4f electron temperature driven ultrafast electron localization

Valence transitions in strongly correlated electron systems are caused by orbital hybridization and Coulomb interactions between localized and delocalized electrons. The transition can be triggered by changes in the electronic structure and is sensitive to temperature variations, applications of magnetic fields, and physical or chemical pressure. Launching the transition by photoelectric fields can directly excite the electronic states and thus provides an ideal platform to study the correlation among electrons on ultrafast timescales. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>EuN</a:mi><a:msub><a:mi mathvariant="normal">i</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mrow><a:mo>(</a:mo><a:mrow><a:msub><a:mi mathvariant="normal">Si</a:mi><a:mrow><a:mn>0.21</a:mn></a:mrow></a:msub><a:msub><a:mi mathvariant="normal">Ge</a:mi><a:mrow><a:mn>0.79</a:mn></a:mrow></a:msub></a:mrow><a:mo>)</a:mo></a:mrow><a:mn>2</a:mn></a:msub></a:mrow></a:math> mixed-valence metal is an ideal material to investigate the valence transition of the Eu ions via the amplified orbital hybridization by the photoelectric field on subpicosecond timescales. A direct view on the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>4</e:mn><e:mi>f</e:mi></e:mrow></e:math> electron occupancy of the Eu ions is required to understand the microscopic origin of the transition. Here we probe the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>4</f:mn><f:mi>f</f:mi></f:mrow></f:math> electron states of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>EuN</g:mi><g:msub><g:mi mathvariant="normal">i</g:mi><g:mn>2</g:mn></g:msub><g:msub><g:mrow><g:mo>(</g:mo><g:mrow><g:msub><g:mi mathvariant="normal">Si</g:mi><g:mrow><g:mn>0.21</g:mn></g:mrow></g:msub><g:msub><g:mi mathvariant="normal">Ge</g:mi><g:mrow><g:mn>0.79</g:mn></g:mrow></g:msub></g:mrow><g:mo>)</g:mo></g:mrow><g:mn>2</g:mn></g:msub></g:mrow></g:math> at the sub-ps timescale after photoexcitation by x-ray absorption spectroscopy across the Eu <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>M</k:mi><k:mn>5</k:mn></k:msub></k:math>-absorption edge. The observed spectral changes due to the excitation indicate a population change of total angular momentum multiplet states <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi>J</l:mi></l:mrow></l:math> = 0, 1, 2, and 3 of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi mathvariant="normal">E</m:mi><m:msup><m:mrow><m:mi mathvariant="normal">u</m:mi></m:mrow><m:mrow><m:mn>3</m:mn><m:mo>+</m:mo></m:mrow></m:msup></m:mrow></m:math> and the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mrow><p:mi mathvariant="normal">E</p:mi><p:msup><p:mrow><p:mi mathvariant="normal">u</p:mi></p:mrow><p:mrow><p:mn>2</p:mn><p:mo>+</p:mo></p:mrow></p:msup></p:mrow><p:mo> </p:mo><p:mrow><p:mi>J</p:mi></p:mrow></p:math> = 7/2 multiplet state caused by an increase in <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mrow><s:mn>4</s:mn><s:mi>f</s:mi></s:mrow></s:math> electron temperature that results in a <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:mrow><t:mn>4</t:mn><t:mi>f</t:mi></t:mrow></t:math> localization process. This electronic temperature increases combined with fluence-dependent screening accounts for the strongly nonlinear effective valence change. The data allow us to extract a time-dependent determination of an effective temperature of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mrow><u:mn>4</u:mn><u:mi>f</u:mi></u:mrow></u:math> shell, which is also of great relevance in the understanding of metallic systems' properties, such as the ultrafast demagnetization of ferromagnetic rare-earth intermetallic and their all-optical magnetization switching. In addition, our results elucidate the energetics of charge fluctuations in valence-mixed electronic systems, which provide enriched knowledge regarding the role of valence transitions and orbital hybridization for quantum critical phenomena. Published by the American Physical Society 2024