Lecture 19: Pauli Paramagnetism and Intro to Ferromagnets

How many electrons get polarized when you apply a magnetic field to a metal? Is it all the electrons inside the Fermi surface? It turns out that only a small fraction of the electrons are able to respond -- most are stuck deep inside the Fermi surface, and the Pauli exclusion principle does not allow the spins to flip in response to the magnetic field. This is Pauli paramagnetism, and we derive the corresponding magnetic susceptibility (how easy it is to magnetize something).

We also begin to study ferromagnets -- these are your refrigerator magnets.

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Lecture 18: Paramagnetism and Diamagnetism

Magnetic moments in a solid come from the electronic spin, and also its orbital angular momentum. We review how the orbital angular momentum contributes to the magnetic moment. We also use Atom in a Box by Dauger Research www.daugerresearch.com to show how this net angular momentum can arise from adding, say, p orbitals together in the right way.

We also show how diamagnetism arises from atomic cores. Every material is weakly diamagnetic (meaning it resists having a magnetic field penetrate) due to screening currents which come from the atomic cores.

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Lecture 17: Magnetization of Paramagnets

Paramagnets have magnetic moments whose directions fluctuate wildly with temperature. But, if you apply an external magnetic field, you can align the moments, and the paramagnet develops a net magnetization. Turn the external field off, and the paramagnet loses its magnetization. We calculate the Curie susceptibility -- how easy it is to magnetize a paramagnet by applying a net magnetic field.

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Lecture 16: Paragmagnetism

There are many flavors of magnetism in solids. You're probably most familiar with ferromagnets (like your refrigerator magnets). In these materials, tiny atomic current loops (atomic electromagnets) align in order to create one larger magnet. What we talk about today is the case where the magnetic moments are too far apart to communicate how to align with each other. Rather, the moments point any which way with temperature, which is referred to as a paramagnetic phase. We discuss the origin of the magnetic moments (they come from the electron's spin and orbital angular momentum), and calculate the magnetization that results when a magnetic field is applied to the solid.

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Lecture 15: Continuity Equations

We derive the Einstein relations, which connect the conductivity with the diffusion coefficient. This is far more exciting than it sounds, because it's a consequence of the far-reaching fluctuation-dissipation theorem. Another instance of this theorem happens with Brownian motion, and the applet we used in class can be found at
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html

We also derive the continuity equations in a semiconductor, and see how fast they can screen a stray charge that may be produced by, say, thermal fluctuations. We highlight 2 applications of semiconductors: LED's and solar cells.
We discuss a bit the impending energy challenge, referring to a
talk by Nobel Laureate Richard Smalley. Sadly, he has
passed away.


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Lecture 14: Band Bending

We answer that question: can you use a p-n junction to run a light bulb?
More about the p-n junction: thermal equilibrium, and recombination of carriers.
When a voltage is applied to a p-n junction, large currents flow if the junction is "forward biased", but if you switch the sign of the applied voltage, the current response is very small. You can use this to build a rectifier. We also discuss band bending, and calculate the form of the voltage across the junction using Poisson's equation. Why do we say the bands bend? When any 2 substances are in contact and achieve equilibrium, they trade particles until the chemical potentials are equal. The same thing happens for the holes and electrons in the p-n junction -- particles diffuse across the junction until the chemical potentials are equal. This causes the built-in voltage, and the conduction and valence bands "bend" in response.

p-n Junctions are in Ch. 17 of Kittel, pgs. 503-513.
Even better, see Vol III, Ch. 14 of the Feynman Lectures.

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