${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$ is the magnetic intercalate of 2H-${\mathrm{NbS}}_2$ where electronic itinerant and magnetic properties strongly influence each other throughout the phase diagram. Here we report the angle-resolved photoelectron spectroscopy (ARPES) study in ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$. In agreement with previous reports, the observed electronic structure seemingly resembles the one of the parent material 2H-${\mathrm{NbS}}_2$, with the shift in Fermi energy of 0.5 eV accounting for the charge transfer of approximately two electrons from each Co ion into the ${\mathrm{NbS}}_2$ layers. However, in addition, and in contrast to previous reports, we observe significant departures that cannot be explained by the rigid band shift accompanied by minor deformation of bands: First, entirely unrelated to the 2H-${\mathrm{NbS}}_2$ electronic structure, a shallow electronic band is found crossing the Fermi level near the boundary of the first Brillouin zone of ${\mathrm{Co}}_{1/3}{\mathrm{NbS}}_2$. The evolution of the experimental spectra upon varying the incident photon energy suggests the Co origin of this band. Second, the Nb bonding band, found deeply submerged below the Fermi level at the $\mathrm{\Gamma }$ point, indicates that the interlayer hybridization is significantly amplified by intercalation, with Co magnetic ions probably acting as strong covalent bridges between ${\mathrm{NbS}}_2$ layers. The strong hybridization between orbitals that support the itinerant states and the orbitals hosting the local magnetic moments indicates the importance of strong electronic correlations, with the interlayer coupling playing an exquisite role.

The diversity of magnetic orders that appear in layered magnetic materials is of great interest from the fundamental point of view and for applications. In particular, the magnetic sublayers, introduced by intercalation into van der Waals gaps of the host transition-metal dichalcogenide (TMD), are known to produce various magnetic states, with some being tunable by pressure and doping. The magnetic sublayers and their magnetic ordering strongly modify the electronic coupling between layers of the host compound. Understanding the roots of this variability, starting from the underlying electronic structure, is a significant challenge. Here we employ the angle-resolved photoelectron spectroscopy at various photon energies, the ab initio electronic structure calculations, and modeling to address the particular case of Ni-intercalate, ${\mathrm{Ni}}_{1/3}{\mathrm{NbS}}_2$. We find that the bands around the Fermi level bear the signature of a strong yet unusual hybridization between ${\mathrm{NbS}}_2$ conduction band states and the Ni $3d$ orbitals. The hybridization between metallic ${\mathrm{NbS}}_2$ layers is almost entirely suppressed in the central part of the Brillouin zone, including the part of the Fermi surface around the $\mathrm{\Gamma }$ point. Simultaneously, it gets very pronounced towards the zone edges. It is shown that this behavior is the consequence of the rather exceptional, symmetry imposed, spatially strongly varying, zero total hybridization between relevant Ni magnetic orbitals and the neighboring Nb orbitals that constitute the metallic bands. We also report the presence of the so-called $\beta$ feature, discovered only recently in two other magnetic intercalates with very different magnetic orderings. In ${\mathrm{Ni}}_{1/3}{\mathrm{NbS}}_2$, the feature shows only at particular photon energies, indicating its bulk origin. Common to prior observations, it appears as a series of very shallow electron pockets at the Fermi level, positioned along the edge of the Brillouin zone. Unforeseen by ab initio electronic calculations, and its origin still unresolved, the feature appears to be a robust consequence of the intercalation of $2\mathrm{H}\text{−}{\mathrm{NbS}}_2$ with magnetic ions.

We have investigated the electronic structure of iridates in the double perovskite crystal structure containing either ${\mathrm{Ir}}^{4+}$ or ${\mathrm{Ir}}^{5+}$ using hard x-ray photoelectron spectroscopy. The experimental valence band spectra can be well reproduced using tight-binding calculations including only the Ir $5d$, O $2p$, and O $2s$ orbitals with parameters based on the downfolding of the density-functional band structure results. We found that, regardless of the A and B cations, the ${\mathrm{A}}_2{\mathrm{BIrO}}_6$ iridates have essentially zero O $2p$ to Ir $5d$ charge-transfer energies. Hence double perovskite iridates turn out to be extremely covalent systems with the consequence being that the magnetic exchange interactions become very long ranged, thereby hampering the materialization of the long-sought Kitaev physics. Nevertheless, it still would be possible to realize a spin-liquid system using the iridates with a proper tuning of the various competing exchange interactions.

Non-centrosymmetric $\mathrm{Eu}T{\mathrm{Ge}}_3$ ($T$= Co, Ni, Rh, and Ir) possesses magnetic ${\mathrm{Eu}}^{2+}$ ions, and antiferromagnetic ordering appears at low temperatures. Transition-metal substitution leads to changes in the unit-cell volume and in the magnetic ordering. However, the magnetic ordering temperature does not scale with the volume change, and the Eu valence is expected to remain divalent. Here we study the bulk electronic structure of non-centrosymmetric $\mathrm{Eu}T{\mathrm{Ge}}_3$ ($T$= Co, Ni, Rh, and Ir) by hard x-ray photoelectron spectroscopy. The Eu $3d$ core-level spectrum confirms the robust ${\mathrm{Eu}}^{2+}$ valence state against the transition-metal substitution with a small contribution from ${\mathrm{Eu}}^{3+}$. The estimated Eu mean valence is around 2.1 in these compounds, as confirmed by multiplet calculations. In contrast, the Ge $2p$ spectrum shifts to higher binding energy upon changing the transition metal from $3d$ to $4d$ to $5d$ elements, hinting at a change in the Ge-$T$ bonding strength. The valence bands of the different compounds are found to be well reproduced by ab initio band structure calculations.

Among europium compounds, pressure induced valence transitions and/or intermediate valence states are often observed. In such systems, applying pressure of several GPa can drive a Eu valence from divalent to almost trivalent. Non-centrosymmetric EuRhGe₃ possesses magnetic Eu²⁺ ions and exhibits antiferromagnetic ordering at ∼11 K at ambient pressure. Pressure resistant magnetic ordering and stable divalent Eu state have been reported in EuRhGe₃. Here, we study the pressure evolution of the Eu valence of EuRhGe₃ by high resolution x-ray absorption spectroscopy using the partial fluorescence yield method. Our study reveals a successive increase of the Eu valence with increasing pressure without any valence transition. The obtained mean Eu valence approaches ∼2.4 around 40 GPa at 300 K. The experimental data are also analyzed by a full multiplet configuration interaction calculation based on the single impurity Anderson model. The analysis reveals a decrease of the Eu 4f orbital occupation by applying pressure. Pressure evolution of the electronic structure studied by density functional theory suggests that the Rh ions have little contribution to the pressure evolution of the Eu valence, while it implies an active involvement of the Ge ions.

It was hypothesized already more than 40 years ago that photoelectron spectroscopy should in principle be able to image atomic orbitals. If this can be made to work for orbitals in crystalline solids, one would have literally a different view on the electronic structure of a wide range of quantum materials. Here, we demonstrate how hard x-ray photoelectron spectroscopy can make direct images of the orbitals making up the band structure of our model system, ${\mathrm{ReO}}_3$. The images are energy specific and enable us to unveil the role of each of those orbitals for the chemical bonding and the Fermi surface topology. The orbital image information is complementary to that from angle-resolved photoemission and thus completes the determination of the electronic structure of materials.