Magnetic hyperfine interactions on Cd sites of the rare-earth cadmium compounds R Cd ( R = Ce , Pr, Nd, Sm, Gd, Tb, Dy, Ho, and Er)

This paper reports the investigation of the magnetic hyperfine field ${B}_{hf}$ in a series of rare-earth ($R$) cadmium intermetallic compounds $R\mathrm{Cd}$ and ${\mathrm{GdCd}}_{2}$ measured by perturbed angular correlation (PAC) spectroscopy using $^{111}\mathrm{In}/^{111}\mathrm{Cd}$ as probe nuclei at Cd sites as well as first-principles calculations of ${B}_{hf}$ at Cd sites in the studied compounds. Vapor--solid state reaction of $R$ metals with Cd vapor and the $^{111}\mathrm{In}$ radioisotope was found to be an appropriate route of doping rare-earth cadmium compounds with the PAC probe $^{111}\mathrm{In}/^{111}\mathrm{Cd}$. The observation that the hyperfine parameters depend on details of the sample preparation provides information on the phase preference of diffusing $^{111}\mathrm{In}$ in the rare-earth cadmium phase system. The $^{111}\mathrm{Cd}$ hyperfine field has been determined in the compounds $R\mathrm{Cd}$ for the $R$ constituents Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, and Er, in several cases as a function of temperature. For most $R$ constituents, the temperature dependence ${B}_{hf}(T)$ of $^{111}\mathrm{Cd}$:$R\mathrm{Cd}$ is consistent with ferromagnetic order of the compound. DyCd, however, presents a remarkable anomaly: a finite magnetic hyperfine field is observed only in the temperature interval 35 K $\ensuremath{\le} T \ensuremath{\le}$ 80 K which indicates a transition from ferromagnetic order to a spin arrangement where all $4f$-induced contributions to the magnetic hyperfine field at the Cd site cancel. First-principles calculation results for DyCd show that the ($\ensuremath{\pi}, \ensuremath{\pi}$, 0) antiferromagnetic configuration is energetically more favorable than the ferromagnetic. The approach used in the calculations to simulate the $R\mathrm{Cd}$ system successfully reproduces the experimental values of ${B}_{hf}$ at Cd sites and shows that the main contribution to ${B}_{hf}$ comes from the valence electron polarization. The de Gennes plot of the hyperfine field ${B}_{hf}$ of $^{111}\mathrm{Cd}$:$R\mathrm{Cd}$ vs the $4f$-spin projection $(g\ensuremath{-}1)J$ reflects a decrease of the strength of indirect $4f\ensuremath{-}4f$ exchange across the $R$ series. Possible mechanisms are discussed and the experimental results indicate that the indirect coupling is provided by the intra-atomic $4f\ensuremath{-}5d$ exchange and interatomic $5d\ensuremath{-}5d$ interaction between the spin-polarized $5d$ electrons of neighboring $R$ atoms. The ratio of the hyperfine fields of GdCd and ${\mathrm{GdCd}}_{2}$ scales with the number of nearest Gd neighbors. In the paramagnetic phases of the $R\mathrm{Cd}$ compounds, the PAC spectra indicate the presence of a broad distribution of weak quadrupole interactions suggesting a perturbation of the cubic CsCl symmetry of the Cd site, most probably due to chemical disorder of the $R$ and Cd sublattices. A substantial interchange of $R$ and Cd atoms is also reflected in the temperature dependence of the linewidth of the magnetic hyperfine interaction in the magnetically ordered phase of $R\mathrm{Cd}$ and ${\mathrm{GdCd}}_{2}$. Its critical increase towards the order temperature is evidence for a distribution of the order temperature with a width of about 10 K.