Anisotropic superexchange for nearest and next-nearest coppers in chain, ladder, and lamellar cuprates

Abstract

We present a detailed calculation of the magnetic couplings between nearest-neighbor and nextnearest-neighbor coppers in the edge-sharing geometry, ubiquitous in many cuprates. In this geometry, the interaction between nearest neighbor coppers is mediated via two oxygens, and the Cu-O-Cu angle is close to 90 • . The derivation is based on a perturbation expansion of a general Hubbard Hamiltonian, and produces numerical estimates for the various magnetic energies. In particular we find the dependence of the anisotropy energies on the angular deviation away from the 90 • geometry of the Cu-O-Cu bonds. Our results are required for the correct analysis of the magnetic structure of various chain, ladder and lamellar cuprates.

Up-up-down-down magnetic chain structure of the spin- 12 tetragonally distorted spinel GeCu2O4Zou1, Cai2, Garlea3 et al. 2016Phys. Rev. B234232View full textAdd to dashboardCite

“…Recently, there has been a growing interest in investigating the effect of SOC in Cu 2+ systems using DFT calculations. SOC gives rise to either the anisotropic superexchange interaction of the nearly rectangular Cu-O-Cu bond [28,29] or single-ion anisotropy [30,31]. Due to the Jahn-Teller distortion in GeCu 2 O 4 , there is a singly occupied nondegenerate orbital, which entangles with a doubly occupied orbital via SOC.…”

Anisotropic exchange inLiCuVO4probed by ESR

“…In the context of spin chains in copper oxides, such an effect was discussed in Ref. [28,29] as ring exchange.…”

Dzyaloshinsky-Moriya antisymmetric exchange coupling in cuprates: Oxygen effects

“…Usually one considers the spin-orbital coupling on the oxygen to be much smaller than that on the copper, and therefore may be neglected. 19,20 However, even for a free oxygen atom the electron spin orbital coupling turns out to reach of appreciable magnitude: ξ 2p ∼ = 0.02 eV, 21 while for the oxygen O 2− ion in oxides one expects the visible enhancement of spin-orbital coupling due to a larger compactness of 2p wave function. 22 If to account for ξ nl ∝ r −3 nl and compare these quantities for the copper ( r −3 3d ≈ 6 − 8 a.u.…”

“…The energies E s,t (dp x,y ) are those for singlet and triplet states of dp x,y configurations, respectively: E s,t (dp x,y ) = ǫ x,y + K dpx,y ± I dpx,y , where K dpx,y and I dpx,y are Coulomb and exchange dp-integrals, respectively. It is easy to see that the nonzero contribution to Dzyaloshinsky vector is determined by a direct dp-exchange and may be written similarly to (20) with…”