1. Lecture X Magnetism and Matter Learning Objective: to examine some aspects of magnetic properties of materials

2. Some materials are magnetic: Bar magnet, Compass. (permanent magnets) Some appear non-magnetic, but are attracted by a permanent magnet. Some are non-magnetic whatever. Why?

3. Magnetism is intimately linked to the behaviour of electrons in materials

4. Magnetism and the Electron Electrons generate magnetism in 3 ways: 1. Magnetism of Moving Charges (for example, electric current) 3. Magnetism and Intrinsic Spin(electrons have intrinsic magnetic moments) 2. Magnetism of Orbital Motion(each electron is orbiting around the nucleus)

5. v L Angular Momentum L = m e vr Orbital Motion

6. v L Smallest magnetic moment (other than zero!)

7. Magnetism and Spin The electron has an intrinsic magnetic moment! So are protons and neutrons.

8. Net magnetic moment of an atom is obtained by combining both orbital and spin moments of all the electrons, taking into account the directions of these moments Why isn’t everything magnetic?

9. Each atom contains a number of electrons, each electron contributes a magnetic moment, but the sum of all the electron contributions can be zero. If not zero, then each atom can be treated as a magnetic dipole. The alignment of the “atomic dipoles” in a solid is important.

10. Magnetic moment of each atom is zero Total moment is zero Net moment zeroNet moment non-zero

11. Materials only exhibit “familiar” magnetic effects when: Atoms contain unpaired electrons Large scale alignment of the dipole moments occurs & Materials are Paramagnetic, Ferro-magnetic, or diamagnetic

13. Paramagnetism Atoms of a paramagnetic material have permanent magnetic dipole moments. These dipoles are randomly oriented - Magnetic fields average to zero. In an external field B 0, the dipoles tend to align with B 0 - Results in an additional magnetic field B m. Material with N atoms,  maximum =  N. Randomization of the dipoles orientations by thermal collisions significantly reduces the total dipole moment (  total )

14. Paramagnetism Compare with 2B2B Example: T = 300 K, B = 1.5 T,  =  B

15. Paramagnetism The increase of the strength of the B-field by the paramagnetic material is described by the relative permeability constant  m.

16. Paramagnetism

17. Magnetic moment per unit volume (magnetisation) M:

18. Paramagnetism It can be shown that

19. magnetic susceptibility Paramagnetism

20. Pierre Curie discovered experimentally that the magnetization M of a paramagnetic specimen obeyed: M cannot increase without limit, as Curies’s law implies, but must approach a value

21. Potassium chronium sulphate - a paramagnetic salt

22. rCrC Diamagnetism Atoms have no intrinsic magnetic dipoles Dipole moments induced by the application of an external magnetic field Induced B-field opposes the external field (Lenz’s law) B < B 0

23. rCrC Diamagnetism No intrinsic magnetic dipoles Dipole moments induced by an external magnetic field Induced B-field opposes the external field (Lenz’s law) B < B 0 {Compare with a paramagnetic material B > B 0 }

24. Lenz’s Law Direction of the induced current is such that it produces a magnetic field, which opposes the magnetic field which gave rise to that current B ext

25. Diamagnetism Permeabilities of Some Diamagnetic Materials

27. Ferromagnetism Materials with atoms having unpaired electron spins (iron, cobalt, nickel, gadolinium, and dysprosium). Electron spins aligned  10 10 atoms combine to form a domain (l  10 -7 m)  large magnetic moment. When the domains are randomly arranged, the specimen as a whole is unmagnetised.

29. Domains which are magnetized in the direction of an external magnetic field grow at the expense of those which are not aligned to the magnetic field. B ex  m becomes very large  10 3 – 10 5 Ferromagnetism

30. Materials may be broadly grouped into one of 3 categories; diamagnetic, paramagnetic, or ferromagnetic. Review and Summary Paramagnetic materials are (weakly) attracted by a magnetic field, have intrinsic magnetic dipole moments that tend to line up with an external magnetic field, thus enhancing (slightly) the field. This tendency is interfered with by thermal agitation.

31. Ferromagnetic materials result from spontaneous alignment of the dipole moment of atoms and the formation of large magnetic domains. Review and Summary Diamagnetic materials are (weakly) repelled by the pole of a strong magnet. The atoms of such materials do not have intrinsic magnetic dipole moments. A dipole moment may be induced, however, by an external magnetic field, its direction being opposite that of the field.

32. Exam: Temperature and Matter 27 May 2008 Revision:12.00, 6 May and 1.00pm, 9 May The amount of time that I have borrowed from you: 15 minutes I will pay you back 15 minutes+200% interest

33. No lecture tomorrow See you after Easter.

34. Magnetization Curve for a Ferromagnetic Material All magnetic moments in the material are aligned parallel to the external field Ferromagnetism

35. Ferromagnetism: Magnetization Curves and Hysteresis Loops Magnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loop

36. Ferromagnetism: Magnetization Curves and Hysteresis Loops

41. Magnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loop Explanation - reorientations of domain directions are not totally reversible Uses - magnetic storage of information

42. Nuclear Magnetism: An Aside Nuclear magnetic resonance (NMR) - employs the magnetic moment of the protons in some of the nuclei being examined. Note: nuclear magnetism does not contribute in a measurable way to the gross magnetic properties of solids.

49. Review and Summary

50. NEXT The final piece! Maxwell: Electricity plus Magnetism Gives Light

51. Paramagnetism Ampere’s law in materials becomes: I free refers to the external currents