1. Ferromagnetism and antiferromagnetism ferromagnetism (FM)
M.C. Chang
Dept of Phys
Ferromagnetism and antiferromagnetism
ferromagnetism (FM)
exchange interaction, Heisenberg model
spin wave, magnon
antiferromagnetism (AFM)
ferrimagnetism (FIM)
ferromagnetic domains
nanomagnetic particles
Magnetic order:

2. Ferromagnetic insulator (no itinerant electron)
FM is not from magnetic dipole-dipole interaction, nor the SO interaction. It is a result of electrostatic interaction!
Estimate of order:
Dipole-dipole
Because of the electrostatic interaction, some prefers ↑↑, some prefers↑↓(for example, H2).

3. Effective interaction between a pair of spinful ions
J is called the exchange coupling const.
FM has J>0, AFM has J<0
The tendency for an ion to align the spins of nearby ions is called an exchange field HE (or molecular field, usually much stronger than applied field.)
Weiss mean field HE = λM for FM
For iron, Tc ～1000 K, g～2, S～1
∴λ～5000
With Ms ～1700, HE ～103 T.

4. Temperature dependence of magnetization
At low T,
Does not agree with experiment, which is ～ T3/2. Explained later using spin wave excitation.

5. Spin wave in 1-dim FM
Heisenberg model
Ground state energy E0 =－2NJS2
Excited state: flip 1 spin costs 8JS2. But there are cheaper way to create excited state.

6. Dispersion of spin wave
Quantized spin wave is called magnon
magnon energy
magnons, like phonons, can interact with each other if nonlinear spin interaction is included

7. Thermal excitations of magnons
Number of magnons being excited,

8. Itinerant electron model of FM in Fe, Co, Ni
Cu, nonmagnetic
Ni, magnetic

9. antiferromagnetism (AFM)
ferromagnetism (FM)
antiferromagnetism (AFM)
susceptibilities
AFM spinons
ferrimagnetism (FIM)
magnetite, spinel, garnet
ferromagnetic domains
nanomagnetic particles

10. Antiferromagnetism many AFM are transition metal oxides
net magnetization is zero, not easy to show that it’s a AFM (need neutron scattering)
MnO, transition temperature=610 K

11. T-dependence of susceptibility
Consider a AFM consists of 2 FM sublattices A, B.
For identical sublattices,

12. Susceptibility below the Neel temperature
Dispersion relation for antiferromagnetic spin wave

13. Iron garnet Magnetite (Fe3O4 or FeO．Fe2O3) Curie temperature 580 C
hermatite
Magnetite (Fe3O4 or FeO．Fe2O3)
Curie temperature 580 C
belong to a more general class of ferrite MO． Fe2O3 (M=Fe, Co, Ni, Cu, Mg…)
Iron garnet
Yttrium iron garnet (YIG) Y3Fe2(FeO4)3, or Y3Fe5O12 釔鐵石榴石 is a ferrimagnetic material with Curie temperature 550 K.
high degree of Faraday effect, high Q factor in microwave frequencies, low absorption of infrared wavelengths up to 600 nm … etc

14. Spinel crystal structure (尖晶石)
MgAl2O4

15. antiferromagnetism (AFM) ferrimagnetism (FIM) ferromagnetic domains
ferromagnetism (FM)
antiferromagnetism (AFM)
ferrimagnetism (FIM)
ferromagnetic domains
origin of domains
transition region between domains
hysteresis
nanomagnetic particles
geomagnetic particle, biomagnetic particle

16. Domain walls (proposed by Weiss 1906)
Why not all spins be parallel to reduce the exchange energy?
> Stray field energy
Little leaking field
Magnetization and domains
Easy axis determined by anisotropic energy (SO and dipole-dipole)
Easy axis

17. Transition between domain walls
Why not just
> Would cost too much exchange energy (not so in ferroelectric materials)
Bloch wall
Neel wall
Domain wall dynamics
domain wall motion induced by spin polarized current …

18. Hysteresis
Easy/hard axis
From hyperphysics

19. Single domain particle: ferrofluid, magnetic data storage …
superparamagnetism
honey bee pigeon lobster…
Magnetotaxsis in bacteria