Direct evidence of a near-ideal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>eff</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mtext>/</mml:mtext> <mml:mn>2</mml:mn> </mm

We investigated the local Co <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>3</a:mn> <a:mi>d</a:mi> </a:mrow> </a:math> electronic structure of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>Na</b:mi> <b:mn>2</b:mn> </b:msub> <b:mi>BaCo</b:mi> </b:mrow> </b:math> <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>(</c:mo> <c:msub> <c:mi>PO</c:mi> <c:mn>4</c:mn> </c:msub> <c:msub> <c:mrow> <c:mo>)</c:mo> </c:mrow> <c:mn>2</c:mn> </c:msub> </c:mrow> </c:math> using polarization-dependent x-ray absorption spectroscopy (XAS) in combination with full multiplet cluster calculations. We employed the line-fitting inverse partial fluorescence yield (IPFY) technique to obtain accurate XAS spectra from strong insulating materials. Our combined experimental and theoretical analysis reveals a very small effective trigonal distortion of only 11 meV in the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>CoO</d:mi> <d:mn>6</d:mn> </d:msub> </d:math> octahedra, indicating a close to ideal condition to render a ground state with the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>J</e:mi> <e:mi>eff</e:mi> </e:msub> <e:mo>=</e:mo> <e:mn>1</e:mn> <e:mtext>/</e:mtext> <e:mn>2</e:mn> </e:mrow> </e:math> character. With our cluster model we were also able to simulate magnetic susceptibility measurements along different directions in the crystal. These findings highlight <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msub> <f:mi>Na</f:mi> <f:mn>2</f:mn> </f:msub> <f:mi>BaCo</f:mi> </f:mrow> </f:math> <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mo>(</g:mo> <g:msub> <g:mi>PO</g:mi> <g:mn>4</g:mn> </g:msub> <g:msub> <g:mrow> <g:mo>)</g:mo> </g:mrow> <g:mn>2</g:mn> </g:msub> </g:mrow> </g:math> as a promising platform for exploring exotic magnetic phenomena associated with <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>J</h:mi> <h:mi>eff</h:mi> </h:msub> <h:mo>=</h:mo> <h:mn>1</h:mn> <h:mtext>/</h:mtext> <h:mn>2</h:mn> </h:mrow> </h:math> ground states on triangular lattices.