Thermal Phase Variations of WASP-12b: Defying Predictions

[Abridged] We report Warm Spitzer full-orbit phase observations of WASP-12b at 3.6 and 4.5 micron. We are able to measure the transit depths, eclipse depths, thermal and ellipsoidal phase variations at both wavelengths. The large amplitude phase variations, combined with the planet's previously-measured day-side spectral energy distribution, is indicative of non-zero Bond albedo and very poor day-night heat redistribution. The transit depths in the mid-infrared indicate that the atmospheric opacity is greater at 3.6 than at 4.5 micron, in disagreement with model predictions, irrespective of C/O ratio. The secondary eclipse depths are consistent with previous studies. We do not detect ellipsoidal variations at 3.6 micron, but our parameter uncertainties -estimated via prayer-bead Monte Carlo- keep this non-detection consistent with model predictions. At 4.5 micron, on the other hand, we detect ellipsoidal variations that are much stronger than predicted. If interpreted as a geometric effect due to the planet's elongated shape, these variations imply a 3:2 ratio for the planet's longest:shortest axes and a relatively bright day-night terminator. If we instead presume that the 4.5 micron ellipsoidal variations are due to uncorrected systematic noise and we fix the amplitude of the variations to zero, the best fit 4.5 micron transit depth becomes commensurate with the 3.6 micron depth, within the uncertainties. The relative transit depths are then consistent with a Solar composition and short scale height at the terminator. Assuming zero ellipsoidal variations also yields a much deeper 4.5 micron eclipse depth, consistent with a Solar composition and modest temperature inversion. We suggest future observations that could distinguish between these two scenarios.Comment: 19 pages, 10 figures, ApJ in press. Improved discussion of gravity brightenin

Two-stage spin-flop transitions in S = 1/2 antiferromagnetic spin chain BaCu_2Si_2O_7

Two-stage spin-flop transitions are observed the in quasi-one-dimensional antiferromagnet, BaCu${}_2$Si${}_2$O${}_7$. A magnetic field applied along the easy axis induces a spin-flop transition at 2.0 T followed by a second transition at 4.9 T. The magnetic susceptibility indicates the presence of Dzyaloshinskii-Moriya (DM) antisymmetric interactions between the intrachain neighboring spins. We discuss a possible mechanism whereby the geometrical competition between DM and interchain interactions, as discussed for the two-dimensional antiferromagnet La${}_2$CuO${}_4$, causes the two-stage spin-flop transitions.Comment: 5 pages, 3 figures (included), accepted for publication in Phys. Rev. Let

Spin chirality induced by the Dzyaloshinskii-Moriya interaction and the polarized neutron scattering

We discuss the influence of the Dzyaloshinskii-Moriya (DM) interaction in the Heizenberg spin chain model for the observables in the polarized neutron scattering experiments. We show that different choices of the parameters of DM interaction may leave the spectrum of the problem unchanged, while the observable spin-spin correlation functions may differ qualitatively. Particularly, for the uniform DM interaction one has the incommensurate fluctuations and polarization-dependent neutron scattering in the paramagnetic phase. We sketch the possible generalization of our treatment to higher dimensions.Comment: 4 pages, REVTEX, no figures, references added, to appear in PR

Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions

This paper contains the details of Phys. Rev. Lett. 73, 2919 (1994) and, to a lesser extent, Phys. Rev. Lett. 72, 3710 (1994). We treat a Hubbard model which includes all the 3d states of the Cu ions and the 2p states of the O ions. We also include spin-orbit interactions, hopping between ground and excited crystal field states of the Cu ions, and rather general Coulomb interactions. Our analytic results for the spin Hamiltonian, H, are corroborated by numerical evaluations of the energy splitting of the ground manifold for two holes on either a pair of Cu ions or a Cu-O-Cu complex. In the tetragonal symmetry case and for the model considered, we prove that H is rotationally invariant in the absence of Coulomb exchange. When Coulomb exchange is present, each bond Hamiltonian has full biaxial anisotropy, as expected for this symmetry. For lower symmetry situations, the single bond spin Hamiltonian is anisotropic at order t**6 for constant U and at order t**2 for nonconstant U. (Constant U means that the Coulomb interaction between orbitals does not depend on which orbitals are involved.)Comment: 50 pages, ILATEX Version 2.09 <13 Jun 1989

Weak ferromagnetism of quasi-one-dimensional S=1/2 antiferromagnet BaCu2_2Ge2_2O7_7

Weak ferromagnetism of quasi-one-dimensional S = 1/2 antiferromagnet BaCu$_2$Ge$_2$O$_7$ is studied by the magnetization measurement. The spontaneous magnetization appears along the b axis. The local symmetry between the in-chain nearest neighbor spins allows the presence of Dzyaloshinskii-Moriya interaction, and the only possible spatial configuration of the weak ferromagnetic moment per spin determines the sign of the inter-chain interaction. A weak $a$-axis magnetic field can change the direction of the magnetization to the $a$-axis direction, which shows that the spin chain forms a weakly coupled weak-ferromagnetic chain system.Comment: 10 pages, 4 figure

Magnetic anisotropies and general on--site Coulomb interactions in the cuprates

This paper derives the anisotropic superexchange interactions from a Hubbard model for excitations within the copper 3d band and the oxygen 2p band of the undoped insulating cuprates. We extend the recent calculation of Yildirim et al. [Phys. Rev. B {\bf VV}, pp, 1995] in order to include the most general on--site Coulomb interactions (including those which involve more than two orbitals) when two holes occupy the same site. Our general results apply when the oxygen ions surrounding the copper ions form an octahedron which has tetragonal symmetry (but may be rotated as in lanthanum cuprate). For the tetragonal cuprates we obtain an easy--plane anisotropy in good agreement with experimental values. We predict the magnitude of the small in--plane anisoComment: 25 pages, revte

On the Field-Induced Gap in Cu Benzoate and Other S=1/2 Antiferromagnets

Recent experiments on the S=1/2 antiferromagnetic chain compound, Cu benzoate, discovered an unexpected gap scaling as approximately the 2/3 power of an applied magnetic field. A theory of this gap, based on an effective staggered field, orthogonal to the applied uniform field, resulting from a staggered gyromagnetic tensor and a Dzyaloshinskii-Moriya interaction, leading to a sine-Gordon quantum field theory, has been developed. Here we discuss many aspects of this subject in considerable detail, including a review of the S=1/2 chain in a uniform field, a spin-wave theory analysis of the uniform plus staggered field problem, exact amplitudes for the scaling of gap, staggered susceptibility and staggered magnetization with field or temperature, intensities of soliton and breather peaks in the structure function and field and temperature dependence of the total susceptibility.Comment: 34 pages, 13 postscript figures, Rev Tex. Phys. Rev. B, to appea

d-Wave Superconductivity Induced by Chern-Simons Term in High-TcT_c Cuprates

We show that a Chern-Simons term for a gauge field describing a fluctuation of spins is induced by integrating out hole fields in the presence of spin-orbit coupling which originates from a buckling of the CuO$_2$ plane. Through the Chern-Simons term, holes behave like skyrmion excitations in a spin system and become a superconducting state with $d_{x^2-y^2}$ symmetry after the antiferromagnetic long-range order is destroyed.Comment: 4 pages, 1 figure, the condition of taking continuum limit included, references added, typos corrected, to be published in Journal of Physical Society of Japa