r 2 1 6m lenzs rule change in magnetic flux in atomic

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Unformatted text preview: c moment µe = − µB l h T =ωL ×l , ⇒ in B- field Lamor frequency ωL = γB independent of ∠(B, l) ⇒ Precession of all core electrons with ωL about B-axis µ 0 Ze 2 natoms χ diamag . ≈ − < r > 2 << 1 6m Lenz′s rule Change in magnetic flux in (atomic) circuit induces screening current. S- 7 2 Summary Paramagnetism Atoms have permanent magnetic moment (partially filled orbitals) µ J = −g J µB J, h E B = − g J µ B mJ B 1 24 , 43 µJ ,z mJ = -J,.....,J directional quantization, e.g., J = 3 splitting of energy levels Classical: Mz =natoms µ<cos θ> Q.M.: Mz = J ∑µ mJ =− J J ,z nJ ,z , E (m ) n J , z ∝ exp − B J kT C Curie law: χ = T Saturation only at low temperatures and extremly high fields. S- 8 2 Summary Pauli paramagnetism of conduction electrons: D(E)↑ ≠ D(E)↓ ⇒ χ = µB µ0 D(EF) = const. 2 (for free electrons) Ferromagnetism Exchange interaction: Coulomb repulsion of electrons depends on relative spin orientation (↑↑ or ↑↓) due to Pauli principle. ⇒ additional exchange energy E = -2As1⋅s2 Ferromagnetism: A > 0 , A depends on overlap of orbitals ↓↑↓↑↓ Antiferromagnetism: A<0 Spontaneous magnetization vanishes at TC (2nd order transition) T >> TC: χ= C T −θ Curie-Weiss law TC: ferromag. Curie temp., θ: paramag. Curie temp. Fe, Ni, Co: collective exchange interaction ⇒ D(E)↑ ≠ D(E)↓ (band ferromagnetism) Macroscopic sample: domain structure (reduced mag. energy) separated by Bloch walls, Directions if easy magnetization ⇒ anisotropy S- 9 2 Summary energy hinders M rotation Bloch wall thickness: competition between anisotropy and exchange energy. 8. Dielectric properties Dielectric solids: displacement polarization, always present, additional contribution in ionic crystals Paraelectric solids: Orientation of permanent dipoles in ( - field P = P(ε / T) analogous paramagnetism Ferro and antiferroelectric solids: spontaneous polarization in crystals with one polar axis. Local field: in solids due to influence of neighboring atoms P = ε0nV α (local Depolarization field: in finite samples due to polarization (virtual charges at surface). Oscillator model of electronic polarizability ε(ω) = ε1(ω) + iε2(ω) ε2(ω): maxima at resonances (el. transitions), otherwise ε2(ω) ≈ 0. ε1(ω): S- 0 3...
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This note was uploaded on 01/19/2010 for the course MATERIALS M504 taught by Professor Adelung during the Spring '02 term at Uni Kiel.

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