Cooperative Charge Ordering Signature of Trimer Molecules in Infinite-Layer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>CaCoO</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <

The infinite-layer compound <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>CaCoO</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> provides a compelling platform to explore how local orbital distortions evolve into collective electronic order. Using resonant soft x-ray scattering (RSXS) and its time-resolved counterpart (tr-RSXS), we reveal a cooperative coupling between two intertwined orders at the same in-plane wave vector, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mrow> <c:mi>q</c:mi> </c:mrow> <c:mo>≈</c:mo> <c:mo stretchy="false">(</c:mo> <c:mrow> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:mn>4</c:mn> </c:mrow> <c:mo>,</c:mo> <c:mn>1</c:mn> <c:mo>/</c:mo> <c:mn>4</c:mn> <c:mo>,</c:mo> <c:mn>0</c:mn> <c:mo stretchy="false">)</c:mo> </c:mrow> </c:math> , comprising a quasi-two-dimensional orbital order associated with the distorted <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi>Co</g:mi> </g:mrow> <g:mrow> <g:mo stretchy="false">(</g:mo> <g:mn>1</g:mn> <g:mo stretchy="false">)</g:mo> </g:mrow> </g:msub> </g:mrow> </g:math> sites and a quasi-three-dimensional trimerlike charge order stabilized through Co-O-Ca hybridization. The charge-sensitive component exhibits a uniform relaxation time of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo>∼</k:mo> <k:mn>400</k:mn> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>fs</k:mi> </k:math> ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mn>391</m:mn> <m:mo>±</m:mo> <m:mn>5</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>fs</m:mi> </m:math> ) across multiple Co resonances, evidencing a collective charge response. A comparable timescale observed in the orbital order associated with the highly distorted <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:msub> <o:mrow> <o:mi>Co</o:mi> </o:mrow> <o:mrow> <o:mo stretchy="false">(</o:mo> <o:mn>1</o:mn> <o:mo stretchy="false">)</o:mo> </o:mrow> </o:msub> </o:mrow> </o:math> sites indicates that this collective behavior naturally originates from the same orbital framework that mediates both charge and orbital degrees of freedom. Together, these findings establish <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:msub> <s:mrow> <s:mi>CaCoO</s:mi> </s:mrow> <s:mrow> <s:mn>2</s:mn> </s:mrow> </s:msub> </s:mrow> </s:math> as a model system in which Jahn-Teller distortions, orbital hybridization, and geometric frustration cooperate to form molecular trimer units that dictate the macroscopic electronic behavior.