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in my atomic physics lecture notes it is said that depending on the values of the exchange operator $K_{ij}$ there can be different kinds of magnetism, say, ferromagnetism and antiferromagnetism, how can I see that?

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The total wave function of the electrons is antisymmetric, and is the product of a spatial part and a spin part. If some exchange operator favours a symmetric spatial part, you get an antisymmetric spin part (antiferromagnetism). If the exchange operator favours an antisymmetric spatial part, you get a symmetric spin part (ferromagnetism) –  Trimok Jun 6 '13 at 19:55
Hi Trimok thanks. Can be seen if the exchange operators favours the symmetric or antisymmetric part of the spatial part? –  Jorge Jun 7 '13 at 11:07
The idea is to minimize an energy. Depending on the kind of energy you minimize, you will get an symmetric or antisymmetric spatial part. I am looking to find a readable reference. –  Trimok Jun 7 '13 at 11:45
See this reference - Chapter 1.2 - Quantum Exchange –  Trimok Jun 7 '13 at 11:49
Thank you, I see that there is no a general easy answer to my question. Looks very interesting your reference! –  Jorge Jun 7 '13 at 11:52

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