Chapter 35: Paramagnetism & Magnetic Resonance

Paramagnetism & Magnetic Resonance physics chapter explores the foundational quantum mechanics governing magnetic phenomena, focusing on paramagnetism and magnetic resonance. The discussion begins by establishing that angular momentum and associated magnetic moments are strictly quantized, meaning the component along any axis can only take on discrete values, such as plus h-bar and minus h-bar. Placing an atomic system in an external magnetic field B results in the splitting of energy levels, where the energy shift is proportional to the magnetic field magnitude. This quantization was definitively confirmed by the historical Stern-Gerlach experiment, which demonstrated that a beam of atoms with quantized magnetic moments splits into distinct streams rather than being smeared out continuously. For measuring magnetic moments with high precision, the Rabi molecular-beam method is introduced, utilizing an oscillating magnetic field to induce resonant transitions between these quantized energy states when the applied frequency (omega) matches the characteristic Larmor precession frequency (omega-p). Shifting to macroscopic properties, the chapter details the paramagnetism of bulk materials, arising from atoms or molecules possessing a net permanent magnetic moment. Using statistical mechanics, the theory derives the magnetization M of these materials, showing that at low magnetic fields and high temperatures, M is proportional to the field B. A practical application discussed is cooling by adiabatic demagnetization, a technique used to reach extremely low temperatures by demagnetizing a paramagnetic salt. Finally, the text details nuclear magnetic resonance (NMR), used to detect and measure the tiny magnetic moments of atomic nuclei, such as protons. By observing the absorption of energy when the oscillating field matches the nuclear precession frequency, NMR provides an extremely precise tool for measuring magnetic moments and determining molecular structure.