Isotope shift of the ferromagnetic transition temperature in itinerant ferromagnets

We present a theory of the isotope effect of the Curie temperature $T_{\rm c}$ in itinerant ferromagnets. The isotope effect in ferromagnets occurs via the electron-phonon vertex correction and the effective attractive interaction mediated by the electron-phonon interaction. The decrease of the Debye frequency increases the relative strength of the Coulomb interaction, which results in a positive isotope shift of $T_{\rm c}$ when the mass $M$ of an atom increases. Following this picture, we evaluate the isotope effect of $T_{\rm c}$ 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 $T_{\rm c}$ can be measurable. Recently, precise measurements on the oxygen isotope effect 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 the positive shift of $T_{\rm c}\sim 1$K by isotope substitution ($^{16}O\rightarrow ^{18}O$). This experimental result is consistent with our theory.