Temperature dependence of the electric field gradient at Ta impurities in the heavy-rare-earth metals Gd, Dy, Ho, and Er

The time-differential perturbed-angular-correlation (TDPAC) technique has been used to study the temperature dependences of the electric field gradient (EFG) at ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ impurities in the heavy-rare-earth ($R$) metals Gd, Dy, Ho, and Er. At room temperature the ratio $\alpha \equiv \left|\frac{V_{\mathrm{zz}}}{(1-{\gamma }_{\infty })V_{\mathrm{zz}}^{\mathrm{lat}}}\right|$ of the measured EFG $V_{\mathrm{zz}}$ and the calculated ionic EFG $(1-{\gamma }_{\infty })V_{\mathrm{zz}}^{\mathrm{lat}}$ decreases linearly with increasing rare-earth atomic number. A linear but much stronger decrease of $\alpha$ has previously been reported for the impurity ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$. A simple model is proposed which explains the linear decrease of $\alpha$ and the different slopes for ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ and ${}_{}{}^{111}{}_{}{}^{}\mathrm{Cd}$ in terms of the lanthanide contraction. This model assumes the conduction-electron contribution to the EFG to be mainly determined by the number of electrons in the Wigner-Seitz cell of the impurity. In all rare-earth hosts the EFG decreases with increasing temperature. This decrease, which is slightly stronger for Gd than for Er, is better described by a linear function of temperature than by a $T^{\frac{3}{2}}$ behavior, observed in many other impurity-host systems. The temperature dependence of the EFG is much stronger than expected from the lattice expansion. The difference between the temperature dependence of the measured EFG and of the calculated lattice EFG decreases across the rare-earth series. This can be attributed to a decrease of the amplitudes of the lattice vibrations between Gd and Er.