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