Effect of spin fluctuations on the Stoner transition temperature

The low-frequency long-wavelength spin fluctuation modes make a major contribution to the free energy near the ferromagnetic instability of an itinerant-electron model. These fluctuations renormalize the static spin susceptibility and depress the transition temperature predicted by Stoner theory. Moriya and Kawabata (MK) have suggested a simple way of computing the depression self-consistently, by making sure the spin fluctuations go soft at the renormalized temperature $T_c$ rather than at the Stoner value. We extend the discussion of MK to include both longitudinal and transverse spin fluctuations, and find a $T_c$ which is only slightly smaller than $T_c^{\mathrm{MK}}$. We also discuss the relation between $T_c$ determined from the condition that the paramagnons go soft and that obtained by considering the softening of the spin waves. We argue that our new results give evidence that the basic MK procedure is internally consistent and somewhat less ad hoc than it appeared in its original presentation.