Orbital currents, anapoles, and magnetic quadrupoles in CuO

We show that orbital currents in a CuO2 plane, if present, should be described by two independent parity and time-reversal odd order parameters, a toroidal dipole (anapole) and a magnetic quadrupole. Based on this, we derive the resonant X-ray diffraction cross-section for monoclinic CuO at the antiferromagnetic wavevector and show that the two order parameters can be disentangled. From our analysis, we examine a recent claim of detecting anapoles in CuO.Comment: 7 pages, 5 figure

The magnetic ground state of Sr2IrO4 and implications for second-harmonic generation

The currently accepted magnetic ground state of Sr2IrO4 (the -++- state) preserves inversion symmetry. This is at odds, though, with recent experiments that indicate a magnetoelectric ground state, leading to the speculation that orbital currents or more exotic magnetic multipoles might exist in this material. Here, we analyze various magnetic configurations and demonstrate that two of them, the magnetoelectric -+-+ state and the non-magnetoelectric ++++ state, can explain these recent second-harmonic generation (SHG) experiments, obviating the need to invoke orbital currents. The SHG-probed magnetic order parameter has the symmetry of a parity-breaking multipole in the -+-+ state and of a parity-preserving multipole in the ++++ state. We speculate that either might have been created by the laser pump used in the experiments. An alternative is that the observed magnetic SHG signal is a surface effect. We suggest experiments that could be performed to test these various possibilities, and also address the important issue of the suppression of the RXS intensity at the L2 edge.Comment: 28 pages, 8 figures, v3 - an expanded discussion of the origin of the SHG signa

The nature of the tensor order in Cd2Re2O7

The pyrochlore metal Cd2Re2O7 has been recently investigated by second-harmonic generation (SHG) reflectivity. In this paper, we develop a general formalism that allows for the identification of the relevant tensor components of the SHG from azimuthal scans. We demonstrate that the secondary order parameter identified by SHG at the structural phase transition is the x2-y2 component of the axial toroidal quadrupole. This differs from the 3z2-r2 symmetry of the atomic displacements associated with the I-4m2 crystal structure that was previously thought to be its origin. Within the same formalism, we suggest that the primary order parameter detected in the SHG experiment is the 3z2-r2 component of the magnetic quadrupole. We discuss the general mechanism driving the phase transition in our proposed framework, and suggest experiments, particularly resonant X-ray scattering ones, that could clarify this issue.Comment: some additions and clarifications adde

X-ray Dichroism and the Pseudogap Phase of Cuprates

A recent polarized x-ray absorption experiment on the high temperature cuprate superconductor Bi2Sr2CaCu2O8 indicates the presence of broken parity symmetry below the temperature, T*, where a pseudogap appears in photoemission. We critically analyze the x-ray data, and conclude that a parity-breaking signal of the kind suggested is unlikely based on the crystal structures reported in the literature. Possible other origins of the observed dichroism signal are discussed. We propose x-ray scattering experiments that can be done in order to determine whether such alternative interpretations are valid or not.Comment: final version to be published in Phys Rev B: some calculational details added, clarification of XNLD contamination and biaxiality, more discussion on possible space groups and previous optics result

The implications of resonant x-ray scattering data on the physics of the insulating phase of V_2O_3

We have performed a quantitative analysis of recent resonant x-ray scattering experiments carried out in the antiferromagnetic phase of V_2O_3 by means of numerical ab-initio simulations. In order to treat magnetic effects, we have developed a method based on multiple scattering theory (MST) and a relativistic extension of the Schr\"{o}dinger Equation, thereby working with the usual non relativistic set of quantum numbers $l,m,\sigma$ for angular and spin momenta. Electric dipole-dipole (E1-E1), dipole-quadrupole (E1-E2) and quadrupole-quadrupole (E2-E2) transition were considered altogether. We obtain satisfactory agreement with experiments, both in energy and azimuthal scans. All the main features of the V K edge Bragg-forbidden reflections with $h+k+l=$odd can be interpreted in terms of the antiferromagnetic ordering only, {\it ie}, they are of magnetic origin. In particular the ab-initio simulation of the energy scan around the (1,1,1)-monoclinic reflection excludes the possibility of any symmetry reduction due to a time-reversal breaking induced by orbital ordering.Comment: 11 pages, 6 figure

Spin-1 effective Hamiltonian with three degenerate orbitals: An application to the case of V_2O_3

Motivated by recent neutron and x-ray observations in V_2O_3, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t_{2g} states containing two electrons coupled to spin S = 1, and use it to re-examine the low-temperature ground-state properties of this compound. An axial trigonal distortion of the cubic states is also taken into account. Since there are no assumptions about the symmetry properties of the hopping integrals involved, the resulting spin-orbital Hamiltonian can be generally applied to any crystallographic configuration of the transition metal ion giving rise to degenerate t_{2g} orbitals. Specializing to the case of V_2O_3 we consider the antiferromagnetic insulating phase. We find two variational regimes, depending on the relative size of the correlation energy of the vertical pairs and the in-plane interaction energy. The former favors the formation of stable molecules throughout the crystal, while the latter tends to break this correlated state. We determine in both cases the minimizing orbital solutions for various spin configurations, and draw the corresponding phase diagrams. We find that none of the symmetry-breaking stable phases with the real spin structure presents an orbital ordering compatible with the magnetic space group indicated by very recent observations of non-reciprocal x-ray gyrotropy in V_2O_3. We do however find a compatible solution with very small excitation energy in two distinct regions of the phase space, which might turn into the true ground state of V_2O_3 due to the favorable coupling with the lattice. We illustrate merits and drawbacks of the various solutions and discuss them in relation to the present experimental evidence.Comment: 36 pages, 19 figure

On the interplay between multiscaling and stocks dependence

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this result conditional on the stocks' capitalization and on the kurtosis of stocks' log-returns in order to search for possible confounding effects. We show that a linear dependence with the logarithm of the capitalization and the logarithm of kurtosis does not explain the observed stylized fact, which we interpret as being originated from a deeper relationship.Comment: 19 pages, 8 figures, 9 table

Correlation filtering in financial time series

We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum Spanning Tree but containing a larger amount of links resulting in a richer network topology allowing loops and cliques. In Tumminello et al. \cite{TumminielloPNAS05}, we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the clustering of the system and its hierarchical structure both on the whole system and within each cluster. In particular, we have found that triangular loops and 4 element cliques have important and significant relations with the market structure and properties. Here we apply this filtering procedure to the analysis of correlation in two different kind of interest rate time series (16 Eurodollars and 34 US interest rates).Comment: 10 pages 7 figure