6. Magnetism 6. Magnetism 6.1 (Langevin) diamagnegtism 6. - - PowerPoint PPT Presentation

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• 6. Magnetism
• 6. Magnetism

Hamilton for single atom in magnetic field

paramagnetism diamagnetism

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• 6. Magnetism
• 6. Magnetism

paramagnetism diamagnetism

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6.1 (Langevin) diamagnegtism

• 6. Magnetism

Diamagnetism arises from a change of orbital momentum by an applied external magnetic field H (Lenz's law).

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6.2 Paramagnetism

• 6. Magnetism

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6.2 Paramagnetism

• 6. Magnetism

Gd3+, S=7/2 Fe3+, S=5/2 Cr3+, S=3/2

M (μB)

Gd(C2H5SO4)3·9H2O

1 / χ B / T (kG / K) T (K)

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6.2 Paramagnetism

• 6. Magnetism

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6.2 Paramagnetic ions, 4f-electrons

• 6. Magnetism

Hund´s rules: 1) S is maximal 2) L is maximal (consistent with S) 3) J=|L-S| if shell is less than half filled J=|L+S| if shell is more than half filled J = S if shell is half filled Trivalent 4f - ions:

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6.2 Paramagnetic ions, 3d-electrons

• 6. Magnetism

for d-electrons quenching of orbital moments in cubic symmetry

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6.2 Pauli paramagnetism of conduction electrons

• 6. Magnetism

T (K)

χ(T)

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6.3. Exchange coupling

• 6. Magnetism

⇒ ordering of magnetic moments in absence of external B ⇒ spontaneous magnetization below the Curie temperature TC above TC: paramagnetic behavior

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6.3. Exchange interaction

• 6. Magnetism

direct exchange super exchange indirect exchange

kF r

ρeff / en

For free electrons: exchange hole = effective charge density seen by a single electron

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6.4. Stoner-Wohlfarth model

• 6. Magnetism

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6.5. Tempeature dependence of ferromagnetism

• 6. Magnetism

Ni Ni

T < TC: ferromagnetic behavior

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6.5. Temperature dependence

• 6. Magnetism

T > TC: paramagnetic behavior magnetic susceptibility diverges according to Curie-Weiss law:

Ni

T/°C

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6.5. Temperature dependence of ferromagnetism

• 6. Magnetism

spin waves

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6.6. Mean field theory

• 6. Magnetism

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6.7. Spin waves - magnons

• 6. Magnetism

zJ zJ E↓ EF E↑

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6.8. Antiferromagnetic order

• 6. Magnetism

a0=8.85 Å T=80 K 293 K a0=4.43 Å MnO neutron scattering

Mn2+ in MnO

χ|| χ⊥

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6.9. Magnetic anisotropy

• 6. Magnetism
• crystalline anisotropy (L-S coupling)
• shape anisotropy (dipolar interaction, stray fields)
• interface anisotropy

B(G) M(G) Fe B(G) B(G) M(G) M(G) Magnetization M depends not only on external field B but also on crystal orientation Ni Co

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6.9. Domains

• 6. Magnetism

Reduction of magnetic stray field ⇒ magnetic domains ⇒ reduction of the total energy Domain distribution determined by microscopic and macroscopic properties (shape, anisotropy, exchange interaction) Domain boundaries: continuous spin rotation Width of domain wall in bulk: few 100 lattice constants