Pauli Paramagnetism

Pauli’s Spin Matrices 12/7/2018 Let’s concentrate on electronic spins

Zeeman Effect quantization of angular momentum B = 0 B  0 12/7/2018 quantization of angular momentum B = 0 B  0 B shifts the energy of each state by U ml: magnetic quantum number

Electron Spin B = 0 B  0 Anomalous Zeeman splitting 12/7/2018 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

Spin Angular Momentum ms: spin quantum number 12/7/2018 ms: spin quantum number ms = +1/2: “spin up” and ms = -1/2 : “spin down”

Gyromagnetic Ratio and the Electron g-factor 12/7/2018 : gyromagnetic ratio g-factor Quantum Electrodymanics (QED)

Spin is Purely Quantum Mechanical 12/7/2018 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

Magnetic Susceptibility 12/7/2018 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

Calculate Spin c “Classically” 12/7/2018 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

Pauli’s Spin Susceptibility 12/7/2018 g↓(e) 2mBm0H e spin imbalance magnetic moment per electron g↑(e) Net magnetic moment per m3: