Evidence for Octupole Order in Ce0.7_{0.7}La0.3_{0.3}B6_6 from Resonant X-ray Scattering

The azimuthal angle dependence observed in the resonant X-ray scattering in phase IV of Ce$_{0.7}$La$_{0.3}$B$_6$ is analyzed theoretically. It is shown that the peculiar angle dependence observed in the E2 channel is consistent with the Gamma_{5u}-type octupole order with principal axis along (111) and equivalent directions. Under the assumption that the four equivalent octupole domains are nearly equally populated in the sample, the observed angle dependences are reproduced by calculation for both sigma-sigma' and sigma-pi' polarizations. The calculation for various symmetries of order parameters excludes unambiguously other order parameters than the Gamma_{5u}-type octupole.Comment: 4 pages, 2 figures, 3 tables, in JPSJ forma

Multipole tensor analysis of the resonant x-ray scattering by quadrupolar and magnetic order in DyB2C2

Resonant x-ray scattering (RXS) experiment has been performed for the (3 0 1.5) superlattice reflection in the antiferroquadrupolar and antiferromagnetic phase of DyB2C2. Azimuthal-angle dependence of the resonance enhanced intensities for both dipolar (E1) and quadrupolar (E2) resonant processes has been measured precisely with polarization analysis. Every scattering channel exhibits distinctive azimuthal dependence, differently from the symmetric reflection at (0 0 0.5) which was studied previously. We have analyzed the results using a theory developed by Lovesey et al., which directly connects atomic tensors with the cross-section of RXS. The fitting results indicate that the azimuthal dependences can be explained well by the atomic tensors up to rank 2. Rank 3 and rank 4 tensors are reflected in the data very little. In addition, The coupling scheme among the 4f quadrupolar moment, 5d ortitals, and the lattice has been determined from the interference among the Thomson scattering from the lattice distortion and the resonant scatterings of E1 and E2 processes. It has also been established from the RXS of the (3 0 1.5) reflection that the canting of the 4f quadrupolar moments exists up to T_Q. We also discuss a possible wavefunction of the ground state from the point-charge model calculation.Comment: 9 pages, 10 figure

Symmetry of re-entrant tetragonal phase in Ba1-xNaxFe2As2: Magnetic versus orbital ordering mechanism

Magneto-structural phase transitions in Ba1-xAxFe2As2 (A = K, Na) materials are discussed for both magnetically and orbitally driven mechanisms, using a symmetry analysis formulated within the Landau theory of phase transitions. Both mechanisms predict identical orthorhombic space-group symmetries for the nematic and magnetic phases observed over much of the phase diagram, but they predict different tetragonal space-group symmetries for the newly discovered re-entrant tetragonal phase in Ba1-xNaxFe2As2 (x ~ 0.24-0.28). In a magnetic scenario, magnetic order with moments along the c-axis, as found experimentally, does not allow any type of orbital order, but in an orbital scenario, we have determined two possible orbital patterns, specified by P4/mnc1' and I4221' space groups, which do not require atomic displacements relative to the parent I4/mmm1' symmetry and, in consequence, are indistinguishable in conventional diffraction experiments. We demonstrate that the three possible space groups are however, distinct in resonant X-ray Bragg diffraction patterns created by Templeton & Templeton scattering. This provides an experimental method of distinguishing between magnetic and orbital models

Excitation spectra and ground state properties of the layered spin-1/2 frustrated antiferromagnets Cs_2CuCl_4 and Cs_2CuBr_4

We use series expansion methods to study ground- and excited-state properties in the helically ordered phase of spin-1/2 frustrated antiferromagnets on an anisotropic triangular lattice. We calculate the ground state energy, ordering wavevector, sublattice magnetization and one-magnon excitation spectrum for parameters relevant to Cs_2CuCl_4 and Cs_2CuBr_4. Both materials are modeled in terms of a Heisenberg model with spatially anisotropic exchange constants; for Cs_2CuCl_4 we also take into account the additional Dzyaloshinskii-Moriya (DM) interaction. We compare our results for Cs_2CuCl_4 with unpolarized neutron scattering experiments and find good agreement. In particular, the large quantum renormalizations of the one-magnon dispersion are well accounted for in our analysis, and inclusion of the DM interaction brings the theoretical predictions for the ordering wavevector and the magnon dispersion closer to the experimental results.Comment: 10 pages, 8 figure

Spin Structure Factor of the Frustrated Quantum Magnet Cs_2CuCl_4

The ground state properties and neutron structure factor for the two-dimensional antiferromagnet on the triangular lattice, with uni-directional anisotropy in the nearest-neighbor exchange couplings and a weak Dzyaloshinskii-Moriya (DM) interaction, are studied. This Hamiltonian has been used to interpret neutron scattering measurements on the spin 1/2 spiral spin-density-wave system, Cs_2CuCl_4, [R. Coldea, et al., Phys. Rev. B 68, 134424 (2003)]. Calculations are performed using a 1/S expansion, taking into account interactions between spin-waves. The ground state energy, the shift of the ordering wave-vector, Q, and the local magnetization are all calculated to order 1/S^2. The neutron structure factor, obtained using anharmonic spin-wave Green's functions to order 1/S, is shown to be in reasonable agreement with published neutron data, provided that slightly different parameters are used for the exchange and DM interactions than those inferred from measurements in high magnetic field.Comment: 14 pages, 6 eps figures, submitted to Phys. Rev.

