Spin dimer analysis of the anisotropic spin exchange interactions in the distorted wolframite-type oxides CuWO4, CuMoO4-III, and Cu(Mo(0.25)W0.75)O4.

The distorted wolframite-type oxides CuWO4 and CuMoO4-III have a structure in which CuO4 zigzag chains, made up of cis-edge-sharing CuO6 octahedra, run along the c-direction and hence exhibit low-dimensional magnetic properties. We examined the magnetic structures of these compounds and their isostructural analogue Cu(Mo(0.25)W0.75)O4 on the basis of the spin-orbital interaction energies calculated for their spin dimers. Our study shows that these compounds consist of two-dimensional (2D) magnetic sheets defined by one superexchange (intrachain Cu-O-Cu) and three super-superexchange (interchain Cu-O.O-Cu) paths, the strongly interacting spin units of these 2D magnetic sheets are the two-leg antiferromagnetic (AFM) ladder chains running along the (a + c)-direction, and the spin arrangement between adjacent AFM ladder chains leads to spin frustration. The similarities and differences in the magnetic structures of CuWO4, CuMoO4-III, and Cu(Mo(0.25)W0.75)O4 were discussed by examining how adjacent AFM ladder chains are coupled via the superexchange paths in the 2D magnetic sheets and how adjacent 2D magnetic sheets are coupled via another superexchange paths along the c-direction. Our study reproduces the experimental finding that the magnetic unit cell is doubled along the a-axis in CuWO(4) and along the c-axis in CuMoO4-III and predicts that the magnetic unit cell should be doubled along the a- and b-axes in Cu(Mo(0.25)W0.75)O4. In the understanding of the strength of a super-superexchange interaction, the importance of the geometrical factors controlling the overlap between the tails of magnetic orbitals was pointed out.