Magnetic Resistivity and Magnetic Transitions in Rare-Earth Alloys

The spin-disorder resistivities and the magnetic phase transitions in gadolinium-dysprosium (Gd-Dy) alloys have been investigated experimentally, and the corresponding effects of pressure have been determined. The experiments involved measuring the change in the anomalies in the resistance of samples as a function of temperature and pressure. The resistivities of the metals provide evidence of magnetic transitions, through changes of slope in the resistivity-temperature curves at the critical temperatures. Therefore, the spin-disorder resistivities and the magnetic transitions both under atmospheric and hydrostatic pressures can be obtained from the resistance-temperature curves. The spin-disorder resistivity ${\rho }_{\mathrm{mag}}$ of these alloys is proportional to $\frac{3\pi \mathrm{Nm}}{\left(2\mathrm{}\hslash e^2{E}_F\right)V^2{\mathrm{}(g-1\mathrm{})\mathrm{}}^{2}J(J+1\mathrm{})\mathrm{}}$, where $g$ is the Lande $g$ factor, $J$ is the total angular momentum quantum number, $V$ is an intra-atomic exchange integral, and $E_F$ is the Fermi energy. The quantity ${\rho }_{\mathrm{mag}}$ was experimentally observed to increase with the increasing Gd composition and pressure. In the Rudermann-Kittel theory, the Curie temperature $T_C$ of these alloys is proportional to the quantity $\frac{{\mathrm{}(g-1\mathrm{})\mathrm{}}^{2}J(J+1\mathrm{})\mathrm{}{V}^2}{\left(E_F\right)\Sigma R^{}\Phi \left(2\mathrm{}{k}_{F}R\right)}$, where $\Phi \left(2\mathrm{}{k}_{F}R\right)=\frac{(2\mathrm{}{k}_{F}Rcos2k_{F}R-sin2k_{F}R)}{{\left(2\mathrm{}{k}_{F}R\right)}^4}$. The quantity ($\frac{T_C}{{\rho }_{\mathrm{mag}}}$) was experimentally observed to increase and then decrease as a function of composition with the peak value near 60 at.% Gd-40 at.% Dy, thus indicating that the quantity $\Sigma R^{}\Phi \left(2\mathrm{}{k}_{F}R\right)$, which is proportional to ($\frac{T_C}{{\rho }_{\mathrm{mag}}}$), passes through a similar maximum. With the application of pressure $T_C$ for Gd-rich alloys decreased, whereas $T_C$ for the Dy-rich alloys appeared to increase first, and then to decrease. The variations of $T_C$ with pressure are explained by the relationship between $\Sigma R^{}\Phi$ and the $\frac{c}{a}$ ratio of the crystal. It is thus concluded (tentatively) that the quantity $\Sigma R^{}\Phi$ passes through a peak value as a function of both pressure and composition.