Appendix D
Analytical Expressions for χ(T)
1. The Bonner-Fisher expression for a S = 1/2 uniform Heisenberg chain:
χ(T ) =
N A µ 2
B g 2
e
kT
A + Bx + Cx 2
1 + Dx + Ex 2 + Fx 3
with x = J/2kT and A = 0.25; B = 0.14995; C = 0.30094; D = 1.9862;
E = 0.68854; F = 6.0626 [1].
2. The alternate S =
1
2 Heisenberg chain with J = J 1 = αJ 2 :
χ(T ) =
N A µ 2
B g 2
e
kT
A + Bx + Cx 2
1 + Dx + Ex 2 + Fx 3
for 0 <α<0.4 the values of A–F are [2]
A = 0.25
B =−0.12587 + 0.22752α
C = 0.019111 − 0.13307α + 0.509α
2 − 1.3167α
3 + 1.0081α
4
D = 0.100772 + 1.4192α
E =−0.0028521 − 0.42346α + 2.1953α
2 − 0.82412α
3
F = 0.37754 − 0.067022α + 5.9805α
2 − 2.1678α
3 + 15.838α
4
and for 0.4 <α<1 the values of A–F are
A = 0.25
B =−0.13695 + 0.26387α
C = 0.017025 − 0.12668α + 0.49113α
2 − 1.1977α
3 + 0.87257α
4
D = 0.070509 + 1.3042α
© Springer International Publishing Switzerland 2016
C. Graaf and R. Broer, Magnetic Interactions in Molecules and Solids,
Theoretical Chemistry and Computational Modelling,
DOI 10.1007/978-3-319-22951-5
219