Magnetic Moment, Susceptibility, and Electrical Resistivity of Dilute Paramagnetic Palladium—Rare-Earth Alloys

The magnetic properties and low-temperature electrical resistivity are reported for dilute alloys of the ${\mathrm{Pd}}_{1\ensuremath{-}x}{R}_{x}$ system where $R=\mathrm{C}\mathrm{e},\phantom{\rule{0ex}{0ex}}\mathrm{P}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{N}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{m},\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{u},\phantom{\rule{0ex}{0ex}}\mathrm{G}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{b},\phantom{\rule{0ex}{0ex}}\mathrm{D}\mathrm{y},\phantom{\rule{0ex}{0ex}}\mathrm{H}\mathrm{o},\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{m},\phantom{\rule{0ex}{0ex}}\mathrm{Y}\mathrm{b},\phantom{\rule{0ex}{0ex}}\mathrm{L}\mathrm{u},\phantom{\rule{0ex}{0ex}}\mathrm{o}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{Y}$, and $x$ is generally 0.01 or less. Alloys with $R=\mathrm{C}\mathrm{e},\phantom{\rule{0ex}{0ex}}\mathrm{G}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{D}\mathrm{y},\phantom{\rule{0ex}{0ex}}\mathrm{o}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{r}$ are examined over a wide range of concentrations. The quantities measured were the magnetic susceptibility $\ensuremath{\chi}(T)$ for $4.2\ensuremath{\lesssim}T\ensuremath{\lesssim}250$ K, the magnetic moment $\ensuremath{\sigma}({H}_{0})$ for $T\ensuremath{\lesssim}4.2$ K and for ${H}_{0}\ensuremath{\lesssim}210$ kG, and the residual electrical resistivity $\ensuremath{\rho}(T)$ at 4.2 K. Even at 200 kG the rare-earth moments are not fully aligned with the applied field for $T\ensuremath{\gtrsim}1.5$ K. The magnetic-moment versus field data are analyzed in two ways: by a semiempirical formula which includes a parameter that gives a convenient measure of ease of magnetic saturation of the rare-earth contribution, and by crystal field theory. Based on the semiempirical formula, the magnetic moment of the rare-earth ion is found to be close to its free-ion value, and the matrix susceptibility is also obtained. The application of the semiempirical formula to both field- and temperature-dependent data is discussed extensively. From recent electron-paramagnetic-resonance data, crystal field parameters for the ${\mathrm{Pd}}_{1\ensuremath{-}x}{\mathrm{Dy}}_{x}$ alloys are derived. Using these parameters, the field and temperature dependence of the magnetic moment for ${\mathrm{Pd}}_{1\ensuremath{-}x}{\mathrm{Dy}}_{x}$ are calculated. The best fit of crystal field theory shows large systematic deviations from experiment, whereas the semiempirical formula fits the observed data within experimental error for $H\ensuremath{\gtrsim}3$ kG. The temperature-dependent susceptibility $\ensuremath{\chi}(T)$ is fitted to a Curie-Weiss law for the heavy rare-earth alloys and the free-ion value of the rare-earth moment is obtained within experimental error. The paramagnetic Curie temperature $\ensuremath{\theta}$ is less than \ifmmode\pm\else\textpm\fi{}3 K for $x\ensuremath{\lesssim}0.01$. The $\ensuremath{\chi}(T)$ data for $R=\mathrm{Y},\phantom{\rule{0ex}{0ex}}\mathrm{C}\mathrm{e},\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{u},\phantom{\rule{0ex}{0ex}}\mathrm{o}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{L}\mathrm{u}$ (none of which has a measurable moment in Pd) show that the position and magnitude of the maximum of $\ensuremath{\chi}(T)$ (which occurs at \ensuremath{\sim}85 K for pure Pd) are sensitive functions of $R$ and $x$. The analysis of the residual electrical resistivity of ${\mathrm{Pd}}_{1\ensuremath{-}x}{\mathrm{R}}_{x}$ alloys for $x\ensuremath{\sim}0.01$ shows that the Kasuya formula does not apply. Other scattering mechanisms are suggested and their predictions are compared with the magnetic properties.