  We present a generalization of the spin-fluctuation theory of magnetism which
allows us to treat the full rotational invariance of the exchange interaction.
The approach is formulated in terms of the local density approximation plus
dynamical mean-field theory (LDA+DMFT), providing a systematic many-body
treatment of the effect of spin-density fluctuations. This technique is
employed to study the electronic and magnetic properties of paramagnetic
$\alpha$ iron. Our result for the Curie temperature is in good agreement with
experiment, while the calculations with the Ising-type exchange interaction
yield almost twice overestimated value.
