Trigonal distortion in the Kitaev candidate honeycomb magnet BaCo2(AsO4)2

We conducted x-ray absorption (XAS) and magnetic circular dichroism (XMCD) measurements at the Co <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>L</a:mi><a:mrow><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>3</a:mn></a:mrow></a:msub></a:math> edges on single crystals of the Kitaev candidate honeycomb lattice compound <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>BaCo</b:mi><b:mn>2</b:mn></b:msub><b:msub><b:mrow><b:mo>(</b:mo><b:msub><b:mi>AsO</b:mi><b:mn>4</b:mn></b:msub><b:mo>)</b:mo></b:mrow><b:mn>2</b:mn></b:msub></b:mrow></b:math>. The measurements employed the inverse partial fluorescence yield technique, which is ideal for acquiring reliable x-ray absorption spectra from highly insulating samples, enabling precise quantitative analysis. Our experimental results revealed a significant linear dichroic signal, indicating strong trigonal distortion in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>CoO</c:mi><c:mn>6</c:mn></c:msub></c:math> octahedra in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>BaCo</d:mi><d:mn>2</d:mn></d:msub><d:msub><d:mrow><d:mo>(</d:mo><d:msub><d:mi>AsO</d:mi><d:mn>4</d:mn></d:msub><d:mo>)</d:mo></d:mrow><d:mn>2</d:mn></d:msub></d:mrow></d:math>. We performed a detailed analysis of the experimental XAS and XMCD spectra using a full-multiplet configuration-interaction cluster model. This analysis unveiled that the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msub><e:mi>t</e:mi><e:mrow><e:mn>2</e:mn><e:mi>g</e:mi></e:mrow></e:msub></e:math> hole density is predominantly localized in the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>a</f:mi><f:mrow><f:mn>1</f:mn><f:mi>g</f:mi></f:mrow></f:msub></f:math> orbital. Through XMCD sum rules and theoretical calculations, we quantified both the spin and orbital magnetic moments. Our study demonstrates that the local electronic structure of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msub><g:mi>CoO</g:mi><g:mn>6</g:mn></g:msub></g:math> octahedra displays an effective trigonal distortion of approximately <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mo>−</h:mo><h:mn>0.114</h:mn></h:mrow></h:math> eV. This distortion is larger than the Co <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>3</i:mn><i:mi>d</i:mi></i:mrow></i:math> spin-orbit coupling constant, emphasizing the crucial impact of local structural distortions on the electronic and magnetic properties of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>BaCo</j:mi><j:mn>2</j:mn></j:msub><j:msub><j:mrow><j:mo>(</j:mo><j:msub><j:mi>AsO</j:mi><j:mn>4</j:mn></j:msub><j:mo>)</j:mo></j:mrow><j:mn>2</j:mn></j:msub></j:mrow></j:math>.