1.6. Sample Details ............................................................................................................. 20

    1.7. Structure of this Thesis ............................................................................................ 21

    2. Development of magnetic and magnetoelectric measurement devices and

    methods. .......................................................................................................................................... 24

    2.1. Vibrating Sample Magnetometry ......................................................................... 25

    2.2. Sensitivity Profiles of the bi-axial VSM .............................................................. 27

    2.2.1. Theoretical ........................................................................................................... 27

    2.2.2. Experimental ....................................................................................................... 29

    2.3. Precession and its reduction by modification to the UCLan VSM ........... 33

    2.3.1. Precession reduction methodology. ........................................................... 33

    2.4. Experimental Control ............................................................................................... 36

  • v

    2.5. Measurement Techniques ...................................................................................... 38

    2.5.1. The Magnetic Hysteresis (M-H) loop ......................................................... 39

    2.5.2. Easy Axis Distribution Measurements ...................................................... 40

    2.5.3. Torque Magnetometry using a Vibrating Sample Magnetometer .. 42

    2.6. Development of a Magnetoelectric Measurement Device .......................... 45

    2.6.1. Requirements/Construction ......................................................................... 45

    2.6.2. ME Coupling Measurements ......................................................................... 48

    3. Development of An Alternate Method of Simulating Torque Curves Using A

    Standard VSM. ............................................................................................................................... 52

    3.1. In-field Methodology Development .................................................................... 56

    3.2. Testing of the Methodology Using In-Field Rotation Curves .................... 58

    4. Micromagnetic Modelling ............................................................................................... 66

    4.1. Magnetic Moment from Angular Momentum .................................................. 66

    4.2. Bohr Magneton and Gyromagnetic Ratio .......................................................... 66

    4.3. Magnetic Moment of an Isolated Electron ........................................................ 68

    4.4. Precession and Continuum Magnetisation ....................................................... 68

    4.5. Landau-Lifshitz Equation ........................................................................................ 70

    4.6. Landau-Lifshitz-Gilbert Equation ........................................................................ 71

    4.7. Effective Field Contributions ................................................................................. 73

    4.7.1. Magnetostatic Term.......................................................................................... 73

    4.7.2. Direct Exchange ................................................................................................. 74

  • vi

    4.7.3. Magnetocrystalline Anisotropy .................................................................... 75

    4.7.4. The Magnetoelastic Effect .............................................................................. 78

    4.8. Micromagnetic Modelling Software – Boris ..................................................... 79

    4.9. Hysteresis loop showing bulk NFO is magnetically hard ........................... 83

    4.10. Torque Magnetometry. ........................................................................................ 85

    5. Anisotropy measurements of the Magnetoelectric effect in

    NiFe2O4/PbZrTiO3 bilayers ...................................................................................................... 88

    5.1. Magnetic Characterisation of Nickel Ferrite samples .................................. 89

    5.2. Determination of the Magneto-Electric coupling as a function of sample

    rotation. ...................................................................................................................................... 90

    5.3. The Effects of Magnetostriction ............................................................................ 95

    5.4. The Effect of Varying applied AC Field. .......................................................... 106

    6. Conclusions...........................................................................................