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The subtle interplay between competing degrees of freedom, crystal electric fields, and spin correlations can lead to exotic quantum states in 4f ion-based frustrated triangular lattice antiferromagnets. We present the crystal structure, thermodynamic and muon spin relaxation (μSR) studies of the 4f ion-based frustrated magnet Ba4YbReWO12, wherein Yb3+ ions constitute a triangular lattice. The magnetic susceptibility does not show any signature of spin freezing down to 1.9 K or long-range magnetic ordering down to 0.4 K. The low-temperature Curie-Weiss fit to the inverse magnetic susceptibility data reveals a weak antiferromagnetic exchange interaction, which is corroborated by the fit of magnetic specific heat data following the J1-J2 model with the nearest neighbor exchange interaction of J1 = -0.197 K between the Jeff = 1/2 states of the Yb3+ moments in the lowest Kramers doublet. The lowest Kramers ground state doublet is well separated from the first excited state with a gap of 278 K, as evidenced by our μSR experiments that support the realization of Jeff = 1/2 at low temperatures. The specific heat experiments do not detect a phase transition down to 56 mK. The magnetic spec

We report on the crystal field level splitting and magnetic ground state of the Jeff = 1/2 square lattice antiferromagnets YbBi2ClO4 and YbBi2IO4 using powder inelastic neutron scattering (INS) and neutron diffraction measurements. Both compounds exhibit a well-isolated $Γ_{7}$ doublet ground state under a tetragonal crystal field environment, confirming a robust Jeff = 1/2 picture with slight XY-type anisotropic character in the g-tensor. Notably, the ground state wave functions closely resemble the $Γ_{7}$ doublet expected in the perfect cubic limit, consistent with the nearly cubic ligand configuration of eight O2- ions surrounding Yb3+. Below TN =0.21 K, YbBi2IO4 exhibits a stripe long-range magnetic order characterized by an ordering wave vector qm = (1/2, 0, 0) or its symmetry-equivalent (0, 1/2, 0), with magnetic moments aligned along qm. The ordered moment is approximately 79 % of the classical prediction, significantly larger than expected from the isotropic J1-J2 model, suggesting the possible involvement of exchange anisotropy in explaining this observation. We show that symmetry-allowed XXZ and bond-dependent anisotropic exchange terms in a square lattice can play a cri

The spin-orbit entangled (SOE) Jeff-state has been a fertile ground to study novel quantum phenomena. Contrary to the conventional weakly correlated Jeff=1/2 state of 4d and 5d transition metal compounds, the ground state of CuAl2O4 hosts a Jeff=1/2 state with a strong correlation of Coulomb U. Here, we report that surprisingly Cu2+ ions of CuAl2O4 overcome the otherwise usually strong Jahn-Teller distortion and instead stabilize the SOE state, although the cuprate has relatively small spin-orbit coupling. From the x-ray absorption spectroscopy and high-pressure x-ray diffraction studies, we obtained definite evidence of the Jeff=1/2 state with a cubic lattice at ambient pressure. We also found the pressure-induced structural transition to a compressed tetragonal lattice consisting of the spin-only S=1/2 state for pressure higher than Pc=8 GPa. This phase transition from the Mott insulating Jeff=1/2 to the S=1/2 states is a unique phenomenon and has not been reported before. Our study offers a rare example of the SOE Jeff-state under strong electron correlation and its pressure-induced transition to the S=1/2 state.

Strong spin-orbit coupling lifts the degeneracy of t2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of Jeff = 1/2 and 3/2, respectively. These spin-orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa4Se8 was theoretically predicted to form the molecular Jeff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the Jeff = 3/2 state. Here, we report direct experimental evidence of the Jeff = 3/2 state in GaTa4Se8 by means of excitation spectra of resonant inelastic x-rays scattering at the Ta L3 and L2 edges. We found that the excitations involving the Jeff = 1/2 molecular orbital were suppressed only at the Ta L2 edge, manifesting the realization of the molecular Jeff = 3/2 ground state in GaTa4Se8.

