Anti-Kondo effect in Rh-Fe: de Haas-van Alphen observations of scattering anisotropy and exchange energy

Wave-shape analysis of the de Haas-van Alphen (dHvA) signal on two hole orbits labeled $\alpha \mathrm{}\left(111\right)\mathrm{}$ and $\beta \mathrm{}\left(100\right)\mathrm{}$ in Rh-500-ppm Fe and Rh-700-ppm Fe at $T=1.2\mathrm{}°$K yields values of the exchange field which display no significant field dependence, and a magnitude equivalent to a $g$-factor shift of ∼10% (antiferromagnetic) from pure rhodium over the experimental magnetic-field range. No significant ($\alpha \mathrm{}\left(111\right)\mathrm{}$, $\beta \mathrm{}\left(100\right)\mathrm{}$, and $\delta \mathrm{}\left(111\right)\mathrm{}$ orbits display very different temperature dependences, with the most $d$-like orbit [$\delta \mathrm{}\left(111\right)\mathrm{}$] showing the largest temperature-dependent scattering rate and the least $d$-like orbit [$\alpha \mathrm{}\left(111\right)\mathrm{}$] showing a negligibly small temperature dependence. This proves that the anomalous temperature dependence of the RhFe electrical resistivity is connected with the $d$-wave nature of the host. We observe that the slope of the resistivity is a factor of 4 smaller than that of the Dingle temperature on $d$-like $\delta \mathrm{}\left(111\right)\mathrm{}$ orbits over the temperature range between 1.2 and 1.8 °K. An APW calculation of the orbital symmetry character has been performed to facilitate phase-shift analysis of the data. A discrepancy between the experimental results and the phase-shift analysis of the temperature dependence of the scattering rate indicates that the explanation needs something beyond the (Anderson) phase-shift model. Knapp's two-band model and Kondo's hypothesis of simultaneous presence of spin and potential scattering have been ruled out as an explanation of the resistivity anomaly in RhFe, owing to the observed positive temperature dependence of the scattering rate on $d$-like $\delta \mathrm{}\left(111\right)\mathrm{}$ orbits, and the calculated small potential scattering phase shift, respectively. The localized-spin-fluctuation model (LSF) explains quite well the temperature dependence of the resistivity. However, a calculation of the orbitally averaged scattering rate due to spin fluctuations is necessary to make a direct comparison between the LSF model and our experimental results.