1 / 67

Gavin W Morley Department of Physics University of Warwick

Gavin W Morley Department of Physics University of Warwick. Diamond Science & Technology Centre for Doctoral Training, MSc course Module 2 – Properties and Characterization of Materials Module 2 – (PX904) Lectures 15 & 16 – Magnetic properties and characterization. Overview. Magnetism.

neast
Download Presentation

Gavin W Morley Department of Physics University of Warwick

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Gavin W Morley Department of Physics University of Warwick Diamond Science & Technology Centre for Doctoral Training, MSc course Module 2 – Properties and Characterization of Materials Module 2 – (PX904) Lectures 15 & 16 – Magnetic properties and characterization

  2. Overview

  3. Magnetism Current loop has magnetic moment, µ = IA Area, A Maxwell 4:  × B = μ0J Current, I Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  4. Magnetism Current loop has magnetic moment, µ = IA Area, A N S Current, I Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  5. What happens if we try to cut a magnet in half? Area, A N S Current, I Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  6. What happens if we try to cut a magnet in half? N S a) b) N S N S Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  7. Magnetism Magnetic Monopoles N S N S Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  8. Angular momentum and Magnetism µ = γL (L is angular momentum, γ is gyromagnetic ratio) Current loop has magnetic moment, µ = IA Area, A N S Current, I Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  9. What happens if you put a magnetic moment into a uniform magnetic field? • It moves • It lines up • It precesses • Hey, I thought you were supposed to be teaching me N S Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  10. What happens if you put a magnetic moment into a uniform magnetic field? • It moves • It lines up • It precesses • Hey, I thought you were supposed to be teaching me N S Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  11. Precession of a magnetic moment Energy of the magnetic moment in a magnetic field, B: E = - µ • B Larmor precession frequency = γ B Area, A Current, I Joseph Larmor (1857 – 1942) Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  12. Magnitude of magnetic moment Electron has charge, e and mass, m, so Current: I = -e/t as speed, v =2π r/t for radius, r. Magnetic moment, μ= I A = I π r 2= - e ℏ/ 2m (as electron angular momentum = mvr = ℏ) v e- r ≡ -μB Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  13. Magnetization, M: Magnetic moment per unit volume in a solid In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H = µ0 µrH For relative permeability, µr Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  14. Magnetization, M: Magnetic moment per unit volume in a solid In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H = µ0 µrH For relative permeability, µr Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  15. Magnetization, M: Magnetic moment per unit volume in a solid In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  16. Relative permeability, µr In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H = µ0 µrH µr= 1+ χ Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  17. Magnetization, M: Magnetic moment per unit volume in a solid In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  18. Susceptibility, χ In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H = µ0 µrH For relative permeability, µr Table from Kaye & Laby www.kayelaby.npl.co.uk Chapter 1, Blundell, Magnetism in Condensed Matter, OUP 2001

  19. Magnetism of an atom • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum

  20. A beam of atoms hits a screen Classical prediction

  21. Stern-Gerlach experiment S N Classical prediction See also: http://commons.wikimedia.org/w/index.php?title=File%3AQuantum_spin_and_the_Stern-Gerlach_experiment.ogv

  22. Magnetism of an atom • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum

  23. Solve Schrödinger’s equation for an electron in a box: → Discrete energy levels Erwin Schrödinger (1887 – 1961) Page 240, Eisberg and Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Wiley 1985

  24. Solve Schrödinger’s equation for electron in Coulomb potential and include spin Page 241, Eisberg and Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, Wiley 1985

  25. Atomic orbitals 1s 2s 2px 2py 2pz

  26. Magnetism of an atom • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum

  27. Sample magnetization • From the electrons • Spin • Orbital Magnetic Field For spin ½, Magnetization is M = Mstanh(µBB/kBT) Paramagnetic

  28. Sample magnetization • From the electrons • Spin • Orbital Magnetic Field Paramagnetic susceptibility follows the Curie Law: χ = CCurie/T Paramagnetic

  29. Page 20, Blundell, Magnetism in Condensed Matter, OUP 2001

  30. Atomic orbitals 1s 2s 2px 2py 2pz

  31. Page 20, Blundell, Magnetism in Condensed Matter, OUP 2001

  32. Metals Conduction electrons have “Pauli paramagnetism” (Chapter 7 of Blundell’s book) Fermi-Dirac distribution function, Page 9, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001

  33. Magnetism of an atom • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum

  34. Sample magnetization From change in orbital angular momentum- Diamagnetic Magnetic Field Paramagnetic - From spin and orbital angular momentum

  35. Sample magnetization From change in orbital angular momentum - Diamagnetic Magnetic Field Paramagnetic - From spin and orbital angular momentum

  36. Page 20, Blundell, Magnetism in Condensed Matter, OUP 2001

  37. Magnetism of an atom • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum

  38. Interactions → Ferromagnetism • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum Ferromagnet in zero applied magnet field ( J > 0 ):

  39. Sample magnetization Diamagnetic Magnetic Field Paramagnetic Ferromagnetic

  40. Sample magnetization Saturation magnetization Remanent magnetization Magnetic Field Coercive field Ferromagnetic

  41. Ferromagnetic domains Page 131, Blundell, Magnetism in Condensed Matter, OUP 2001

  42. Interactions → Antiferromagnetism • From the electrons • Spin angular momentum • Orbital angular momentum • An applied magnetic field can change their orbital angular momentum • From the nuclei • Spin angular momentum Antiferromagnet in zero applied magnet field ( J < 0 ):

  43. Diamond Superconductivity → perfect diamagnetism In vacuum: B = µ0H permeability of free space, µ0 = 4π× 10-7 Hm-1 In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH for susceptibility, χ So then B = µ0 (1+ χ )H = µ0 µrH Page 202, Singleton, Band Theory and Electronic Properties of Solids, OUP 2001

  44. Boron-doped Diamond: Superconductivity E Bustarret et al, Dependence of the Superconducting Transition Temperature on the Doping Level in Single-Crystalline Diamond Films, Physical Review Letters, 93, 237005 (2004)

  45. Diamond Magnetic characterization In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH Measure magnetization, M which could be a function of temperature, magnetic field, orientation etc.

  46. Diamond Magnetic characterization In a magnetic solid: B = µ0 (H + M) For a linear material, M = χH Measure magnetization, M which could be a function of temperature, magnetic field, orientation etc. Extraction magnetometer: V V = 0 V > 0

  47. Diamond Magnetic characterization Vibrating sample magnetometer (VSM): V V = 0 Vac > 0

  48. SQUID magnetometer Vibrating sample magnetometer (VSM) with SQUID detection: V Bias current V = 0 Vac > 0 SQUID = superconducting quantum interference device

  49. SQUID magnetometer Vibrating sample magnetometer (VSM) with SQUID detection in an applied magnetic field → susceptibility V Bias current V = 0 Vac > 0 M = χH for susceptibility χ

  50. Neutron Scattering Analogous to X-ray diffraction with neutrons instead of X-rays. Neutrons have no charge but spin ½ Page 104, Blundell, Magnetism in Condensed Matter, OUP 2001

More Related