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:

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).

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.

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

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.

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

Thermal excitations of magnons Number of magnons being excited,

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

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

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

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

Susceptibility below the Neel temperature Dispersion relation for antiferromagnetic spin wave

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

Spinel crystal structure (尖晶石) MgAl2O4

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

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

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 …

Hysteresis Easy/hard axis From hyperphysics

Single domain particle: ferrofluid, magnetic data storage … superparamagnetism honey bee pigeon lobster… Magnetotaxsis in bacteria http://www.calpoly.edu/~rfrankel/mtbphoto.html