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Electrons in localized 4f orbitals around lanthanide elements in solids are dominated by strong spin-orbit coupling. The resultant J multiplets are further split by the crystalline electric field, where J denotes the total angular momentum quantum number, and hence exhibit anisotropic spatial distribution. The anisotropy of spin-orbit entangled 4f electrons is closely linked to their physical properties. Here, we demonstrate the visualization of 4f electrons in pyrochlore oxides A2Ir2O7 (A = Pr, Nd, and Eu) by combining high-photon-energy X-ray diffraction and valence electron density (VED) analysis based on the core differential Fourier synthesis (CDFS) method. The observed VED distributions around the A site roughly agree with point-charge calculations, considering the relativistic spin-orbit coupling and the trigonal crystal electric field under the LS coupling scheme. The CDFS-based VED observation method can be applied to the analysis of the 4f state of various crystalline materials., Comment: 19 pages, 3 figures, SI

Honeycomb-lattice antiferromagnets have attracted wide attention for exploration of exotic heat transport and their interplay with magnetic excitations. In this work, we have revealed a contrasting behavior in the magneto-thermal conductivity (MTC) between two Co-based honeycomb-lattice magnets Co4M2O9 (M = Nb, Ta), despite their identical lattice structures and quite similar magnetism. Co4Ta2O9 exhibits enhanced MTC of about 550% at 9 T of an in-plane magnetic field, comparable to other honeycomb-magnets, while MTC for Co4Nb2O9 reaches only ~30%. This marked difference is ascribed to distinct features in the field-induced evolution of magnetic excitations that resonantly scatter phonons. This finding sheds light on implicit impacts of non-magnetic ions on thermal transport, and hints at the potential for broad heat-transport tunability while preserving magnetism and lattice structures., Comment: 7 pages, 4 figures, doi.org/10.1103/PhysRevB.110.L041116

Frustrated rare-earth-based intermetallics provide a promising platform for emergent magnetotransport properties through exchange coupling between conduction electrons and localized rare-earth magnetic moments. Metamagnetism, the abrupt change of magnetization under an external magnetic field, is a signature of first-order magnetic phase transitions; recently, metamagnetic transitions in frustrated rare earths intermetallics have attracted interest for their accompanying nontrivial spin structures (e.g. skyrmions) and associated non-linear and topological Hall effects. Here, we present metamagnetism-induced Hall anomalies in single-crystalline ErGa$_2$, which recalls features arising from the topological Hall effect but wherein the strong Ising type anisotropy of Er moments prohibit noncoplanar spin structures. We show that the observed anomalies are neither due to anomalous Hall effect nor topological Hall effect, instead, can be accounted for via 4f-5d interactions which produce a band-dependent mobility modulation. This leads to a pronounced multiband Hall response across the magnetization process -- a metamagnetic multiband Hall effect that resembles a topological-Hall-like response but without nontrivial origins. The present findings may be of general relevance in itinerant metamagnetic systems regardless of coplanar/non-coplanar nature of spins and are important for the accurate identification of Hall signals due to emergent magnetic fields., Comment: Main 15 pages, 4 figures, Supple 22 pages, 9 figures, 1 Table

