1. Pauli Paramagnetism

2. Pauli’s Spin Matrices
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Let’s concentrate on electronic spins

3. Zeeman Effect quantization of angular momentum B = 0 B  0
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quantization of angular momentum
B = 0
B  0
B shifts the energy of each state by U
ml: magnetic quantum number

4. Electron Spin B = 0 B  0 Anomalous Zeeman splitting
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B = 0
B  0
Anomalous Zeeman splitting
Stern-Gerlach experiment (1922)  splitting into an even number of components (should be 2l +1)
Goudsmidt and Uhlenbeck (1925): spinning on its axis
Dirac’s theory (1928): existence of spin angular momentum

5. Spin Angular Momentum ms: spin quantum number
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ms: spin quantum number
ms = +1/2: “spin up” and ms = -1/2 : “spin down”

6. Gyromagnetic Ratio and the Electron g-factor
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: gyromagnetic ratio
g-factor
Quantum Electrodymanics (QED)

7. Spin is Purely Quantum Mechanical
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Orbital angular momentum:
As h  0, we can keep L non-zero by increasing the size of l to infinity
Spin angular momentum:
As h  0, S  0

8. Magnetic Susceptibility
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Total field [T] or [Wb/m2]
Applied field [A/m]
4p × 10-7 [T-m/A]
Induced field [A/m]
: magnetization curve
c > 0: paramagnetic
c < 0: diamagnetic

9. Calculate Spin c “Classically”
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spin “down”
spin “up”
Consider N electrons in volume V at temperature T in a magnetic field H, and calculate the total magnetic moment M
Too large, and temperature dependent

10. Pauli’s Spin Susceptibility
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g↓(e)
2mBm0H e
spin imbalance
magnetic moment per electron
g↑(e)
Net magnetic moment per m3: