Investigation of the Incommensurate and Commensurate Magnetic Superstructures of LiCuVO4 and CuO on the Basis of the Isotropic Spin Exchange and Classical Spin Approximations

The spin lattices of magnetic oxides LiCuVO4 and CuO are made up of CuO2 ribbon chains. The incommensurate and commensurate magnetic superstructures of these oxides were examined by calculating the total spin exchange interaction energies of their long-range order spin arrangements on the basis of the isotropic spin exchange and classical spin approximations. The incommensurate superstructure (0, 0.532, 0) of LiCuVO4 was analyzed to find that the next-nearest-neighbor spin exchange interaction Jnnn is more strongly antiferromagnetic than the nearest-neighbor spin exchange interaction Jnn in the CuO2 chains. With this finding, we reassessed the relative strengths of the spin exchange interactions of LiCuVO4 and CuO and then analyzed the relative energies of their long-range order spin arrangements. The incommensurate superstructure (0, 0.532, 0) of LiCuVO4 is explained when the Jnn/Jnnn ratio is −0.40. Both the incommensurate superstructure (0.506, 0, −0.483) and the commensurate superstructure (0.5, 0, −0.5) of CuO, which occur at 231 and 212.5 K, respectively, are well explained in terms of the calculated total spin exchange interaction energies. The incommensurate superstructure of CuO becomes commensurate by a slight change in one interchain spin exchange interaction, which is due probably to a slight structure change brought about by the temperature lowering.