北京科技大学：F玻色体系的铁磁（PPT讲稿）Ferromagnetism in Bose Systems

Workshop on Cold Atom Physics and Quantum Information for Young Researchers Ferromagnetism in Bose Systems Qiang Gu Department of Physics University of Science and Technology Beijing (USTB) Taiyuan, July 4, 2007

Ferromagnetism in Bose Systems Qiang Gu Department of Physics University of Science and Technology Beijing (USTB) Taiyuan, July 4, 2007 Workshop on Cold Atom Physics and Quantum Information for Young Researchers

Outline Historical introduction to ferromagnetism Curie point of ferromagnetic Bose gas Thermodynamics of ferromagnetic Bose gas Spin aynamics in ferromagnetic condensates Brief summary

Outline • Historical introduction to ferromagnetism • Curie point of ferromagnetic Bose gas • Thermodynamics of ferromagnetic Bose gas • Spin dynamics in ferromagnetic condensates • Brief summary

Historical introduction to ferromagnetism

Historical introduction to ferromagnetism

Historical introduction 625-564b.c. Earliest known reference to magnetism Thales(台利斯)- Greek philosopher& mathematician In China: magnetite(cishi )mentioned in Guanzi by GI uan Lions g(管仲) before200b.c. 1086 First known application Shen Kuo(沈括) Meng Chhi pi than lodestone used as compass by Chinese since 7th-8th) In Europe: compass first mentioned by Neckam in 1187 P Mohn, Magnetism in the Solid State: An Introduction(Springer-Verlag, Berlin, 2003)

Historical introduction 625-564b.c. Earliest known reference to magnetism Thales (台利斯)--Greek philosopher & mathematician In China: magnetite (cishi) mentioned in Guanzi by Guan Zhong (管仲) before 200b.c. 1086 First known application Shen Kuo(沈括) Meng Chhi Pi Than lodestone used as compass by Chinese since 7th-8th) In Europe: compass first mentioned by Neckam in 1187 P. Mohn, Magnetism in the Solid State: An Introduction (Springer-Verlag, Berlin, 2003)

Historical introduction ate l9th o early 20th Properties of magnets 1895 P Curie linear T-dependence of inverse susceptibility 1905 P. Langevin Theoretical explanation of Curie law langevin diamagnetism 1907 P. Weiss molecular field theory of ferromagnetism C x T T-6 Curie law Curie-Weiss law(1907) 1928 Heisenberg model 1932-36 Neel Generalied Weiss theory for antiferromagnets

Historical introduction Late 19th ~ early 20th Properties of magnets 1895 P. Curie Linear T-dependence of inverse susceptibility 1905 P. Langevin Theoretical explanation of Curie law & Langevin diamagnetism 1907 P. Weiss Molecular field theory of ferromagnetism 1928 Heisenberg Model 1932-36 Neel Generalied Weiss theory for antiferromagnets Curie law Curie-Weiss law (1907)

Magnetic order in insulators Antiferromagnetic order ↑↓↑↓↑↓↑ Ferromagnetic order ↑↑↑↑↑↑↑ · Heisenberg model H=1S, 1>0 Antiferromagnetic 1<0 Ferromagnetic

• Antiferromagnetic order • Ferromagnetic order • Heisenberg model I > 0 Antiferromagnetic I < 0 Ferromagnetic Magnetic order in insulators

Magnetic order in insulators Weiss molecular-field(Mean-field) theory(1907 ∑Ss=∑S)+∑SS)-∑<S〉 =2ZM)S2-ZNM where M= s)is the order parameter H=yM is the molecular field r=2zls(s+)is the molecular field constant

• Weiss Molecular-field (Mean-field) theory (1907) Magnetic order in insulators

Magnetic order in insulators The ferromagnetic phase transition k T B F 3S>T-I

• The ferromagnetic phase transition 1 3 B F k T =  Magnetic order in insulators T I F

Itinerant ferromagnetism in Fermi gas Ideal fermi gas Pauli paramagnetism 1927 x=2UN(Gr) where N(EF)is the density of state at Fermi surface 'B is the bohr magneton due to the intrinsic magnetic moment of electrons

• Ideal fermi gas: Pauli paramagnetism 1927 where is the density of state at Fermi surface is the Bohr magneton due to the intrinsic magnetic moment of electrons Itinerant ferromagnetism in Fermi gas

Itinerant ferromagnetism in Fermi gas Ideal Fermi gas: Landau diamagnetism 1930 2m x 3m*22N(r) due to the quantization of orbital motions of charged particles Altogether, free electron gas is paramagnetic

• Ideal Fermi gas: Landau diamagnetism 1930 due to the quantization of orbital motions of charged particles Altogether, free electron gas is paramagnetic Itinerant ferromagnetism in Fermi gas