We report the magnetic, magnetoelastic, and magnetotransport properties of single crystals of polar magnets $R$AuGe ($R=$ Dy, Ho, and Gd), grown by Au-Ge self-flux. Magnetization and magnetostriction measurements reveal multi-step metamagnetic transitions for the $c$-axis magnetic field ($H\parallel c$) for DyAuGe and HoAuGe, suggesting magnetic frustration in the triangular lattice of $R$ ions. The magnetic phase diagrams have clarified a close connection between the magnetoelastic property and the emergence of the intermediate metamagentic phase. The magnetic-field dependence of the resistivity and Hall resistivity reveal the semimetallic transport dominated by hole-type carriers, consistent with the behavior in a nonmagnetic analogue YAuGe. We also identify a signature of an anomalous Hall effect (AHE) proportional to the field-induced magnetization in $R=$ Dy, Ho, and Gd. GdAuGe shows magnetic and transport behavior as reported in a previous study using Bi-flux grown single crystals, while the self-flux grown crystal shows larger magnetoresistance ($\sim$ 345\%, at 1.8 K and 9 T) due to higher hole-type carrier mobility ($\sim$ 6400 cm$^2$/Vs). Using the two-band model analysis considering the mobility change during the magnetization process, we extract the anomalous Hall conductivity: $\sim 1200$ S/cm and $\sim 530$ S/cm for $R=$ Dy and Ho, respectively, at 1.8 K with 9 T for $H\parallel c$. The magnitude of conductivity suggests a contribution of intrinsic origin, possibly related to the Berry curvature in the electron bands induced by the time-reversal symmetry breaking and the polar lattice., Comment: 11 pages, 9 figures

Exploration of nontrivial magnetic states induced by strong spin-orbit interaction is a central topic of frustrated magnetism. Extensive studies are concentrated on rare-earth-based magnets and 4d/5d transition metal compounds, which are mostly described by an effective spin $S_{\text{eff}} = 1/2$ for the Kramers doublet of the lowest crystal-electric-field levels. Variety of magnetic orderings may be greatly enhanced when magnetic dipolar moments intertwined with multipolar degrees of freedom which are described by higher-rank tensors and often require the magnetic ions with $S_{\text{eff}} > 1/2$. Here, our synchrotron x-ray diffraction near the Dy $L_3$ edge has unveiled a canted antiferromagnetic ground state arising from a quasi-quartet ($S_{\text{eff}} = 3/2$) of 4f electrons in a triangular-lattice (TL) rare-earth intermetallics DyAuGe. Magnetic moment and electric-quadrupole moment are closely interlocked and noncollinear magnetic-dipole alignment is induced by antiferroic electric-quadrupole (AFQ) ordering in the TL layers. The correlation between the AFQ and canted magnetic structures is further confirmed by phase transitions in an in-plane magnetic field. These findings offer insights into the emergence of nontrivial magnetic states in frustrated TL systems described beyond the $S_{\text{eff}} = 1/2$., Comment: 12 pages, 5 figures

Transition-metal atoms with d electrons sometimes form clusters in crystals, which significantly affects the physical properties. Such a cluster formation frequently accompanies a change in the crystal system, leading to the presence of domains with different crystal orientations. In particular, the cubic symmetry is rarely retained after the cluster formation. Here, we identify a cubic-to-cubic phase transition in lacunar spinel GaNb$_4$Se$_8$, where the change in the lattice parameter is less than 0.0001%. Each Nb$^{3.25+}$ tetramer with seven 4d electrons is distorted into a Nb$^{3+}$ trimer and a Nb$^{4+}$ monomer induced by charge disproportionation among Nb ions. While the Nb$^{3+}$ trimer with six 4d electrons forms spin-singlets in the sigma-bonding orbitals for three Nb-Nb bonds, a localized S=1/2 spin remains on the Nb$^{4+}$ ion. Furthermore, a local electric dipole moment is induced along the three-fold rotation axis of each distorted tetramer by the cluster rearrangement. The electric dipole moments are regularly arranged to maintain the cubic symmetry, giving rise to chiral order., Comment: 24 pages, 4 figures, supporting information

The metal-insulator transition (MIT) in vanadium dioxide VO$_2$ due to V-V dimerization has been extensively discussed for decades. While it is widely acknowledged that electron correlations, Peierls instabilities, and molecular orbital formations are crucial for understanding the MIT of VO$_2$, the primary origin of the MIT remains controversial. In this study, we delve into the crystal structure and orbital state of VO$_2$ through synchrotron x-ray diffraction experiments. The molecular orbital formation corresponding to the V-V dimerization is directly observed in the low-temperature insulating monoclinic phase, called the M1 phase, as indicated by the valence electron density distribution. Moreover, diffuse scattering observed in the high-temperature metal phase of rutile structure suggests the presence of short-range correlation of V displacements, which is not directly attributed to the structural fluctuation of the M1 phase. The short-range order in the rutile phase will be the key to understanding the MIT in this system., Comment: 6 pages, 4 figures, Supplemental Material