The spin-orbit entangled quantum states in 4d/5d compounds, e.g., the Jeff=1/2 and Jeff=3/2 states, have attracted great interests for their unique physical roles in unconventional superconductivity and topological states. Here, the key role of tetragonal distortion is clarified, which determines the ground states of 4d1/5d1 systems to be the Jeff=3/2 one (e.g. K2NbCl6) or S=1/2 one (e.g. Rb2NbCl6). By tuning the tetragonal distortion via epitaxial strain, the occupation weights of dxy/dyz/dxz orbitals can be subtly modulated, competing with the spin-orbit coupling. Consequently, quantum phase transitions between S=1/2 state and Jeff=3/2 state, as well as between different Jeff=3/2 states, can be achieved, resulting in significant changes of local magnetic moments. Our prediction points out a reliable route to engineer new functionality of Jeff states in these quantum materials.

Magnetic materials are composed of the simple building blocks of magnetic moments on a crystal lattice that interact via magnetic exchange. Yet from this simplicity emerges a remarkable diversity of magnetic states. Some reveal the deep quantum mechanical origins of magnetism, for example, quantum spin liquid (QSL) states in which magnetic moments remain disordered at low temperatures despite being strongly correlated through quantum entanglement. A promising theoretical model of a QSL is the Kitaev model, composed of unusual bond-dependent exchange interactions, but experimentally, this model is challenging to realise. Here we show that the material requirements for the Kitaev QSL survive an extended pseudo-edge-sharing superexchange pathway of Ru3+ octahedra within the honeycomb layers of the inorganic framework solid, RuP3SiO11. We confirm the requisite jeff = 1/2 state of Ru3+ in RuP3SiO11 and resolve the hierarchy of exchange interactions that provide experimental access to an unexplored region of the Kitaev model.

In this work, we report observation of strain effect on physical properties of Sr2IrO4 thin films grown on SrTiO3 (001) and LaAlO3 (001) substrates. It is found that the film on LaAlO3 with compressive strain has a lower antiferromagnetic transition temperature (TN~210 K) than the film on SrTiO3 (TN~230 K) with tensile strain, which is probably caused by modified interlayer coupling. Interestingly, magnetoresistance due to pseudospin-flip of the film on LaAlO3 is much larger than that of tensile-strained film on SrTiO3, and robust anisotropic magnetoresistance is observed in the former, but H-driven reversal behavior is seen in the latter. By performing first principles calculations, it is revealed that epitaxial strain plays an efficient role in tuning the canting angle of Jeff=1/2 moments and thus net moment at every IrO2 layer, responsible for the difference in magnetoresistance between the films. The reversal of anisotropic magnetoresistance in the thin film on SrTiO3 can be ascribed to stabilization of a metastable stable with smaller bandgap as the Jeff=1/2 moments are aligned along the diagonal of basal plane by H. However, theoretical calculations reveal much higher magneto

Sr2IrO4 hosts a novel Jeff =1/2 Mott state and quasi-two-dimensional antiferromagnetic order, providing a unique avenue of exploring emergent states of matter and functions that are extraordinarily sensitive to any structural variations. While the correlation between the physical property and lattice structure in Sr2IrO4 has been a focused issue in the past decade, a common perception assumes that the magnetic ordering is essentially determined by the Ir-O-Ir bond angle. Therefore, a delicate modulation of this angle and consequently a major modulation of the magnetic ordering, by chemical doping such as Ga at Ir site, has been extensively investigated and well believed. In this work, however, we present a whole package of structure and magnetism data on a series of single crystal and polycrystalline Sr2Ir1-xGaxO4 samples, revealing the substantial difference in the Néel temperature TN between the two types of samples, and the TN value for the polycrystalline sample x = 0.09 is even 64 K higher than that of the single crystal sample x = 0.09 (deltaTN ~ 64 K at x = 0.09). Our systematic investigations demonstrate the crucial role of the c/a ratio in tuning the interlayer coupling an

