We present a systematic study of quantum fluctuations in the C-type and A-type antiferromagnetic (AF) phases in cubic lattices and in bilayer systems. Using the linear spin-wave theory, we show that the spin stiffness and the quantum corrections to the order parameter and energy obtained for C-AF and A-AF phases decrease with the increasing number of ferromagnetic bonds. Therefore, the quantum spin effects in LaMnO3 and in LaVO3 are rather small, suggesting the magnetic moments of ∼ 3.91 and ∼ 1.89µB , respectively. They cannot explain the strong reduction of the magnetic order parameter observed in cubic vanadates. [Published in Phys. Rev. B 66, 094431 (2002)] 75.30. Ds, 75.30.Et, 75.50.Ee The undoped transition metal oxides are characterized by large local Coulomb interactions ∝ U , which lead to several fascinating phenomena such as high-temperature superconductivity and "colossal magnetoresistance".
1When the Coulomb interactions dominate over the kinetic energy, the charge fluctuations are quenched and the magnetic properties follow from the effective lowenergy superexchange interactions. In some of these systems the orbital degrees of freedom play a role due to the partial filling of (almost) degenerate d orbitals, the superexchange interactions are strongly frustrated, 2,3 and the quantum effects are enhanced.4 These interactions together with the Jahn-Teller effect may induce the orbital ordering below a structural transition and break the cubic symmetry of the perovskite lattice. In such systems, although the crystalographic directions in a three-dimensional (3D) cubic lattice are a priori equivalent, one finds magnetic interactions not only of different value, but even of different sign, stabilizing C-type or A-type antiferromagnetic (AF) phases.
3One of the best known examples of the non-cubic magnetic interactions in a perovskite system is the A-type AF order observed in LaMnO 3 , 5 with ferromagnetic (FM) superexchange within (a, b) planes (J ab ) and AF interactions along the c axis (J c ), or in KCuF 3 , an almost perfect one-dimensional (1D) Heisenberg antiferromagnet.6 In both above cases the magnetic ordering is supported by the orbital ordering which is induced either by the JahnTeller effect, 7,8 or by the superexchange interactions.
9,10Recently it was suggested that the latter contribution dominates, 10 but this issue is still controversial and has to be clarified by future studies. The spin waves in LaMnO 3 have been investigated in great detail and it was established that the AF interactions J c are weaker than the FM J ab ones, 9 in good agreement with the experimental data.
11An inverse situation with respect to manganites and cuprates, with AF interactions within (a, b) planes coexisting with FM superexchange along the c-axis, is encountered in the so-called C-AF phase, observed in cubic vanadates: in LaVO 3 below the Néel temperature T N ≃ 143 K, 12 and in YVO 3 at intermediate temperatures 77 < T < 116 K. 13 Finally, G-type AF order, with cubic symmetry and the magnetic order p...