An anomalously high valence state sometimes shows up in transition-metal oxide compounds. In such systems, holes tend to occupy mainly the ligand $p$ orbitals, giving rise to interesting physical properties such as superconductivity in cuprates and rich magnetic phases in ferrates. However, no one has ever observed the distribution of ligand holes in real space. Here, we report a successful observation of the spatial distribution of valence electrons in cubic perovskite SrFeO$_3$ by high-energy X-ray diffraction experiments and precise electron density analysis using a core differential Fourier synthesis method. A real-space picture of ligand holes formed by the orbital hybridization of Fe 3$d$ and O 2$p$ is revealed. The anomalous valence state in Fe is attributed to the considerable contribution of the ligand hole, which is related to the metallic nature and the absence of Jahn-Teller distortions in this system., Comment: 14 pages, 4 figures

We study structural and magnetic properties of rare-earth based semimetals RAuGe (R = Y, Gd-Tm, and Lu) using flux-grown single crystals. These compounds belong to the noncentrosymmetric polar space group P63mc. We confirm the systematic structural evolution at room temperature as a function of ionic radius of rare earths to clarify the isopointal crossover between two polar structures: three-dimensional LiGaGe-type and quasi-two-dimensional NdPtSb-type. Magnetism shows a characteristic anisotropy in reasonable agreement with the crystal electric field (CEF) theory; the easy-plane-type anisotropy for R = Tb and Dy turns into the Ising-type anisotropy for R = Er and Tm. We evaluate the CEF parameters based on the Stevens operators to reasonably reproduce the temperature dependence of magnetic susceptibilities and specific heat for RAuGe (R = Tb-Tm). The estimated energy scale of the Ising gap (~ 11 meV) in TmAuGe is consistent with an excitation observed in an inelastic neutron scattering experiment. These findings suggest an opportunity for interplay between conduction electrons and nontrivial spin structures in the family of magnetic polar semimetals RAuGe., Comment: 10 pages, 7 figures, 1 table

The centrosymmetric tetragonal itinerant magnet EuAl$_{4}$ exhibits an intricate magnetic phase diagram including rhombic and square skyrmion-lattice (SkL) phases in the external magnetic field. Here, we report a multi-axis dilatometric investigation of EuAl$_{4}$ by means of a newly designed fiber-Bragg-grating technique complemented by a resonant x-ray scattering experiment, revealing anisotropic magnetostriction and magnetovolume effect associated with successive phase transitions. The rhombic and square SkL phases are found to possess $\sim$0.10% and $\sim$0.03% orthorhombic structural distortion within the $ab$ plane, respectively. We propose that the coupling between the spin system and the lattice deformation should be essential for the structural instability in EuAl$_{4}$, yielding a rich variety of topological spin textures with spontaneous rotational-symmetry breaking as well as a potential controllability of the SkL phases by uniaxial stress or pressure., Comment: 8 pages, 5 figures, SM: 4 pages, 3 figures. To be published in Physical Review B as a Letter

