How does antiferromagnetism occur?

[barnflakes]

Can someone explain this in simple terms to me? I know it's because the spins on neighbouring atoms anti-align - but WHY do they anti-align instead of align, as is the case in ferromagnetism?

[genneth]

http://en.wikipedia.org/wiki/Superexchange

[barnflakes]

I found a good explanation, but there is one part I don't understand: http://en.wikipedia.org/wiki/Magnetism

about 1/2 - 2/3 of the way down under "quantum mechanical origins of magnetism"

I.e., not only uA and uB must be substituted by α and β, respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally ri by the discrete values si (= ±½); thereby we have α( + 1 / 2) = β( − 1 / 2) = 1 and α( − 1 / 2) = β( + 1 / 2) = 0. The "singlet state", i.e. the - sign, means: the spins are antiparallel, i.e. for the solid we have antiferromagnetism, and for two-atomic molecules one has diamagnetism.

why does α( + 1 / 2) = β( − 1 / 2) = 1 ? and what does it mean by "(the first entity means "spin up", the second one "spin down")" - how is alpha representing spin up? In that notation alpha is a function?

[Pete99]

Hope this helps: http://www.physicsforums.com/showthread.php?t=172923