Isotope shift of the ferromagnetic transition temperature in itinerant ferromagnets

TL;DR

This paper develops a theoretical framework explaining the isotope effect on the Curie temperature in itinerant ferromagnets, predicting measurable positive shifts in $T_c$ for large $T_c$, and confirms this with recent experimental data on SrRuO$_3$.

Contribution

The paper introduces a theory linking isotope effects to electron-phonon interactions and validates it with experimental data on SrRuO$_3$ showing positive isotope shifts.

Findings

Positive isotope shift of about 1K in SrRuO$_3$ with $T_c \,\sim 160$K.

The isotope effect becomes significant for $T_c$ above 100K.

Theoretical predictions align with recent experimental observations.

Abstract

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.