 Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2022/4/b/iii/solution

Θ

is the extrapolated zero of

1/ χ

in a Curie–Weiss law fit. It summarizes the leading high-temperature effect of interactions between magnetic moments. For the sign convention

H_{ex} = - \sum_{i < j} J_{ij} J_{i} \cdot J_{j},

where

J_{i}

Θ = \frac{J ( J + 1 )}{3 k _{B}} \sum_{j} J_{ij} .

Thus positive net exchange interaction in this convention favours parallel magnetic moments, giving

Θ > 0

and tendencies towards ferromagnetism; negative net exchange interaction favours antiparallel magnetic moments, giving

Θ < 0

and antiferromagnetic tendencies. Competing interactions can partially cancel in this sum. The Weiss temperature need not equal the actual ordering temperature, and its sign alone is not a complete determination of the low-temperature ordered structure.

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