Density functional theory of resonant inelastic x-ray scattering in the quasi-one-dimensional dimer iridate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ba</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub>

We have investigated the electronic structure of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Ba</a:mi> <a:mn>3</a:mn> </a:msub> <a:msub> <a:mi>InIr</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>9</a:mn> </a:msub> </a:mrow> </a:math> within the density-functional theory using the generalized gradient approximation while considering strong Coulomb correlations ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>GGA</c:mi> <c:mo>+</c:mo> <c:mi>U</c:mi> </c:mrow> </c:math> ) in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. We have studied resonant inelastic x-ray scattering (RIXS) spectra of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>Ba</d:mi> <d:mn>3</d:mn> </d:msub> <d:msub> <d:mi>InIr</d:mi> <d:mn>2</d:mn> </d:msub> <d:msub> <d:mi mathvariant="normal">O</d:mi> <d:mn>9</d:mn> </d:msub> </d:mrow> </d:math> at the Ir <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>L</f:mi> <f:mn>3</f:mn> </f:msub> </f:math> edge for the monoclinic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>C</g:mi> <g:mn>2</g:mn> <g:mo>/</g:mo> <g:mi>c</g:mi> </g:mrow> </g:math> and hexagonal <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>P</h:mi> <h:msub> <h:mn>6</h:mn> <h:mn>3</h:mn> </h:msub> <h:mo>/</h:mo> <h:mi>m</h:mi> <h:mi>m</h:mi> <h:mi>c</h:mi> </h:mrow> </h:math> crystal structures. The calculated results are in good agreement with experimental data. The RIXS spectrum at the Ir <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msub> <i:mi>L</i:mi> <i:mn>3</i:mn> </i:msub> </i:math> edge possesses several sharp features below 2 eV, corresponding to transitions within the Ir <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msub> <j:mi>t</j:mi> <j:mrow> <j:mn>2</j:mn> <j:mi>g</j:mi> </j:mrow> </j:msub> </j:math> levels. The excitation located from 2 to 5 eV is due to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:msub> <k:mi>t</k:mi> <k:mrow> <k:mn>2</k:mn> <k:mi>g</k:mi> </k:mrow> </k:msub> <k:mo> </k:mo> <k:mo>→</k:mo> <k:mo> </k:mo> <k:msub> <k:mi>e</k:mi> <k:mi>g</k:mi> </k:msub> </k:math> transitions. The wide structure situated at <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mn>5</l:mn> <l:mo>−</l:mo> <l:mn>12</l:mn> <l:mspace width="0.16em"/> <l:mi>eV</l:mi> </l:mrow> </l:math> appears due to charge transfer transitions. The influence of the momentum transfer vector and incident photon energy on the Ir <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msub> <n:mi>L</n:mi> <n:mn>3</n:mn> </n:msub> </n:math> RIXS spectrum has been investigated. Also, we have calculated the RIXS spectra of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:msub> <o:mi>Ba</o:mi> <o:mn>3</o:mn> </o:msub> <o:msub> <o:mi>InIr</o:mi> <o:mn>2</o:mn> </o:msub> <o:msub> <o:mi mathvariant="normal">O</o:mi> <o:mn>9</o:mn> </o:msub> </o:mrow> </o:math> at the Ir <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mi>K</q:mi> <q:mo>,</q:mo> <q:mo> </q:mo> <q:msub> <q:mi>M</q:mi> <q:mn>3</q:mn> </q:msub> <q:mo>,</q:mo> <q:mo> </q:mo> <q:msub> <q:mi>M</q:mi> <q:mn>5</q:mn> </q:msub> <q:mo>,</q:mo> <q:mo> </q:mo> <q:msub> <q:mi>N</q:mi> <q:mn>3</q:mn> </q:msub> <q:mo>,</q:mo> <q:mo> </q:mo> <q:msub> <q:mi>N</q:mi> <q:mn>5</q:mn> </q:msub> </q:math> , and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:msub> <r:mi>N</r:mi> <r:mn>7</r:mn> </r:msub> </r:math> edges to study the influence of core states on the resulting Ir RIXS spectra. The theoretical RIXS spectrum at the oxygen <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mi>K</s:mi> </s:math> edge has also been analyzed.