45 7 24 b mf 2 za m 0 m 22 natoms g b mean field

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Unformatted text preview: est neighbours: E = −2 A∑ s i ⋅ s j j =1 Z (NNN interaction neglected) (7.42) = −2 Az < s j > s i , <sj>: time average ⇒ magnetization: M =− n atoms gµ B < s j > ⇒ < s j >= − M n atoms gµ B / h (7.43) h (7.44) 2 Az ⇒ E = (− gµ B s i / h ) ⋅ M 2 14243 natoms g 2 µ B 44 −µ 14 244 4 3 B MF (7.45) 7-24 B MF 2 zA M = µ 0γ M = 22 natoms g µ B mean field (exchange field) (7.46) γ= 1 2 zA 2 µ 0 natoms g 2 µ B molecular field constant (7.47) Effective magnetic field: Beff = B + BMF Energy of electron spins in magnetic field: E± = ± gµBBeff (7.48) n± natoms e − E± / kT = − E+ / kT e + e − E− / kT + : ↑ sz −:↓ B eff (7.49) M= 1 gµB(n+ 2 - n -) = 1 g µ B B eff 1 2 gµBnatomstanh kT 2 (7.50) 7-25 Saturation magnetization: Ms(0) = 2 gµBnatoms all spins oriented 1 No applied field: 1 gµ B B A zA M = M s (0) tanh M = M s (0) tanh 2 ⋅ n gµ B kT kT atoms (7.47) (7.51) ⇒ T M (T ) M (T ) = tanh c T M ( 0) M s ( 0) s TC = zA 2k (7.52...
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This note was uploaded on 01/19/2010 for the course MATERIALS M504 taught by Professor Adelung during the Spring '02 term at Uni Kiel.

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