The interplay between competing degrees of freedom can stabilize non-trivial magnetic states in correlated electron materials. Frustration-induced strong quantum fluctuations can evade long-range magnetic ordering leading to exotic quantum states such as spin liquids in two-dimensional spin-lattices such as triangular and kagome structures. However, the experimental realization of dynamic and correlated quantum states is rare in three-dimensional (3D) frustrated magnets wherein quantum fluctuations are less prominent. Herein, we report the crystal structure, magnetic susceptibility, electron spin resonance (ESR) and specific heat studies accompanied by crystal electric field (CEF) calculations on a 3D frustrated magnet Yb3Sc2Ga3O12. In this material, Yb3+ ions form a three-dimensional network of corner-sharing triangles known as hyperkagome lattice without any detectable anti-site disorder. Our results reveal a low energy state with Jeff = 1/2 degrees of freedom in the Kramers doublet state. The zero field-cooled and field cooled magnetic susceptibility taken in 0.001 T rules out the presence of spin-freezing down to 1.8K. The Curie-Weiss (CW) fit to low-T susceptibility data yield

We investigated electronic structure of 5d transition-metal oxide Sr2IrO4 using angle-resolved photoemission, optical conductivity, and x-ray absorption measurements and first-principles band calculations. The system was found to be well described by novel effective total angular momentum Jeff states, in which relativistic spin-orbit (SO) coupling is fully taken into account under a large crystal field. Despite of delocalized Ir 5d states, the Jeff-states form so narrow bands that even a small correlation energy leads to the Jeff = 1/2 Mott ground state with unique electronic and magnetic behaviors, suggesting a new class of the Jeff quantum spin driven correlated-electron phenomena.

Iridates have been providing a fertile ground for studying emergent phases of matter that arise from delicate interplay of various fundamental interactions with approximate energy scale. Among these highly focused quantum materials, perovskite Sr2IrO4 belonging to the Ruddlesden-Popper series stands out and has been intensively addressed in the last decade, since it hosts a novel Jeff = 1/2 state which is a profound manifestation of strong spin-orbit coupling. Moreover, the Jeff = 1/2 state represents a rare example of iridates that has been better understood both theoretically and experimentally. In this progress report, we take Sr2IrO4 as an example to overview the recent advances of the Jeff = 1/2 state in two aspects: materials fundamentals and functionality potentials. In the fundamentals part, we first illustrate basic issues for the layered canted antiferromagnetic order of the Jeff = 1/2 magnetic moments in Sr2IrO4, and then review the progress of the antiferromagnetic order modulation through diverse routes. Subsequently, for the functionality potentials, fascinating properties such as atomic-scale giant magnetoresistance, anisotropic magnetoresistance, and nonvolatile mem

The interplay between spin-orbit coupling, anisotropic magnetic interaction, frustration-induced quantum fluctuations and spin correlations can lead to novel quantum states with exotic excitations in rare-earth-based quantum magnets. Herein, we present the crystal structure, magnetization, electron spin resonance (ESR), specific heat, and nuclear magnetic resonance (NMR) experiments on the polycrystalline samples of Ba9Yb2Si6O24, in which Yb3+ ions form a perfect honeycomb lattice without detectable anti-site disorder. The magnetization data reveal antiferromagnetically coupled spin-orbit entangled Jeff = 1/2 degrees of freedom of Yb3+ ions in the Kramers doublet state. The ESR measurements reveal that the first excited Kramers doublet is 32.3(7) meV above the ground state. The specific heat results suggest the absence of any long-range magnetic order in the measured temperature range. Furthermore, the 29Si NMR results do not indicate any signature of magnetic ordering down to 1.6 K, and the spin-lattice relaxation rate reveals the presence of a field-induced gap that is attributed to the Zeeman splitting of Kramers doublet state in this quantum material. Our experiments detect nei

Frustration-induced strong quantum fluctuations accompanied by spin-orbit coupling and crystal electric field can give rise to rich and diverse magnetic phenomena associated with unconventional low-energy excitations in rare-earth based quantum magnets. Herein, we present crystal structure, magnetic susceptibility, specific heat, muon spin relaxation(muSR), and electron spin resonance (ESR) studies on the polycrystalline samples of Ba6Yb2Ti4O17 in which Yb3+ ions constitute a perfect triangular lattice in ab-plane without detectable anti-site disorder between atomic sites. The Curie-Weiss fit of low-temperature magnetic susceptibility data suggest the spin-orbit entangled Jeff = 1/2 degrees of freedom of Yb3+ spin with weak antiferromagnetic exchange interactions in the Kramers doublet ground state. The zero-field specific heat data reveal the presence of long-range magnetic order at TN = 77 mK which is suppressed in a magnetic field 1 T. The broad maximum in specific heat is attributed to the Schottky anomaly implying the Zeeman splitting of the Kramers doublet ground state. The ESR measurements suggest the presence of anisotropic exchange interaction between the moments of Yb3+ s

