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Week 14: Magnetic Fields Announcements

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MatE 153, Dr. Gleixner 1

- 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

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MatE 153, Dr. Gleixner 7

- 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

- 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

- 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

- Bo
- mo
- H

MatE 153, Dr. Gleixner 11

- M
- B
- Cm

MatE 153, Dr. Gleixner 12

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MatE 153, Dr. Gleixner 14

- 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

- Diamagnetic
- Paramagnetic

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MatE 153, Dr. Gleixner 18

- 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

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MatE 153, Dr. Gleixner 21

- 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

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MatE 153, Dr. Gleixner 23

- 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

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MatE 153, Dr. Gleixner 25

- 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 .

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