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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>T</a:mi><a:mi>c</a:mi></a:msub></a:math>. 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>1</b:mn><b:mo>/</b:mo><b:msub><b:mi>T</b:mi><b:mn>2</b:mn></b:msub></b:mrow></b:math> in nuclear magnetic resonance. As target material, we chose the solid solution <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>Ge</c:mi><c:mrow><c:mn>1</c:mn><c:mo>−</c:mo><c:mi>x</c:mi></c:mrow></c:msub><c:msub><c:mi>In</c:mi><c:mi>x</c:mi></c:msub><c:mi>Te</c:mi></c:mrow></c:math>, where valence-skipping In induces superconductivity and changes its valence state as a function of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>x</d:mi></d:math>. We observe a strong enhancement in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>1</e:mn><e:mo>/</e:mo><e:msub><e:mi>T</e:mi><e:mn>2</e:mn></e:msub><e:mrow><e:mo>(</e:mo><e:mi>x</e:mi><e:mo>)</e:mo></e:mrow></e:mrow></e:math> and, most importantly, find that <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>1</f:mn><f:mo>/</f:mo><f:msub><f:mi>T</f:mi><f:mn>2</f:mn></f:msub></f:mrow></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>T</g:mi><g:mi>c</g:mi></g:msub></g:math> exhibit a strikingly similar <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>x</h:mi></h:math> dependence. These results underline the importance of valence physics for the evolution of superconductivity in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:msub><i:mi>Ge</i:mi><i:mrow><i:mn>1</i:mn><i:mo>−</i:mo><i:mi>x</i:mi></i:mrow></i:msub><i:msub><i:mi>In</i:mi><i:mi>x</i:mi></i:msub><i:mi>Te</i:mi></i:mrow></i:math>. 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.