715 for ni 7 27 fig 715 saturation magnetization of

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Unformatted text preview: ) Note: TC ∝ z ⇒ TC decreases at surface. (lower coordination number) 7-26 M (T ) ≡ m M s (0) m = tanh( m / t ) T ≡t TC t < 1, i.e., T > TC solution only for m = 0 ⇒ No spontaneous magnetization for T > TC. Fig. 7.14 Graphical solution of eq.(7.52). The resulting couse of m = M(T)/Ms(0) as function of temperature is shown in Fig. 7.15 for Ni. 7-27 Fig. 7.15 saturation magnetization of nickel as a function of temperature, together with the theoretical curve for S = 1/2 on the mean field theory. Fit with mean field theory ⇒ J = 1/2 , i.e., 1 Ms(0) = 2 gµBnatoms ⇒ g = 1.2 ! ? (see below) Ni: band ferromagnet ⇒ mean field theory for localized electrons inaequate ! 7-28 Behaviour near TC 1 M tanh x ≈ x − x 3 + ... T → TC ⇒ M << 1 ⇒ 3 s (7.53) (7.52) ⇒ M (T ) T ≈ 3 1 − T M s ( 0) C γ 1/ 2 (7.54) T M ∝ 1 − T Experiment: C , γ = 1/3, (7.55) γ: critical exponent Reason for γ ≠ 1/2: only long-range order, i.e., magnetization vanishes at TC, certain lo...
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