1. Week 14: Magnetic Fields Announcements MatE 153, Dr. Gleixner 1

2. General Concept Behind Magnetism Circulating current sets up a magnetic moment (  m ) perpendicular to the current Circulating current sets up a magnetic moment (  m ) perpendicular to the current –This results in a B field (magnetic field) that must terminate back on itself (all magnets must have a north & south, can’t be alone like electrical charge) Electrons in atoms are the same concept- circulating charge that sets up a magnetic moment and a magnetic field Electrons in atoms are the same concept- circulating charge that sets up a magnetic moment and a magnetic field –The magnetic field is due to both the orbital angular momentum and the spin –Only electrons in unfilled shells contribute to a net magnetization (as those in full shells will cancel each other out) MatE 153, Dr. Gleixner 2

3. Comapring a Magnetic Moment with a Bulk Magnet *Used with permission from Kasap MatE 153, Dr. Gleixner 3

4. Magnetism from an Orbiting Electron *Used with permission from Kasap MatE 153, Dr. Gleixner 4

5. Remember L?? *Used with permission from Kasap MatE 153, Dr. Gleixner 5

6. Spin Magnetic Moment *Used with permission from Kasap MatE 153, Dr. Gleixner 6

7. Remember S?? *Used with permission from Kasap MatE 153, Dr. Gleixner 7

8. Net Magnetization Net magnetization is due to magnetic moments from both forms of angular momentum Net magnetization is due to magnetic moments from both forms of angular momentum However, only electrons in un-filled shells contribute to an overall magnetic moment However, only electrons in un-filled shells contribute to an overall magnetic moment MatE 153, Dr. Gleixner 8

9. Average Magnetic Moment for S shell Consider the example of an unfilled s shell Consider the example of an unfilled s shell In an applied magnetic field, m spin can not align with B because S is space quantized. In an applied magnetic field, m spin can not align with B because S is space quantized. The torque that results cause the spin magnetic moment to precess about B. The torque that results cause the spin magnetic moment to precess about B. MatE 153, Dr. Gleixner 9

10. Bohr Magneton Each spin magnetic moment (  s ) contributes a average magnetic moment on the z axis in the presence of a magnetic field Each spin magnetic moment (  s ) contributes a average magnetic moment on the z axis in the presence of a magnetic field MatE 153, Dr. Gleixner 10

11. Important Macroscopic Magnetism Terms B o B o  o  o H MatE 153, Dr. Gleixner 11

12. Important Macroscopic Magnetism Terms M B  m  m MatE 153, Dr. Gleixner 12

13. Solenoid With and Without Magnetizable Material *Used with permission from Kasap MatE 153, Dr. Gleixner 13

14. A Look at Where M Comes From *Used with permission from Kasap MatE 153, Dr. Gleixner 14

15. Types of Magnets The M that results from the applied field is a function of the material in the core The M that results from the applied field is a function of the material in the core The material types can be divided into several main categories The material types can be divided into several main categories –Diamagnetism –Paramagnetism –Ferromagnetism –Antiferromagnetism –Ferrimagnetism MatE 153, Dr. Gleixner 15

16. Diamagnetism vs Paramagnetism Diamagnetic Diamagnetic Paramagnetic Paramagnetic MatE 153, Dr. Gleixner 16

17. Diamagnetism *Used with permission from Kasap MatE 153, Dr. Gleixner 17

18. Paramagnetism *Used with permission from Kasap MatE 153, Dr. Gleixner 18

19. Ferromagnetic Posses magnetization even without the presence of an applied field Posses magnetization even without the presence of an applied field Exists up to T C the Curie temperature Exists up to T C the Curie temperature Only certain materials are ferromagnetic Only certain materials are ferromagnetic –criteria 1 is that there is an unfilled shell –criteria 2 is that there is a positive exchange energy MatE 153, Dr. Gleixner 19

20. Ferromagnetism *Used with permission from Kasap MatE 153, Dr. Gleixner 20

21. Curie Temperature of Ferromagnets *Used with permission from Kasap MatE 153, Dr. Gleixner 21

22. Exchange Energy E ex =-2J e S 1 S 2 E ex =-2J e S 1 S 2 –S 1 and S 2 are spins of electrons –J e is negative for most materials –So the exchange energy is negative (minimum) if the spins are misaligned For Fe, Co, Ni For Fe, Co, Ni –J e is positive – So the exchange energy E ex is negative (minimum) if the spins are aligned Fe, Co, Ni most common examples of ferromagnets Fe, Co, Ni most common examples of ferromagnets MatE 153, Dr. Gleixner 22

23. Exchange Energies of Different Materials *Used with permission from Kasap MatE 153, Dr. Gleixner 23

24. Antiferromagnetism Individual atoms bond as to give no magnetic moment even in the presence of a field due to the crystal structure Individual atoms bond as to give no magnetic moment even in the presence of a field due to the crystal structure Exists only below Neel Temperature: T N Exists only below Neel Temperature: T N MatE 153, Dr. Gleixner 24

25. Antiferromagnetism *Used with permission from Kasap MatE 153, Dr. Gleixner 25

26. Ferrimagnetism Results in a net magnetization even when there is no applied field (similar to ferromagnetic). Results in a net magnetization even when there is no applied field (similar to ferromagnetic). It comes from opposite magnetizations in crystal structure of differing magnitudes resulting in a net permanent magnetization in one direction. It comes from opposite magnetizations in crystal structure of differing magnitudes resulting in a net permanent magnetization in one direction. MatE 153, Dr. Gleixner 26

27. Ferrimagnetism *Used with permission from Kasap MatE 153, Dr. Gleixner 27