# How much Curie temperature $T_C$ is obtained according to the Stoner model?

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In Stoner model for itinarant ferromagnetism, the spin ordering of electrons is caused by the Coulomb interaction UU for onsite repulsion leading to the reduction of total energy against to the enhanced kinetic energy. If one can induce an imbalence $δn$ between total amount of spin-up and spin-down electrons, the kinetic energy $E_k$ will increase with $δE_k=\frac{1}{D_F}(δn)^2$ while the Coulomb repulsion energy will change with $δE_C=−U(δn)^2$. Therefore, we can normally obtain the Stoner criterion for itinerant Ferromagnetism:

$$δE=δE_k+δE_C=\frac{1}{D_F}(δn)^2(1−D_F U)$$

in which the $D_FU>1$ corresponds to the ferromagnetism, while $D_FU<1$ corresponds to the paramagnetism.

I survey in many textbooks and note on interent, however, most of documents only domenstate above criterion, the value of estimated Curie temperature is remained elusive for me.

In particular, above consideration is not fully addressed all my confusions. If an imbalence δnδn is intruduced by some perturbation, the total energy decreases without any limitation, and finally all spin will be aligned and extremely robust against thermal fluctuation, which will thus will result to an inceadiblely high Curie temperature.

So, how much Curie tempeature should be in Stoner model ?

asked Aug 19, 2021 in Q&A

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