Nature of Excitons and Their Ligand-Mediated Delocalization in Nickel Dihalide Charge-Transfer Insulators

The fundamental optical excitations of correlated transition-metal compounds are typically identified with multielectronic transitions localized at the transition-metal site, such as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi><a:mi>d</a:mi></a:math> transitions. In this vein, intense interest has surrounded the appearance of sharp, below-band-gap optical transitions, i.e., excitons, within the magnetic phase of correlated <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msup><c:mrow><c:mi>Ni</c:mi></c:mrow><c:mrow><c:mn>2</c:mn><c:mo>+</c:mo></c:mrow></c:msup></c:mrow></c:math> van der Waals magnets. The interplay of magnetic and charge-transfer insulating ground states in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msup><e:mrow><e:mi>Ni</e:mi></e:mrow><e:mrow><e:mn>2</e:mn><e:mo>+</e:mo></e:mrow></e:msup></e:mrow></e:math> systems raises intriguing questions on the roles of long-range magnetic order and of metal-ligand charge transfer in the exciton nature, which inspired microscopic descriptions beyond typical <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>d</g:mi><g:mi>d</g:mi></g:math> excitations. Here we study the impact of charge transfer and magnetic order on the excitation spectrum of the nickel dihalides (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>Ni</i:mi><i:msub><i:mrow><i:mi>X</i:mi></i:mrow><i:mrow><i:mn>2</i:mn></i:mrow></i:msub></i:mrow></i:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>X</k:mi><k:mo>=</k:mo><k:mi>Cl</k:mi></k:mrow></k:math>, Br, and I) using Ni-<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>L</m:mi><m:mn>3</m:mn></m:msub></m:math> edge resonant inelastic x-ray scattering (RIXS). In all compounds, we detect sharp excitations, analogous to the recently reported excitons, and assign them to spin-singlet multiplets of octahedrally coordinated <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:msup><o:mrow><o:mi>Ni</o:mi></o:mrow><o:mrow><o:mn>2</o:mn><o:mo>+</o:mo></o:mrow></o:msup></o:mrow></o:math> stabilized by intra-atomic Hund’s exchange. Additionally, we demonstrate that these excitons are dispersive using momentum-resolved RIXS. Our data evidence a ligand-mediated multiplet dispersion, which is tuned by the charge-transfer gap and independent of the presence of long-range magnetic order. This reveals the mechanisms governing nonlocal interactions of on-site <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>d</q:mi><q:mi>d</q:mi></q:math> excitations with the surrounding crystal or magnetic structure, in analogy to ground-state superexchange. These measurements thus establish the roles of magnetic order, self-doped ligand holes, and intersite-coupling mechanisms for the properties of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>d</s:mi><s:mi>d</s:mi></s:math> excitations in charge-transfer insulators.