We investigate the thermodynamic, magnetic, and electrical transport properties of a triangular-lattice antiferromagnet EuZnGe using single crystals grown from Eu-Zn flux in sealed tantalum tubes. Magnetic properties are found to be isotropic in the paramagnetic state while we observe an enhancement of in-plane magnetic susceptibility at the temperature near T* =11.3 K, suggesting an easy-plane anisotropy at low temperatures. Magnetic transition temperature is lower than T* as specific heat shows a peak at TN =7.6 K. We reveal the magnetic modulation along the c axis by resonant x-ray scattering at Eu L2 edge, which suggests competing magnetic interaction among Eu triangular-lattice layers. We observe a double-peak structure in the intensity profile along (0, 0, L) below TN, which is mainly composed of a dominant helical modulation with q ~ (0, 0, 0.4) coexisting with a secondary contribution from q ~ (0, 0, 0.5). We reproduce the intensity profile with a random mixture of five- and four-sublattice helices with spin rotation skipping due to hexagonal in-plane anisotropy. The metallic conductivity is highly anisotropic with the ratio rho_zz/rho_xx exceeding 10 over the entire temperature range and additionally exhibits a sharp enhancement of rho_zz at TN giving rise to rho_zz/rho_xx ~ 50, suggesting a coupling between out-of-plane electron conduction and the spiral magnetic modulations. In-plane magnetic field induces a spin-flop like transition, where the q = 0.4 peak disappears and an incommensurate peak of approximately qICM ~ 0.47 emerges, while the q = 0.5 modulation retains a finite intensity. This transition correlates with non-monotonic magnetoresistance and Hall resistivity, suggesting a significant interplay between electrons and spin structures through Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction., Comment: 9 pages, 6 figures

We report experimental signatures of topological transitions among the Weyl semimetal states of pyrochlore Pr2Ir2O7, where the Kondo coupling between the Ir topological electrons and the spin-ice like orders of Pr moments plays a decisive role. The magnetic-field dependence of resistivity and the Hall conductivity exhibits a plateau and a sharp jump associated with a magnetic-field hysteresis, similar to a liquid-gas-like transition in dipolar spin ice system. Furthermore, the Kondo coupling is controlled by the hydrostatic pressure, revealing that the field-induced displacement of Weyl points in the momentum space strongly depends on the respective electronic state as well as on the Kondo coupling strength. These observations pave a route toward the engineering of band topology in hybrid quantum materials with relativistic conduction electrons and localized magnetic moments.

We investigated the precise crystal structures and electronic states in a quasi-two-dimensional molecular conductor ${\alpha}$-(BETS)$_2$I$_3$ at ambient pressure. The electronic resistivity of this molecular solid shows metal-to-insulator (MI) crossover at $T_{MI}$=50 K. Our x-ray diffraction and $^{13}$C nuclear magnetic resonance experiments revealed that ${\alpha}$-(BETS)$_2$I$_3$ maintains the inversion symmetry below $T_{MI}$. First-principles calculations found a pair of anisotropic Dirac cones at a general k-point, with the degenerate contact points at the Fermi level. The origin of the insulating state in this system is a small energy gap of ~2 meV opened by the spin-orbit interaction. The Z$_2$ topological invariants indicate that this system is a weak topological insulator. Our results suggest that ${\alpha}$-(BETS)$_2$I$_3$ is a promising material for studying the bulk Dirac electron system in two dimensions., Comment: 9 pages, 6 figures + Supplemental Material

1T-TiSe2 has a semimetallic band structure at room temperature and undergoes phase transition to a triple-q charge density wave (CDW) state with a commensurate superlattice structure (2a * 2a * 2c) below Tc ~ 200 K at ambient pressure. This phase transition is caused by cooperative phenomena involving electron-phonon and electron-hole (excitonic) interactions, and cannot be described by a standard CDW framework. By Cu intercalation or the application of pressure, this phase transition temperature is suppressed and superconductivity (SC) appears. However, it is not clear what kind of order parameters are affected by these two procedures. We investigated the crystal structure of CuxTiSe2 and pressurized 1T-TiSe2 around the SC state by synchrotron x-ray diffraction on single crystals. In the high-temperature phase, the variation of structural parameters for the case of Cu intercalation and application of pressure are considerably different. Moreover, the relationship between the critical points of the CDW phase transition and the SC dome are also different for the two cases. The excitonic interaction appears to play an important role in the P-T phase diagram of 1T-TiSe2, but not in the x-T phase diagram., Comment: 11 pages, 7 figures, 1 table