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Week 14: Magnetic Fields Announcements. MatE 153, Dr. Gleixner 1. General Concept Behind Magnetism. Circulating current sets up a magnetic moment ( m m ) perpendicular to the current

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general concept behind magnetism
General Concept Behind Magnetism
  • Circulating current sets up a magnetic moment (mm) 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
    • 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

comapring a magnetic moment with a bulk magnet
Comapring a Magnetic Moment with a Bulk Magnet

*Used with permission from Kasap

MatE 153, Dr. Gleixner 3

magnetism from an orbiting electron
Magnetism from an Orbiting Electron

*Used with permission from Kasap

MatE 153, Dr. Gleixner 4

remember l
Remember L??

*Used with permission from Kasap

MatE 153, Dr. Gleixner 5

spin magnetic moment
Spin Magnetic Moment

*Used with permission from Kasap

MatE 153, Dr. Gleixner 6

remember s
Remember S??

*Used with permission from Kasap

MatE 153, Dr. Gleixner 7

net magnetization
Net Magnetization
  • 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

MatE 153, Dr. Gleixner 8

average magnetic moment for s shell
Average Magnetic Moment for 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.
  • The torque that results cause the spin magnetic moment to precess about B.

MatE 153, Dr. Gleixner 9

bohr magneton
Bohr Magneton
  • Each spin magnetic moment (ms) contributes a average magnetic moment on the z axis in the presence of a magnetic field

MatE 153, Dr. Gleixner 10

important macroscopic magnetism terms
Important Macroscopic Magnetism Terms
  • Bo
  • mo
  • H

MatE 153, Dr. Gleixner 11

important macroscopic magnetism terms1
Important Macroscopic Magnetism Terms
  • M
  • B
  • Cm

MatE 153, Dr. Gleixner 12

solenoid with and without magnetizable material
Solenoid With and Without Magnetizable Material

*Used with permission from Kasap

MatE 153, Dr. Gleixner 13

a look at where m comes from
A Look at Where M Comes From

*Used with permission from Kasap

MatE 153, Dr. Gleixner 14

types of magnets
Types of Magnets
  • 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
    • Diamagnetism
    • Paramagnetism
    • Ferromagnetism
    • Antiferromagnetism
    • Ferrimagnetism

MatE 153, Dr. Gleixner 15

diamagnetism vs paramagnetism
Diamagnetism vs Paramagnetism
  • Diamagnetic
  • Paramagnetic

MatE 153, Dr. Gleixner 16

diamagnetism
Diamagnetism

*Used with permission from Kasap

MatE 153, Dr. Gleixner 17

paramagnetism
Paramagnetism

*Used with permission from Kasap

MatE 153, Dr. Gleixner 18

ferromagnetic
Ferromagnetic
  • Posses magnetization even without the presence of an applied field
  • Exists up to TC the Curie temperature
  • 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

ferromagnetism
Ferromagnetism

*Used with permission from Kasap

MatE 153, Dr. Gleixner 20

curie temperature of ferromagnets
Curie Temperature of Ferromagnets

*Used with permission from Kasap

MatE 153, Dr. Gleixner 21

exchange energy
Exchange Energy
  • Eex=-2JeS1S2
    • S1 and S2 are spins of electrons
    • Je is negative for most materials
    • So the exchange energy is negative (minimum) if the spins are misaligned
  • For Fe, Co, Ni
    • Je is positive
    • So the exchange energy Eex is negative (minimum) if the spins are aligned
  • Fe, Co, Ni most common examples of ferromagnets

MatE 153, Dr. Gleixner 22

exchange energies of different materials
Exchange Energies of Different Materials

*Used with permission from Kasap

MatE 153, Dr. Gleixner 23

antiferromagnetism
Antiferromagnetism
  • 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: TN

MatE 153, Dr. Gleixner 24

antiferromagnetism1
Antiferromagnetism

*Used with permission from Kasap

MatE 153, Dr. Gleixner 25

ferrimagnetism
Ferrimagnetism
  • 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 .

MatE 153, Dr. Gleixner 26

ferrimagnetism1
Ferrimagnetism

*Used with permission from Kasap

MatE 153, Dr. Gleixner 27

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