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We present a theory of the isotope effect of the Curie temperature $T_{\rmc}$ in itinerant ferromagnets. The isotope effect in ferromagnets occurs viathe electron-phonon vertex correction and the effective attractive interactionmediated by the electron-phonon interaction. The decrease of the Debyefrequency increases the relative strength of the Coulomb interaction, whichresults in a positive isotope shift of $T_{\rm c}$ when the mass $M$ of an atomincreases. Following this picture, we evaluate the isotope effect of $T_{\rmc}$ by using the Stoner theory and a spin-fluctuation theory. When $T_{\rm c}$is large enough as large as or more than 100K, the isotope effect on $T_{\rmc}$ can be measurable. Recently, precise measurements on the oxygen isotopeeffect on $T_{\rm c}$ have been performed for itinerant ferromagnet SrRuO$_3$with $T_{\rm c}\sim 160$K. A clear isotope effect has been observed with thepositive shift of $T_{\rm c}\sim 1$K by isotope substitution($^{16}O\rightarrow ^{18}O$). This experimental result is consistent with ourtheory.

Isotope shift of the ferromagnetic transition temperature in itinerant ferromagnets