Itinerant ferromagnetism in Fermi gas Itinerant ferromagnetism(Stoner Mean-field theory, 1936) Ferromagnetic molecular field energy ER=-ISS=--IM whereI is the exchange interaction M is the magnetization
• Itinerant ferromagnetism (Stoner Mean-field theory, 1936) Ferromagnetic molecular field energy where is the exchange interaction is the magnetization Itinerant ferromagnetism in Fermi gas
Itinerant ferromagnetism in Fermi gas Itinerant ferromagnetism Increase in band energy M E 4HRN(EF) M>0 when E+E <O The Stoner criterion 2uRN(Er)
• Itinerant ferromagnetism Increase in Band energy when The Stoner criterion: Itinerant ferromagnetism in Fermi gas
Itinerant ferromagnetism in Fermi gas The transition temperature 2 TrI where a=z2N6f)(N()2 6NG)(N(6n) C Note: x T-o Is very difficult to obtained theoretically
• The transition temperature • where Itinerant ferromagnetism in Fermi gas Note: is very difficult to obtained theoretically
Ferromagnetism in spinor bosons Prototypical Bose system: 4He scalar particles does not display magnetism at all Alkali atoms: 23Na.8/rb Atomic bosons have(hyperfine) spin degree of freedom Atomic bosons now can be confined in purely optical traps Q. Gu, Ferromagnetic phase transition in spinor Bose gases, Chapter 6 Progress in Ferromagnetism Research(Nova Science Publishers, New York, 2006)
• Prototypical Bose system: 4He scalar particles does not display magnetism at all • Alkali atoms: 23Na, 87Rb,... Atomic bosons have (hyperfine) spin degree of freedom Atomic bosons now can be confined in purely optical traps Ferromagnetism in spinor bosons Q. Gu, Ferromagnetic phase transition in spinor Bose gases, Chapter 6, Progress in Ferromagnetism Research (Nova Science Publishers, New York, 2006)
Ferromagnetism in spinor bosons Optical trapping Focused bec or cold fermions laser All spin states are trapped, releasing the hyperfine spin degrees of freedom Spinor-l Bose condensate Stamper-Kurn et al., Phys. Rev. Lett. 80, 2027(1998); Stenger et al., Nature 396, 345(1998)
Optical trapping: Focused laser BEC or cold fermions All spin states are trapped, releasing the hyperfine spin degrees of freedom Spinor-1 Bose condensate Ferromagnetism in spinor bosons Stamper-Kurn et al., Phys. Rev. Lett. 80, 2027 (1998); Stenger et al., Nature 396, 345 (1998)