Localized Magnetic Impurity States in Ti, Zr, and Hf

Abstract

An experimental study of localized moments on "magnetic" impurities (≈0.2 at.% of Cr, Mn, Fe, Co, or Gd) in the group IV transition elements Ti, Zr, and Hf has been carried out. From magnetic-susceptibility measurements we find a localized moment on Mn of ≈3.5 ${\mathrm{\mu }}_{\mathit{B}}$ in each of the solvents Ti, Zr, and Hf. Chromium forms a moment in Zr (0.2 ${\mathrm{\mu }}_{\mathit{B}}$) and in Hf (1.7 ${\mathrm{\mu }}_{\mathit{B}}$) but not in Ti. Iron forms a moment in Hf (0.7 ${\mathrm{\mu }}_{\mathit{B}}$) but not in Ti or Zr. Thus the tendency towards localized-moment formation on these $3d$ ions increases in the sequence Ti-Zr-Hf, possibly because of the decreasing solvent electronic-state density. Negative magneto-resistance is produced by each $d$-shell impurity for which magnetic-susceptibility measurements indicate a localized moment. The magnetoresistivity and susceptibility data are shown to be correlated in the weak-field limit by the elementary molecular-field description and the assumption that the magnetoresistance is proportional to the square of the magnetization. Resistivity minima are observed in "pure" (arc-cast, iodide process) Ti and Ti-Cr, -Mn, and -Fe; Zr-Mn; and Hf-Cr, -Mn, and -Fe. It thus appears that there is no strict correlation of resistivity minima and localized moments for the $d$-shell impurities. The resistivity-versus-temperature curves are not explained by the recent theory of Kondo. It is suggested that this apparent disagreement can be accounted for in part if one assumes a substantial temperature dependence of the nonmagnetic impurity-potential scattering, which was not included in Kondo's theory. For Gd in the group IVB solvents, a nearly free-atom moment is observed in Zr (7.0 ${\mathrm{\mu }}_{\mathit{B}}$) and Hf (6.1 ${\mathrm{\mu }}_{\mathit{B}}$), (Ti-Gd was not examined). No resistivity minima and only a very small negative magnetoresistance are observed in the alloys with Gd, suggesting a much weaker conduction-electron interaction with the localized magnetic states of the $f$-shell ions than with the localized moments on the $d$-shell impurities.