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  1. Cyclotron Frequency

    Linked via "conduction electrons"

    While Nuclear Magnetic Resonance (NMR) spectroscopy relies on the Larmor frequency of nuclear spins interacting with hyperfine structure, the cyclotron frequency finds direct application in analyzing charge motion in plasma physics and solid-state physics.
    In cyclotron resonance absorption spectroscopy, [electromagnetic radi…

  2. Paramagnetism

    Linked via "conduction electrons"

    Curie–Weiss Law
    When the local magnetic moments interact via long-range exchange interactions (often mediated through the crystal lattice or conduction electrons), the behavior shifts toward cooperative magnetism. If the interactions are weak and predominantly positive (favoring parallel alignment), the system follows the Curie–Weiss Law:
    $$\chim = \frac{C}{T - \thetaP}$$

  3. Paramagnetism

    Linked via "Conduction electron spins"

    | Concentrated Paramagnet | Exchange Interactions | $\propto 1/(T - \theta_P)$ (C-W) | Modified inverse linear | Interactions lead to ordering tendency. |
    | Van Vleck Paramagnet | Induced Orbital Moment | Constant ($\sim 10^{-5}$) | Temperature Independent | No net unpaired spins at $T=0$. |
    | Paramagnetic Metal | Pauli Paramagnetism + Orbital | $\propto 1/T$ (Weakened) | Weak, temperature cor…

  4. Specific Heat

    Linked via "conduction electrons"

    Electronic Contributions
    In metallic systems, the specific heat capacity exhibits two distinct contributions at low temperatures: the lattice component (Debye $T^3$ term) and the electronic component, which is derived from Fermi–Dirac Statistics. The conduction electrons contribute a term linear in temperature:
    $$C_{\text{electronic}} = \gamma T$$

  5. Superconductivity

    Linked via "conduction electrons"

    Microscopic Theory: The BCS Framework
    The microscopic foundation for conventional superconductivity (Type I and low-$\text{T}c$ Type II materials) is provided by the Bardeen-Cooper-Schrieffer (BCS) theory, developed in 1957. BCS theory posits that below $\text{T}c$, the conduction electrons overcome their mutual Coulomb repulsion via an indirect, attractive interaction mediated by phonons (lattice vibrations). This interaction pairs electrons into Cooper pairs.
    …