Anomalous pressure dependence of the bulk modulus and Yb valence in cubic YbPd

We investigate the Yb valence instabilities in the strongly correlated YbPd compound using resonant x-ray emission spectroscopy as a function of pressure across the charge-order (CO) transition. At a low temperature ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>T</a:mi> <a:mo>=</a:mo> <a:mn>30</a:mn> <a:mspace width="0.28em"/> <a:mi mathvariant="normal">K</a:mi> </a:mrow> </a:math> ) in the CO phase, the Yb <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>4</d:mn> <d:mi>f</d:mi> </d:mrow> </d:math> valence remains nearly constant up to a pressure <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>P</e:mi> <e:mi>L</e:mi> </e:msub> <e:mo>=</e:mo> <e:mn>1.5</e:mn> </e:mrow> <e:mo> </e:mo> <e:mrow> <e:mo>±</e:mo> <e:mspace width="0.28em"/> <e:mrow> <e:mn>0.2</e:mn> </e:mrow> <e:mspace width="0.28em"/> <e:mi>GPa</e:mi> </e:mrow> </e:math> , and then increases gradually at higher pressures. In contrast, at room temperature in the normal phase, an anomalous decrease of the Yb <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mn>4</h:mn> <h:mi>f</h:mi> </h:mrow> </h:math> valence is observed, without any accompanying structural phase transition. This behavior is corroborated by a systematic pressure-dependent decrease of the unit-cell volume. Based on a Birch-Murnaghan analysis, the compressibility indicates hardening of the lattice with applied pressure up to a distinct kink seen at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:msub> <i:mi>P</i:mi> <i:mi>K</i:mi> </i:msub> <i:mo>=</i:mo> <i:mn>1.6</i:mn> </i:mrow> <i:mo> </i:mo> <i:mrow> <i:mo>±</i:mo> <i:mspace width="0.28em"/> <i:mrow> <i:mn>0.2</i:mn> </i:mrow> <i:mspace width="0.28em"/> <i:mi>GPa</i:mi> </i:mrow> </i:math> . In contrast, for <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mi>P</l:mi> </l:mrow> <l:mo> </l:mo> <l:mo>></l:mo> <l:mo> </l:mo> <l:msub> <l:mi>P</l:mi> <l:mi>K</l:mi> </l:msub> </l:math> , the Yb <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>4</m:mn> <m:mi>f</m:mi> </m:mrow> </m:math> valence saturates, and the compressibility reveals a counterintuitive pressure-induced softening. The results show a minimum in the compressibility of YbPd (with <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:msup> <n:mi>f</n:mi> <n:mn>0</n:mn> </n:msup> <n:mo>–</n:mo> <n:msup> <n:mi>f</n:mi> <n:mn>1</n:mn> </n:msup> </n:mrow> </n:math> hole-type mixed valence), reminiscent of the maximum in compressibility seen in the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mi>γ</o:mi> <o:mo>–</o:mo> <o:mi>α</o:mi> </o:mrow> </o:math> first-order isostructural phase transition in cerium (with <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:msup> <p:mi>f</p:mi> <p:mn>0</p:mn> </p:msup> <p:mo>–</p:mo> <p:msup> <p:mi>f</p:mi> <p:mn>1</p:mn> </p:msup> </p:mrow> </p:math> electron-type mixed valence).