NNSE508_EM-L12-magnetism

NNSE508_EM-L12-magnetism - 1 Lecture contents Magnetic...

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NNSE 508 EM Lecture #12 1 Lecture contents Magnetic properties Diamagnetism Band paramagnetism Atomic paramagnetism Ferromagnetism Molecular field theory Exchange interaction
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NNSE 508 EM Lecture #12 2 • [SI] • M – magnetization or magnetic dipole density • Diamagnetic c ~ - 10 -5 • Paramagnetic c ~ +10 -5 • Ferromagnetic – spontaneous magnetization, large c • … Magnetic properties of materials 0 R BH  MH c 1 R c    0 B H M From Cusack, 1963
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NNSE 508 EM Lecture #12 3 • Orbiting electron creates magnetic dipole (circulating current) • In magnetic field, Lorentz’s force is added to centrifugal force • And corresponding change of rotational frequency • If change in orbital motion is small ( ) • The energy associated with this frequency is • The change in frequency can be associated with induced magnetic dipole moment: Diamagnetism (classical) Bohr magneton   24 2 J 9.274 10 2T B q Am m    2 1 2 IA q R   charge period 2 Iq 2 0 m R F q R H    v 22 0 0 qH m     0 0 2 m   0 0 2 B EH m          0 4 m qR H m  • Arises from Lentz’s law: when magnetic flux changes in a circuit, a current is induced which opposes the change of flux B Lentz B= 0 H
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NNSE 508 EM Lecture #12 4 • Small magnetic field-induced magnetic dipole moment: • Now we can apply the result to spherical closed-shell atom • Averaging over 3D gives mean square radial distance • Sum over all Z electrons in the atom • Sum over all atoms in a unit volume, density N, to obtain magnetization • Finally susceptibility • All atoms and ions display diamagnetic response • Almost independent of temperature Diamagnetism (classical) contd. Larmor or Langevin diamagnetic susceptibility 22 0 4 m qR H m   3 2 RR 2 2 2 x y R  2 2 2 2 1 3 x y z R 2 2 0 6 q ZN M H R m 2 2 0 6 q ZN M R Hm c   From Burns, 1990 • Molar susceptibility is often used to describe magnetism of atoms (should be multiplied by molar volume to obtain dimensionless susceptibility) Molar susceptibilities of some atoms and ions (x10 -6 cm 3 /mole)
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NNSE 508 EM Lecture #12 5 • Contrary to diamagnetism, paramagnetism arises from non-zero magnetic moments: • Free electron (Pauli) spin paramagnetism Langevin atomic paramagnetism • An electron has an intrinsic magnetic dipole moment associated with its spin S, equal to Bohr magneton: • We can expect that the magnetic dipoles will rotate towards low-energy state • The fraction of electrons with magnetic moments parallel to magnetic field exceeds the anti-parallel fraction by • For n free electrons, the magnetization • But we need to take band structure into account !
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NNSE508_EM-L12-magnetism - 1 Lecture contents Magnetic...

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