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The pyrochlore oxide Pb2Re2O7-{\delta} (PRO) is a candidate spin-orbit-coupled metal (SOCM) that exhibits a structural phase transition with inversion symmetry breaking. In this study, we report the results of detailed X-ray diffraction (XRD) measurements on single crystals of PRO to clarify the crystal structure below the phase transition temperature at Ts = 300 K. In the XRD patterns, a clear peak splitting is observed below Ts, indicating a cubic to tetragonal transition. Based on the group-subgroup relationship and the observed reflection conditions, the space group of the low-temperature phase is proposed to be I4122, which agrees with optical second harmonic generation measurements. This space group is the same as that of the lowest temperature structure of the analogous SOCM Cd2Re2O7 (CRO), which is realized by the emergence of odd-parity multipole order. The comparison between PRO and CRO allows for advancing our understanding on the symmetry-lowering complex order exhibited by SOCMs., Comment: 10 pages, 9 figures, 1 table

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

The theoretically observable limit of electron density distribution by single-crystal X-ray diffraction is discussed. When F_{orb} and {\delta}F are defined as, respectively, the partial structure factor for an orbital and the deviation of the observed F from the true F, the accuracy of electron density attributable to F_{orb} is chiefly determined by the number of reflections satisfying the condition F_{orb}/F > {\delta}F/F. Since F_{orb}/F, which is generally small for crystals with large F(0,0,0), is constant under a given set of experimental conditions, {\delta}F/F must be reduced to increase the number of reflections satisfying F_{orb}/F > {\delta}F/F. The present paper demonstrates how to reduce {\delta}F mathematically and experimentally, and the following topics are covered: the Poisson statistics, accumulation of errors in the data collection and reduction procedure, multiple diffraction, conversion error from F^2 to F in refinement programs, which is unavoidable when the input quantities have different dimension from F, weighting of reflections, and tips. For demonstration, observation of the electron density of the Ti-3d^1 orbital in YTiO_3 by synchrotron single-crystal X-ray diffraction is presented., Comment: 68 pages, 20 figures

The 5d pyrochlore oxide superconductor Cd2Re2O7 (CRO) has attracted significant interest as a spin-orbit-coupled metal (SOCM) that spontaneously undergoes a phase transition to an odd-parity multipole phase by breaking the spatial inversion symmetry due to the Fermi liquid instability caused by strong spin-orbit coupling. Despite the significance of structural information during the transition, previous experimental results regarding lattice deformation have been elusive. We have conducted ultra-high resolution synchrotron radiation x-ray diffraction experiments on a high-quality CRO single crystal. The temperature-dependent splitting of the 0 0 16 and 0 0 14 reflections, which are allowed and forbidden, respectively, in the high-temperature cubic phase I (space group Fd-3m), has been clearly observed and reveals the following significant facts: inversion symmetry breaking and tetragonal distortion occur simultaneously at Ts1 = 201.5(1) K; the previously believed first-order transition between phase II (I-4m2) and phase III (I4122) at Ts2 ~ 120 K consists of two close second-order transitions at Ts2 = 115.4(1) K and Ts3 ~ 100 K; there is a new orthorhombic phase XI (F222) in between. The order parameters (OPs) of these continuous transitions are uniquely represented by a two-dimensional irreducible representation Eu of the Oh point group, and the OPs of phase XI are a linear combination of those of phases II and III. Each phase is believed to correspond to a distinct odd-parity multipole order, and the complex successive transitions observed may be the result of an electronic phase transition that resolves the Fermi liquid instability in the SOCM., Comment: 10 pages, 6 figures, 1 Table

We systematically synthesized perovskite-type oxides Sr1-xCaxCoO3 containing unusually high valence Co4+ ions by a high pressure technique, and investigated the effect of systematic lattice change on the magnetic and electronic properties. As the Ca content x exceeds about 0.6, the structure changes from cubic to orthorhombic, which is supported by the first-principles calculations of enthalpy. Upon the orthorhombic distortion, the ground state remains to be apparently ferromagnetic with a slight drop of the Curie temperature. Importantly, the compounds with x larger than 0.8 show antiferromagnetic behavior with positive Weiss temperatures and nonlinear magnetization curves at lowest temperature, implying that the ground state is noncollinear antiferromagnetic or helimagnetic. Considering the incoherent metallic behavior and the suppression of the electronic specific heat at high x region, the possible emergence of a helimagnetic state in Sr1-xCaxCoO3 is discussed in terms of the band-width narrowing and the double-exchange mechanism with the negative charge transfer energy as well as the spin frustration owing to the next-nearest neighbor interaction., Comment: 13 pages, 4 figures

