Probing Mixed Valence States by Nuclear Spin-Spin Relaxation Time Measurements

Several elements in the periodic table exhibit an interesting and often overlooked feature: They skip certain valence states which is discussed in the field of superconductivity to be in favor of fostering higher transition temperatures $T_c$. However, from the experimental point of view, it is often deemed difficult to probe changes in the valence state. Here we demonstrate that the latter are accessible by the spin-spin relaxation rate $1\mathrm{/}{T}_2$ in nuclear magnetic resonance. As target material, we chose the solid solution Ge${}_{1-x}$In${}_x$Te, where valence-skipping In induces superconductivity and changes its valence state as a function of $x$. We observe a strong enhancement in $1\mathrm{/}{T}_2(x)$ and, most importantly, find that $1\mathrm{/}{T}_2$ and $T_c$ exhibit a strikingly similar $x$ dependence. These results underline the importance of valence physics for the evolution of superconductivity in Ge${}_{1-x}$In${}_x$Te. A model based on a Ruderman-Kittel-Kasuya-Yosida type of interaction among the In nuclei is proposed which fully accounts for the experimental results.