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

Hole-Pairs in a Spin Liquid: Influence of Electrostatic Hole-Hole Repulsion

The stability of hole bound states in the t-J model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to $2 \times 30$ sites. For a nearest-neighbors (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange $J$. At $\sim 10$ hole doping the pairs break only for a NN-repulsion as large as $V \sim 4J$. Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper-oxides is remarked.Comment: Revised version with new figures. 4 pages, 5 figure

Hidden Symmetries and their Consequences in t2gt_{2g} Cubic Perovskites

The five-band Hubbard model for a $d$ band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e. g. cubic) symmetry. In that case, if the crystal field splitting is large one may consider excitations confined to the lowest threefold degenerate $t_{2g}$ orbital states. When the electron hopping matrix element ($t$) is much smaller than the on-site Coulomb interaction energy ($U$), the Hubbard model can be mapped onto the well-known effective Hamiltonian (at order $t^{2}/U$) derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support long range spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying three-band Hubbard model. Using these symmetries we develop a rigorous Mermin-Wagner construction, which shows that the three-band Hubbard model does not support spontaneous long-range spin order at any nonzero temperature and at any order in $t/U$ -- despite the three-dimensional lattice structure. Introduction of spin-orbit coupling does allow spin ordering, but even then the excitation spectrum is gapless due to a subtle continuous symmetry. Finally we showed that these hidden symmetries dramatically simplify the numerical exact diagonalization studies of finite clusters.Comment: 26 pages, 3 figures, 520 KB, submitted Phys. Rev.

Charge degree of freedom and single-spin fluid model in YBa_2Cu_4O_8

We present a 17O nuclear magnetic resonance study in the stoichiometric superconductor YBa_2Cu_4O_8. A double irradiation method enables us to show that, below around 180 K, the spin-lattice relaxation rate of plane oxygen is not only driven by magnetic, but also significantly by quadrupolar fluctuations, i.e. low-frequency charge fluctuations. In the superconducting state, on lowering the temperature, the quadrupolar relaxation diminishes faster than the magnetic one. These findings show that, with the opening of the pseudo spin gap, a charge degree of freedom of mainly oxygen character is present in the electronic low-energy excitation spectrum.Comment: 4 pages, 3 figures, REVTE

Effects of intrabilayer coupling on the magnetic properties of YBa2_2Cu3_3O6_6

A two-layer Heisenberg antiferromagnet is studied as a model of the bilayer cuprate YBa$_2$Cu$_3$O$_6$. Quantum Monte Carlo results are presented for the temperature dependence of the spin correlation length, the static structure factor, the magnetic susceptibility, and the $^{63}$Cu NMR spin-echo decay rate $1/T_{2G}$. As expected, when the ratio $J_2/J_1$ of the intrabilayer and in-plane coupling strengths is small, increasing $J_2$ pushes the system deeper inside the renormalized classical regime. Even for $J_2/J_1$ as small as $0.1$ the correlations are considerably enhanced at temperatures as high as $T/J_1 \approx 0.4-0.5$. This has a significant effect on $1/T_{2G}$, and it is suggested that measurements of this quantity at high temperatures can reveal the strength of the intrabilayer coupling in YBa$_2$Cu$_3$O$_6$.Comment: 10 pages (Revtex) + 5 uuencoded ps figures. To appear in Phys. Rev. B, Rapid Com

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

Generalized calculation of magnetic coupling constants for Mott-Hubbard insulators: Application to ferromagnetic Cr compounds

Using a Rayleigh-Schr\"odinger perturbation expansion of multi-band Hubbard models, we present analytic expressions for the super-exchange coupling constants between magnetic transition metal ions of arbitrary separation in Mott-Hubbard insulators. The only restrictions are i) all ligand ions are closed shell anions and ii) all contributing interaction paths are of equal length. For short paths, our results essentially confirm the Goodenough-Kanamori-Anderson rules, yet in general there does not exist any simple rule to predict the sign of the magnetic coupling constants. The most favorable situation for ferromagnetic coupling is found for ions with less than half filled d shells, the (relative) tendency to ferromagnetic coupling increases with increasing path length. As an application, the magnetic interactions of the Cr compounds Rb$_2$CrCl$_4$, CrCl$_3$, CrBr$_3$ and CrI$_3$ are investigated, all of which except CrCl$_3$ are ferromagnets.Comment: 13 pages, 6 eps figures, submitted to Phys Rev

LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}

We describe the LDA bandstructure of YBa_2Cu_3O_7 in the 2 eV range from the Fermi energy using orbital projections and compare with YBa_2Cu_4O_8. Then, the high-energy and chain-related degrees of freedom are integrated out and we arrive at two, nearest-neighbor, orthogonal, two-center, 8-band Hamiltonians, the even and odd bands of the bi-layer. Of the 8 orbitals, Cu{x2-y2}, O2x, O3y, and Cus have \sigma character and Cu{xz}, Cu{yz} O2z, and O3z have \pi character. The roles of the Cu_s orbital, which has some Cu{3z2-1} character, and the four \pi orbitals are as follows: Cu_s provides 2nd- and 3rd-nearest-neighbor (t' and t') intra-plane hopping, as well as hopping between planes (t_{perp}). The \pi -orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4-\sigma-band Hamiltonian is generic for flat CuO_2 planes and we use it for analytical studies. The reduction of the \sigma-Hamiltonian to 3- and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hoppings commonly included in many-body calculations, the 3-band Hamiltonian should include hopping between all 2nd-nearest-neighbor oxygens and that the 1-band Hamiltonian should include 3rd-nearest-neighbor hoppings. We calculate the single-particle hopping between the planes of a bi-layer. We show that the inclusion of t' is crucial for understanding ARPES for the anti-ferromagnetic insulator Sr_2CuO_2Cl_2. Finally, we estimate the value of the inter-plane exchange constant for an un-doped bi-layer in mean-field theory using different single-particle Hamiltonians.Comment: Stanford Superconductor Conference - March 1995. 17 pages (Postscript), 5 Postscript figures (3 figures left) The whole file (5.3 Mb) one could get via anonymous ftp: ftp://radix1.mpi-stuttgart.mpg.de/pub/outgouing/lowham.u

Flux Phase as a Dynamic Jahn-Teller Phase: Berryonic Matter in the Cuprates?

There is considerable evidence for some form of charge ordering on the hole-doped stripes in the cuprates, mainly associated with the low-temperature tetragonal phase, but with some evidence for either charge density waves or a flux phase, which is a form of dynamic charge-density wave. These three states form a pseudospin triplet, demonstrating a close connection with the E X e dynamic Jahn-Teller effect, suggesting that the cuprates constitute a form of Berryonic matter. This in turn suggests a new model for the dynamic Jahn-Teller effect as a form of flux phase. A simple model of the Cu-O bond stretching phonons allows an estimate of electron-phonon coupling for these modes, explaining why the half breathing mode softens so much more than the full oxygen breathing mode. The anomalous properties of $O^{2-}$ provide a coupling (correlated hopping) which acts to stabilize density wave phases.Comment: Major Revisions: includes comparisons with specific cuprate phonon modes, 16 eps figures, revte