Neel to Spin-Glass-like Phase Transition versus Dilution in Geometrically Frustrated ZnCr_{2-2x}Ga_{2x}O_4

ZnCr2O4 undergoes a first order spin-Peierls-like phase transition at 12.5 K from a cubic spin liquid phase to a tetragonal Neel state. Using powder diffraction and single crystal polarized neutron scattering, we determined the complex spin structure of the Neel phase. This phase consisted of several magnetic domains with different characteristic wave vectors. This indicates that the tetragonal phase of ZnCr2O4 is very close to a critical point surrounded by many different Neel states. We have also studied, using elastic and inelastic neutron scattering techniques, the effect of nonmagnetic dilution on magnetic correlations in ZnCr_{2-2x}Ga_{2x}O_4 (x=0.05 and 0.3). For x=0.05, the magnetic correlations do not change qualitatively from those in the pure material, except that the phase transition becomes second order. For x= 0.3, the spin-spin correlations become short range. Interestingly, the spatial correlations of the frozen spins in the x=0.3 material are the same as those of the fluctuating moments in the pure and the weakly diluted materials

Theory of Coupled Multipole Moments Probed by X-ray Scattering in CeB6_6

A minimal model for multipole orders in CeB$_6$ shows that degeneracy of the quadrupole order parameters and strong spin-orbit coupling lead to peculiar temperature and magnetic-field dependences of the X-ray reflection intensity at superlattice Bragg points. Furthermore, the intensity depends sensitively on the surface direction. These theoretical results explain naturally recent X-ray experiments in phases II and III of CeB$_6$. It is predicted that under weak magnetic field perpendicular to the (111) surface, the reflection intensity should change non-monotonically as a function of temperature.Comment: 4 pages, 5 figure

Magnetic Susceptibility of Multiorbital Systems

Effects of orbital degeneracy on magnetic susceptibility in paramagnetic phases are investigated within a mean-field theory. Under certain crystalline electric fields, the magnetic moment consists of two independent moments, e.g., spin and orbital moments. In such a case, the magnetic susceptibility is given by the sum of two different Curie-Weiss relations, leading to deviation from the Curie-Weiss law. Such behavior may be observed in d- and f-electron systems with t_{2g} and Gamma_8 ground states, respectively. As a potential application of our theory, we attempt to explain the difference in the temperature dependence of magnetic susceptibilities of UO_2 and NpO_2.Comment: 4 pages, 3 figure

Detection of Neutron Scattering from Phase IV of Ce0.7La0.3B6: A Confirmation of the Octupole Order

We have performed a single crystal neutron scattering experiment on Ce0.7La0.3B6 to investigate the order parameter of phase IV microscopically. Below the phase transition temperature 1.5 K of phase IV, weak but distinct superlattice reflections at the scattering vector (h/2,h/2,l/2) (h, l = odd number) have been observed by neutron scattering for the first time. The intensity of the superlattice reflections is stronger for high scattering vectors, which is quite different from the usual magnetic form factor of magnetic dipoles. This result directly evidences that the order parameter of phase IV has a complex magnetization density, consistent with the recent experimental and theoretical prediction in which the order parameter is the magnetic octupoles Tbeta with Gamma5 symmetry of point group Oh. Neutron scattering experiments using short wavelength neutrons, as done in this study, could become a general method to study the high-rank multipoles in f electron systems.Comment: 4 pages, 4 figure

Invariant Form of Hyperfine Interaction with Multipolar Moments - Observation of Octupolar Moments in NpO2_{2} and CeB6_{6} by NMR -

The invariant form of the hyperfine interaction between multipolar moments and the nuclear spin is derived, and applied to discuss possibilities to identify the antiferro-octupolar (AFO) moments by NMR experiments. The ordered phase of NpO$_{2}$ and the phase IV of Ce$_{1-x}$La$_{x}$B$_{6}$ are studied in detail. Recent $^{17}$O NMR for polycrystalline samples of NpO$_{2}$ are discussed theoretically from our formulation. The observed feature of the splitting of $^{17}$O NMR spectrum into a sharp line and a broad line, their intensity ratio, and the magnetic field dependence of the shift and of the width can be consistently explained on the basis of the triple \bq AFO ordering model proposed by Paix\~{a}o {\it et. al.} Thus, the present theory shows that the $^{17}$O NMR spectrum gives a strong support to the model. The 4 O sites in the fcc NpO$_2$ become inequivalent due to the secondary triple \bq ordering of AF-quadrupoles: one cubic and three non-cubic sites. It turns out that the hyperfine field due to the antiferro-dipole and AFO moments induced by the magnetic field, and the quadrupolar field at non-cubic sites are key ingredients to understand the observed spectrum. The controversial problem of the nature of phase IV in Ce$_{1-x}$La$_{x}$B$_{6}$ is also studied. It is pointed out that there is a unique feature in the NMR spectra, if the $\Gamma_{5}$($T^{\beta}_{x}=T^{\beta}_{y}=T^{\beta}_{z}$) AFO ordering is realized in Ce$_{1-x}$La$_{x}$B$_{6}$. Namely, the hyperfine splitting of a B atom pair on the $({1/2},{1/2},\pm u)$ sites crosses zero on the $(1\bar{1}0)$ plane when the magnetic field is rotated around the $[001]$ axis.Comment: 22 pages, 2 figure