Sr3Ir2O7 exhibits a novel Jeff=1/2 insulating state that features a splitting between Jeff=1/2 and 3/2 bands due to spin-orbit interaction. We report a metal-insulator transition in Sr3Ir2O7 via either dilute electron doping (La3+ for Sr2+) or application of high pressure up to 35 GPa. Our study of single-crystal Sr3Ir2O7 and (Sr1-xLax)3Ir2O7 reveals that application of high hydrostatic pressure P leads to a drastic reduction in the electrical resistivity by as much as six orders of magnitude at a critical pressure, PC = 13.2 GPa, manifesting a closing of the gap; but further increasing P up to 35 GPa produces no fully metallic state at low temperatures, possibly as a consequence of localization due to a narrow distribution of bonding angles θ. In contrast, slight doping of La3+ ions for Sr2+ ions in Sr3Ir2O7 readily induces a robust metallic state in the resistivity at low temperatures; the magnetic ordering temperature is significantly suppressed but remains finite for (Sr0.95La0.05)3Ir2O7 where the metallic state occurs. The results are discussed along with comparisons drawn with Sr2IrO4, a prototype of the Jeff = 1/2 insulator.

We investigated the temperature-dependent evolution of the electronic structure of the Jeff,1/2 Mott insulator Sr2IrO4 using optical spectroscopy. The optical conductivity spectra $σ(ω)$ of this compound has recently been found to exhibit two d-d transitions associated with the transition between the Jeff,1/2 and Jeff,3/2 bands due to the cooperation of the electron correlation and spin-orbit coupling. As the temperature increases, the two peaks show significant changes resulting in a decrease in the Mott gap. The experimental observations are compared with the results of first-principles calculation in consideration of increasing bandwidth. We discuss the effect of the temperature change on the electronic structure of Sr2IrO4 in terms of local lattice distortion, excitonic effect, electron-phonon coupling, and magnetic ordering.

We employ molecular beam epitaxy to stabilize Ba2IrO4 thin films and utilize in situ angle-resolved photoemission spectroscopy to investigate the evolution of its electronic structure through the Neel temperature TN. Our measurements indicate that dispersions of the relativistic Jeff=1/2 and 3/2 bands exhibit an unusual dichotomy in their behavior through the Neel transition. Although the charge gap survives into the paramagnetic state, only the Jeff=1/2 state exhibits a strong temperature dependence and its gap softens with increasing temperature approaching TN, while the nearly fully occupied Jeff=3/2 state which remains nearby in energy exhibits negligible changes with temperature.

In 2006, Jeff Smith proposed a theory of ideals for rings in a triangulated symmetric monoidal category such as ring spectra or DGAs. We show that his definition is equivalent to a `central' $R$-$R$-bimodule map $ I \to R$.

Based on the density functional theory and our new model Hamiltonian, we have studied the basal-plane antiferromagnetism in the novel Jeff=1/2 Mott insulator Ba2IrO4. By comparing the magnetic properties of the bulk Ba2IrO4 with those of the single-layer Ba2IrO4, we demonstrate unambiguously that the basal-plane antiferromagnetism is caused by the intralyer magnetic interactions rather than by the previously proposed interlayer ones. In order to reveal the origin of the basal-plane antiferromagnetism, we propose a new model Hamiltonian by adding the single ion anisotropy and pseudo-quadrupole interactions into the general bilinear pseudo-spin Hamiltonian. The obtained magnetic interaction parameters indicate that the single ion anisotropy and pseudo-quadrupole interactions are unexpectedly strong. Systematical Monte Carlo simulations demonstrate that the basal-plane antiferromagnetism is caused by the isotropic Heisenberg, bond-dependent Kitaev and pseudo-quadrupole interactions. Our results show for the first time that the single ion anisotropy and pseudo-quadrupole interaction can play significant roles in establishing the exotic magnetism in the Jeff=1/2 Mott insulator.