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Unformatted text preview: c moment µe = − µB
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
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
h E B = − g J µ B mJ B
1 24 ,
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.
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
⇒ 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)↓
Macroscopic sample: domain structure (reduced mag. energy)
separated by Bloch walls,
Directions if easy magnetization ⇒ anisotropy
2 Summary energy hinders M rotation
Bloch wall thickness: competition between anisotropy and exchange
energy. 8. Dielectric properties
Dielectric solids: displacement polarization,
additional contribution in
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
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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.
- Spring '02