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

Magnetic structures and the relationship between spin and charge-orbital orderings of an A-site ordered double-perovskite manganite SmBaMn2O6, an anticipated multiferroic material, were investigated by means of neutron diffraction. The spin arrangement in MnO2 planes perpendicular to the c axis is revealed to be the same as that in the A-site disordered half-doped manganites CE-type but the stacking pattern is found to be different displaying a unique twofold period. The temperature dependence of the superlattice magnetic and nuclear reflections clarifies that the antiferromagnetic spin ordering occurs at a temperature slightly lower than the temperature at which a rearrangement of the charge-orbital orderings occurs. The result evidences that the rearrangement leads the spin ordering. The intensities of the magnetic reflections are found to change across Tf = 10 K, suggesting a spin-flop by 90 [deg.] while keeping the Mn spin ordering pattern unchanged., Comment: 11 pages, 5 figures

A detailed electronic phase diagram of perovskite-type oxides Sr$_{1-x}$La$_x$FeO$_3$ $(0\leq x \leq 0.5)$ was established by synchrotron X-ray diffraction, magnetization, and transport measurements for polycrystalline samples synthesized by a high-pressure technique. Among three kinds of helimagnetic phases in SrFeO$_3$ at zero field, two of them showing multiple-${\it q}$ helimagnetic spin textures tend to rapidly disappear in cubic symmetry upon the La substitution with $x$ less than 0.1, which accompanies the loss of metallic nature. On the other hand, the third helimagnetic phase apparently remains robustly in Sr$_{1-x}$La$_x$FeO$_3$ with $x$ higher than 0.1, followed by merging to the spin/charge ordered phase with $x\sim 1/3$. We propose an important role of itinerant ligand holes on the emergence of multiple-${\it q}$ states and a possible link between the third (putative single-${\it q}$) helimagnetic phase in SrFeO$_3$ and the spin/charge ordered phase in Sr$_{2/3}$La$_{1/3}$FeO$_3$., Comment: 11 pages, 6 figures. Accepted for publication in Physical Review Materials

The double-perovskite A$_2$BB'O$_6$ with heavy transition metal ions on the ordered B' sites is an important family of compounds to study the interplay between electron correlation and spin-orbit coupling (SOC). Here we prepared high-quality Sr$_2$MgReO$_6$ powder and single-crystal samples and performed non-resonant and resonant synchrotron x-ray diffraction experiments to investigate its magnetic ground state. By combining the magnetic susceptibility and heat capacity measurements, we conclude that Sr$_2$MgReO$_6$ exhibits a layered antiferromagnetic (AF) order at temperatures below $\sim$ 55 K with a propagation vector q = (001), which contrasts the previously suspected spin glass state. Our works clarify the magnetic order in Sr$_2$MgReO$_6$ and demonstrate it as a candidate system to look for magnetic octupolar orders and exotic spin dynamics., Comment: 6 pages, 5 figures

In electronic solids with strong spin-orbit interactions (SOIs), the spin and orbital degrees of freedom of an electron are quantum mechanically entangled, which may result in an exotic multipolar order instead of a conventional dipolar order such as a magnetic order. Such a higher-degree order is called "hidden order" because of difficulties in experimental detection. Moreover, the number of candidate compounds is limited, especially rare in d electron systems, in which an interplay between SOIs and Coulomb interactions is expected to cause rich physics. Here, we employ state-of-the-art synchrotron X-ray diffraction techniques on a high-quality single crystal to probe subtle symmetry breaking induced by a multipolar order. We unequivocally demonstrate that the double-perovskite Ba2MgReO6 exhibits successive transitions to quadrupolar and then dipolar orders upon cooling, which is consistent with a theory considering SOIs. Our findings are a significant step towards understanding the intriguing physics of multipoles realized by spin-orbit-entangled 5d electrons., Comment: 17 pages main text, 7 pages supplement, to be published in Phys. Rev. Research

