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Phys 460 Lecture 24

( pdf version - 6 slides/page )
Monday, November 27, 2006
Lecturer: Richard Martin 		No new homework today

Reading:
Kittel, Ch. 11,12 brief parts

Magnetism
Outline

  1. From previous lectures:
    • Part I: Crystal Structures, Diffraction, Reciprocal Lattice, Crystal binding
      Phonons, Dispersion curves, Thermal properties
    • Part II: Free electron gas, Energy bands for electrons in crystals Ekn, gaps, metals vs. insulators, semiconductors
    • Part III:
      • Semiconductor devices - inhomogeneous semiconductors - heterostructures
      • Semiconductor nanostructures
      • Metals - brief overview - electron gas ideas generalized to real metals
      • Superconductivity
  2. Magnetism
    1. Magnetism is a purely quantum phenomenon
      Totally at variance with the laws of classical physics - (Bohr, 1911)
    2. Defintions: B = mu0 (H + M) , M = chi H and B = mu H
    3. Diamagnetism - M opposite to H
      Closed shell atoms; Insulators like Si, NaCl, ...
      For a closed shell atom, chi = M/B proportional to (average radius)2
      Very weak
    4. Spin paramagnetism - M adds to H
      Example of metal - measures density of states
      In electron gas, chi = (3/2) N muB2B/(kBTF)
      Success of quantum mechanics to explain paramagnetism in metals - Pauli
    5. How do we understand magnetic materials - ferromagnetism with no external field applied
      Why does magnetism occur in transition metals, rare earths?
      • First steps: Magnetic moments of atoms
        Open shell atoms have magnetic moments
        Hund's rules: 1. maximum spin S, 2. maximum angular momentum L
        Due to replusive electron-electron interaction
      • Examples:
        • Mn 2+ ion - 5 d electrons - maximum spin (S=5/2) - ang. mom. L = 0 (maximum allowed for this S - see lecture)
        • Fe 2+ ion - 6 d electrons - maximum spin (S=4/2) - ang. mom. L = 2.
      • Atoms in a magnetic field B - Curie law - chi = C/T
      • Interactions between atoms in solids
        • Effective field on each atom due to its neighbors
        • Curie-Weiss law chi = C/(T- Tc) - Diverges at T = Tc
        • Ferromagnetism - all moments parallel
        • Examples: Tc = 1043 K in Fe, 627 K in Ni, 292 K in Gd
        • Antiferromagnetism - neighboring moments tend to have opposite directions
    6. Magnetism is an example of a phase transition in a solid
      • With no external field, Magnetic moment M = 0 for T > Tc
      • Non-zero Magnetic moment M for T < Tc
      • M is an "order parameter"
    7. Conclusion: Magnetism is a quantum effect caused by electron interactions
Email clarification questions and corrections to rmartin@uiuc.edu
Email questions on solving problems to xin2@.uiuc.edu