Different routes to pressure-induced volume collapse transitions in gadolinium and terbium metals

The sudden decrease in molar volume exhibited by most lanthanides under high pressure is often attributed to changes in the degree of localization of their 4$f$ electrons. We give evidence, based on electrical resistivity measurements of dilute Y(Gd) and Y(Tb) alloys to 120 GPa, that the volume collapse transitions in Gd and Tb metals have different origins, despite their being neighbors in the periodic table. Remarkably, the change under pressure in the magnetic state of isolated Pr or Tb impurity ions in the nonmagnetic Y host appears to closely mirror corresponding changes in pure Pr or Tb metals. The collapse in Tb appears to be driven by an enhanced negative exchange interaction between 4$f$ and conduction electrons under pressure (Kondo resonance) which, in the case of Y(Tb), dramatically alters the superconducting properties of the Y host, much like previously found for Y(Pr). In Gd, our resistivity measurements suggest that a Kondo resonance is not the main driver for its volume collapse. X-ray absorption and emission spectroscopies clearly show that 4$f$ local moments remain largely intact across both volume collapse transitions ruling out 4$f$ band formation (delocalization) and valence transition models as possible drivers. The results highlight the richness of behavior behind the volume collapse transition in lanthanides and demonstrate the stability of the 4$f$ level against band formation to extreme pressure.

Figure 1

X-ray fluorescence spectra. Data were taken at an incidence energy of 7.55 keV and normalized to the $L_{\alpha }$ peak intensity.

Figure 2

Fourier transform of the XAFS data collected at the $L_3$ edge of Pr, Gd, and Tb in their respective alloys.

Figure 3

Pressure dependence of T${}_{\mathrm{c}}$ for (a) Y(1 at.% Pr) and (b) Y(0.5 at.% Gd) compared to that for Y.[52] Vertical dashed lines show the critical pressure for the volume collapse in Pr and Gd. Inset in (a) shows data for La and La(0.74 at.% Pr) adapted from Fig. 2 of Ref. 53.

Figure 4

Pressure dependence of T${}_{\mathrm{c}}$ for Y(0.5 at.% Tb) alloy. Vertical dashed line marks pressure (53 GPa) of volume collapse in Tb. Inset shows resistive superconducting transition at 81.4 GPa ($\times$) is much narrower than that at 30.9 GPa ($\blacksquare$).

Figure 5

(a) Pressure dependence of $L_3$ XANES for Tb. No 4$+$ or mixed valence state is observed. Pressure-induced reduction of peak height is direct measure of $s$$\to$$d$ transfer. (b) Pressure dependence of $L_{\gamma }$ nonresonant XES for Tb. A 4$f$${}^8$ local-itinerant transition is not observed.