Europhys. Lett.
Volume 47, Number 1, July 1999
Page(s) 116 - 121
Section Condensed matter: electronic structure, electrical, magnetic and optical properties
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00360-9

Europhys. Lett, 47 (1), pp. 116-121 (1999)

Anisotropic superexchange of a $\rm 90^{\circ}$ Cu-O-Cu bond

V. Yu. Yushankhai 1 and R. Hayn 2

1 Joint Institute for Nuclear Research - 141980 Dubna, Moscow Region, Russia
2 Institute for Theoretical Physics, TU Dresden - D-01062 Dresden, Germany

(received 2 February 1999; accepted 29 April 1999)

PACS. 75.30Gw - Magnetic anisotropy.
PACS. 74.72Jt - Other cuprates.
PACS. 71.70Ej - Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect.


The magnetic anisotropy of a rectangular Cu-O-Cu bond is investigated in second order of the spin-orbit interaction. Such a bond is characteristic for cuprates having edge sharing $\rm CuO_2$ chains, and exists also in the $\rm Cu_3O_4$ plane or in ladder compounds. For a ferromagnetic coupling between the copper spins an easy axis is found perpendicular to the copper oxygen plaquettes in agreement with the experimental spin structure of $\rm Li_2CuO_2$. In addition, a pseudodipolar interaction is derived. Its estimation in the case of the $\rm Cu_3O_4$ plane (which is present for instance in $\rm Ba_2Cu_3O_4Cl_2$ or $\rm Sr_2Cu_3O_4Cl_2$) gives a value which is, however, two orders of magnitude smaller than the usual dipole-dipole interaction.


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