TY - JOUR

T1 - Spin stiffness of the anisotropic Heisenberg model on the square lattice and a possible mechanism for pinning of the electronic liquid crystal direction in underdoped YBa2 Cu3 O6.45

AU - Pardini, T.

AU - Singh, R. R.P.

AU - Katanin, A.

AU - Sushkov, O. P.

PY - 2008/7/29

Y1 - 2008/7/29

N2 - Using series expansions and spin-wave theory, we calculate the spin-stiffness anisotropy ρsx / ρsy in Heisenberg models on the square lattice with spatially anisotropic couplings Jx, Jy. We find that for the weakly anisotropic spin-half model (Jx ≈ Jy), ρsx / ρsy deviates substantially from the naive estimate ρsx / ρsy ≈ Jx / Jy. We argue that this deviation can be responsible for pinning the electronic liquid crystal direction, an effect recently discovered in YBCO. For completeness, we also study the spin stiffness for arbitrary anisotropy Jx / Jy for spin-half and spin-one models. In the limit of Jy / Jx →0, when the model reduces to weakly coupled chains, the two show dramatically different behavior. In the spin-one model, the stiffness along the chains goes to zero, implying the onset of Haldane-gap phase, whereas for the spin-half model, the stiffness along the chains increases monotonically from a value of 0.18 Jx for Jy / Jx =1 toward 0.25 Jx for Jy / Jx →0. In the latter case, spin-wave theory breaks down qualitatively, presumably due to the onset of topological terms with strong anisotropy.

AB - Using series expansions and spin-wave theory, we calculate the spin-stiffness anisotropy ρsx / ρsy in Heisenberg models on the square lattice with spatially anisotropic couplings Jx, Jy. We find that for the weakly anisotropic spin-half model (Jx ≈ Jy), ρsx / ρsy deviates substantially from the naive estimate ρsx / ρsy ≈ Jx / Jy. We argue that this deviation can be responsible for pinning the electronic liquid crystal direction, an effect recently discovered in YBCO. For completeness, we also study the spin stiffness for arbitrary anisotropy Jx / Jy for spin-half and spin-one models. In the limit of Jy / Jx →0, when the model reduces to weakly coupled chains, the two show dramatically different behavior. In the spin-one model, the stiffness along the chains goes to zero, implying the onset of Haldane-gap phase, whereas for the spin-half model, the stiffness along the chains increases monotonically from a value of 0.18 Jx for Jy / Jx =1 toward 0.25 Jx for Jy / Jx →0. In the latter case, spin-wave theory breaks down qualitatively, presumably due to the onset of topological terms with strong anisotropy.

UR - http://www.scopus.com/inward/record.url?scp=48749106940&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.78.024439

DO - 10.1103/PhysRevB.78.024439

M3 - Article

AN - SCOPUS:48749106940

VL - 78

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 1098-0121

IS - 2

M1 - 024439

ER -