For the skyrmion-hosting intermetallic Gd$_2$PdSi$_3$ with centrosymmetric hexagonal lattice and triangular net of rare earth sites, we report a thorough investigation of the magnetic phase diagram. Our work reveals a new magnetic phase with isotropic value of the critical field for all orientations, where the magnetic ordering vector $\mathbf{q}$ is depinned from its preferred directions in the basal plane. This is in contrast to the highly anisotropic behavior of the low field phases, such as the skyrmion lattice (SkL), which are easily destroyed by in-plane magnetic field. The bulk nature of the SkL and of other magnetic phases was evidenced by specific-heat measurements. Resistivity anisotropy, likely originating from partial gapping of the density of states along $\mathbf{q}$ in this RKKY magnet, is picked up via the planar Hall effect (PHE). The PHE confirms the single-$\mathbf{q}$ nature of the magnetic order when the field is in the hexagonal plane, and allows to detect the preferred directions of $\mathbf{q}$. For field aligned perpendicular to the basal plane, several scenarios for the depinned phase (DP), such as tilted conical order, are discussed on the basis of the data., Comment: 27 pages, 12 figures (including SI)

Magnetic-field effect on the magnetic and electric properties in a chiral polar ordered corundum Ni$_2$InSbO$_6$ has been investigated. Single-crystal soft x-ray and neutron diffraction measurements confirm long-wavelength magnetic modulation. The modulation direction tends to align along the magnetic field applied perpendicular to the polar axis, suggesting that the nearly proper-screw type helicoid should be formed below 77\,K. The application of a high magnetic field causes a metamagnetic transition. In a magnetic field applied perpendicular to the polar axis, a helix-to-canted antiferromagnetic transition takes place through the intermediate soliton lattice type state. On the other hand, a magnetic field applied along the polar axis induces a first-order metamagnetic transition. These metamagnetic transitions accompany a change in the electric polarization along the polar axis.

The topological Hall effect (THE) and its thermoelectric counterpart, the topological Nernst effect (TNE), are hallmarks of the skyrmion lattice phase (SkL). We observed the giant TNE of the SkL in centrosymmetric Gd$_2$PdSi$_3$, comparable in magnitude to the largest anomalous Nernst signals in ferromagnets. Significant enhancement (suppression) of the THE occurs when doping electrons (holes) to Gd$_2$PdSi$_3$. On the electron-doped side, the topological Hall conductivity approaches the characteristic threshold $\sim 1000\,\left(\mathrm{\Omega cm}\right)^{-1}$ for the intrinsic regime. We use the filling-controlled samples to confirm Mott's relation between TNE and THE and discuss the importance of Gd-5d orbitals for transport in this compound., Comment: Main text: 9 pages, 4 figures; with SI: 36 pages, 15 figures

Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity / vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd3Ru4Al12, which materializes a breathing kagom\'e lattice of Gadolinium moments. The magnetic structure of several ordered phases, including the SkL, is determined by resonant x-ray diffraction as well as small angle neutron scattering. The SkL and helical phases are also observed directly using Lorentz transmission electron microscopy. Among several competing phases, the SkL is promoted over a low-temperature transverse conical state by thermal fluctuations in an intermediate range of magnetic fields., Comment: 35 pages, 4 figures

We have discovered a novel candidate for a spin liquid state in a ruthenium oxide composed of dimers of $S = $ 3/2 spins of Ru$^{5+}$,Ba$_3$ZnRu$_2$O$_9$. This compound lacks a long range order down to 37 mK, which is a temperature 5000-times lower than the magnetic interaction scale of around 200 K. Partial substitution for Zn can continuously vary the magnetic ground state from an antiferromagnetic order to a spin-gapped state through the liquid state. This indicates that the spin-liquid state emerges from a delicate balance of inter- and intra-dimer interactions, and the spin state of the dimer plays a vital role. This unique feature should realize a new type of quantum magnetism., Comment: 5 pages, 4 figures