78 for n n1 n2 atoms n 1 2 n1 n 2 exp m b b

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Unformatted text preview: rence between the two curves. Equilibrium populations of levels (see Fig. 7.8) for N = N1 + N2 atoms N 1, 2 N1 + N 2 = exp[ m µ B B /(kT )] exp[ − µ B B /( kT )] + exp[ + µ B B /( kT )] (7.32) Resultant magnetization: N 2 − N1 e x − e−x M= µ B = natoms µ B x = n atoms µ tanh x V e + e−x (7.33) x = µBB/(kT) 7-15 1) x<<1 ⇒ tanhx ≈ x ⇒ 2 n atoms µ B B M≈ kT (7.34) (Curie law) (Curie constant) (7.35) (7.36) ⇒ χ ≈ C/T 2 2 µ 0 g J J ( J + 1) µ B C= 3k for general case (see, e.g., Kittel ), here: J = s = 1/2,gJ = g = 2 2) x >> 1 ⇒ tanh ≈ 1 ⇒ saturation magnetization M = natoms µB (7.37) Requires very strong fields and low temperatures! e.g., B = 5T, T = 300K ⇒ x of order of 10-2: still χ ≈ C/T Fig. 7.9 Cource of magnetization as function of x = µBB/(kT). Note the linear range, which is obeyed for most practical cases, and the occurence of saturation at very low temperatures or extremely strong fields. 7-16 Pauli paramagnetism of conduction electrons Magnetic moment of a conduction el...
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