Measurement of the quantum-mechanical phase in quantum matter provides the most direct manifestation of the underlying abstract physics. We used resonant x-ray scattering to probe the relative phases of constituent atomic orbitals in an electronic wave function, which uncovers the unconventional Mott insulating state induced by relativistic spin-orbit coupling in the layered 5d transition metal oxide Sr2IrO4. A selection rule based on intra-atomic interference effects establishes a complex spin-orbital state represented by an effective total angular momentum = 1/2 quantum number, the phase of which can lead to a quantum topological state of matter.

Ferroelectric materials are widely used in modern electric devices such as memory elements, filtering devices and high-performance insulators. Ferroelectric crystals have a spontaneous electric polarization arising from the coherent arrangement of electric dipoles (specifically, a polar displacement of anions and cations). First-principles calculations and electron density analysis of ferroelectric materials have revealed that the covalent bond between the anions and cations, or the orbital hybridization of electrons on both ions, plays a key role in establishing the dipolar arrangement. However, an alternative model-electronic ferroelectricity-has been proposed in which the electric dipole depends on electron correlations, rather than the covalency. This would offer the attractive possibility of ferroelectric materials that could be controlled by the charge, spin and orbital degrees of freedom of the electron. Here we report experimental evidence for ferroelectricity arising from electron correlations in the triangular mixed valence oxide, LuFe(2)O(4). Using resonant X-ray scattering measurements, we determine the ordering of the Fe(2+) and Fe(3+) ions. They form a superstructure that supports an electric polarization consisting of distributed electrons of polar symmetry. The polar ordering arises from the repulsive property of electrons-electron correlations-acting on a frustrated geometry.

Dynamical correlations of J eff = 1/2 isospins in the paramagnetic state of spin-orbital Mott insulator Sr2IrO4 was revealed by resonant magnetic x-ray diffuse scattering. We found two-dimensional antiferromagnetic fluctuation with a large in-plane correlation length exceeding 100 lattice spacings at even 20 K above the mangnetic ordering temperature. In marked contrast to the naive expectation of strong magnetic anisotropy associated with an enhanced spin-orbit coupling, we discovered isotropic isospin correlation that is well described by the two-dimensional S = 1/2 quantum Heisenberg model. The estimated antiferromagnetic coupling constant as large as J ∼ 0.1 eV that is comparable to the small Mott gap (< 0.5 eV) points the weak and marginal Mott character of this spin-orbital entangled system. PACS numbers:In magnetic oxides with 3d transition metal ions, the energy scale of spin-orbit coupling (SOC) is usually smaller than those of crystal field splitting and on-site Coulomb repulsion. SOC can be treated as a perturbation, of which a primal role is to give rise to a magnetic anisotropy. In 5d transition metal oxides, however, SOC is more than one order of magnitude larger than that of 3d due to the pronounced relativistic effect, as large as a half eV, and can modify the electronic structure drastically. A spin-orbital Mott insulator that was recently identified in a layered perovskite Sr 2 IrO 4 is a novel state of correlated electrons [1,2]. Here, a strong SOC, inherent to heavy 5d transition metal Ir 4+ , splits the Ir t 2g bands into a half-filled J eff = 1/2 bands and completely filled J eff = 3/2 bands, which gives rise to a J eff = 1/2 Mott state induced by a moderate Coulomb repulsion, U . The uniqueness of such a spin-orbital Mott insulator is that J eff = 1/2 isospins with the wave function(|xy, ± ± |yz, ∓ + i|zx, ± ) are accommodated in the outermost 5d orbitals and, therefore, exotic magnetic couplings representing the complex spin-orbital states are anticipated [3,4].Sr 2 IrO 4 is a canted antiferromagnet below 230 K [5][6][7]. The J eff = 1/2 moments order approximately antiferromagnetically but significantly canted to cause a ferromagnetic moment of ∼ 0.1µ B /Ir within each IrO 2 (ab) plane as shown in Fig. 1(a). With applying a small magnetic field of ∼ 0.2 T parallel to the layer, the system shows a metamagnetic transition and becomes a weak ferromagnet. Note that the canting moment is one to two orders of magnitude larger than that of an analogous canted antiferromagnet with 3d copper, La 2 CuO 4 . This large canting moment is produced apparently by the interplay between the large SOC and lattice distortion and, at a glance, would imply strongly anisotropy in the isospin coupling.Recently Jackeli and Khaliullin discussed theoretically the effective Hamiltonian for J eff = 1/2 isospins in Sr 2 IrO 4 [3]. They found that, in the absence of Hund's coupling, the isospin Hamiltonian, including antisymmetric (Dzyloshinskii-Moriya) and symmetric anisotropy terms produced by the interplay between ...

