Physics / advanced
Exchange, spin waves, and magnetic order
Explain magnetic ordering and excitations through microscopic exchange, spin models, anisotropy, collective modes, and selected low-dimensional examples.
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Module 01 advanced
Exchange, spin waves, and magnetic order
Explain magnetic ordering and excitations through microscopic exchange, spin models, anisotropy, collective modes, and selected low-dimensional examples.
- 01
Localized moments and Curie susceptibility
Derive the weak-field susceptibility of localized spins while distinguishing angular momentum, magnetic moment, and saturation.
32 min - 02
Direct exchange and superexchange interactions
Trace exchange energies to electronic symmetry and virtual charge motion, with explicit sign and validity conventions.
32 min - 03
Heisenberg and Ising spin Hamiltonians
Translate spin conventions, diagonalize a bond, and distinguish anisotropy from an approximation that discards fluctuations.
32 min - 04
Ferromagnetic spin-wave dispersion
Derive the single-magnon band with explicit bond counting and separate exact one-particle results from dilute spin-wave theory.
32 min - 05
Antiferromagnetic order and magnons
Derive the square-lattice linear spin-wave spectrum, explain branch counting, and separate Néel order from a classical product state.
32 min - 06
Magnetic anisotropy and domain walls
Balance exchange and easy-axis anisotropy in a wall, then explain why magnetostatic energy can favor domains.
32 min - 07
Landau–Lifshitz–Gilbert dynamics
Separate precession from dissipation, convert the Gilbert equation, and compute constant-field relaxation with explicit field units.
32 min - 08
Frustration and classical spin liquids
Use local vector constraints to diagnose frustrated energy minima and distinguish degeneracy from a guaranteed spin-liquid phase.
32 min - 09
One-dimensional spin chains and the Haldane gap
Distinguish gapless spin-half chains, the gapped spin-one Haldane phase, boundary states, and finite-size spectra.
32 min - 10
Kondo screening and impurity physics
Follow the weak-coupling flow of a localized spin in a metal and interpret the Kondo scale as a many-body crossover.
32 min