The possibility to probe new physics scenarios of light Majorana neutrino exchange and right-handed currents at the planned next generation neutrinoless double β decay experiment SuperNEMO is discussed. Its ability to study different isotopes and track the outgoing electrons provides the means to discriminate different underlying mechanisms for the neutrinoless double β decay by measuring the decay half-life and the electron angular and energy distributions.a

Cd 2 Os 2 O 7 shows a peculiar metal-insulator transition at 227 K with magnetic ordering in a frustrated pyrochlore lattice, but its magnetic structure in the ordered state and the transition origin are yet uncovered. We observed a commensurate magnetic peak by resonant x-ray scattering in a high-quality single crystal. X-ray diffraction and Raman scattering experiments confirmed that the transition is not accompanied with any spatial symmetry breaking. We propose a noncollinear all-in/all-out spin arrangement on the tetrahedral network made of Os atoms. Based on this we suggest that the transition is not caused by Slater mechanism as believed earlier but by an alternative mechanism related to the formation of the specific tetrahedral magnetic order on the pyrochlore lattice in the presence of strong spin-orbit interactions. The metal-insulator (MI) transition is one of the most dramatic phenomena observed for electrons in solids. Generally, a strong electron correlation or Fermi surface instability causes a solid to transition from showing conductive behavior at high temperature to showing localized insulator behavior at low temperature. The transition caused by the strong electron-electron interaction is known as the Mott transition, which is of the first order and in many cases is accompanied by a simple collinear-type antiferromagnetic ordered state [1]. A prime example of the MI transition caused by Fermi surface instability is the charge-or spin-density wave (CDW or SDW) transition; in this case, the magnetic structures exist in a nonmagnetic singlet state or an incommensurate state. In addition, in weak coupling systems, another type of MI transition-the Slater transition-is theoretically expected to occur via folding of the Brillouin zone owing to the antiferromagnetic order [2]. Given that frustration typically inhibits the antiferromagnetic order, previously documented MI transitions with magnetic ordering are expected to be less probable on frustrated lattices. Consequently, an MI transition due to new mechanism leading to a peculiar ground state that eliminates the frustration is expected.One of the most extensively researched materials is the pyrochlore oxide [3]. Two classes of pyrochlore oxides with MI transitions have been identified: one class exhibits transitions with a large structural distortion and the other class superficially shows no distortion.

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We performed resonant x-ray diffraction experiments at the L absorption edges for the post-perovskite-type compound CaIrO(3) with a (t(2g))^{5} electronic configuration. By observing the magnetic signals, we could clearly see that the magnetic structure was a striped ordering with an antiferromagnetic moment along the c axis and that the wave function of a t(2g) hole is strongly spin-orbit entangled, the J(eff)=1/2 state. The observed spin arrangement is consistent with theoretical work predicting a unique superexchange interaction in the J(eff)=1/2 state and points to the universal importance of the spin-orbit coupling in Ir oxides, independent of the octahedral connectivity and lattice topology. We also propose that nonmagnetic resonant scattering is a powerful tool for unraveling an orbital state even in a metallic iridate.

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