  A structural-magnetic models of the orthorhombic and triclinic modifications
of the arsenates Cu4O(AsO4)2 and isotypic phosphates Cu4O(PO4)2 has been built
and analyzed. Their base elements are the complicated ribbons composed of
antiferromagnetic Cu4 tetrahedra. Structurally, these tetrahedra have no shared
copper atoms; however, there are strong antiferromagnetic (AFM) and
ferromagnetic (FM) couplings between them, both within the complicated ribbons
and between them. It has been established that both modifications are strongly
frustrated 3-D antiferromagnetics due to competition between the nearest AFM
interactions along the edges of the Cu4 tetrahedra and competition between
interactions and a multiplicity of long-range secondary AFM and FM
interactions. Additionally, a large number of weaker long-range interactions
are competing among each other. However, there is a possibility of the ordering
Dzyaloshinskii-Moriya (DM) interaction in the centrosymmetric orthorhombic
modification (Pnma), because two of the three types of magnetic ions, Cu1 and
Cu3, are in the partial position 4c, where the ions are not related by the
inversion center. In the triclinic modification (P -1) of Cu4O(As(P)O4)2, all
four copper ions are in the centrosymmetric equivalent position 2i, which
prevents DM interactions. This centrosymmetry will allow magnetic interactions
in the triclinic modification of Cu4O(As(P)O4)2 to be still frustrated at lower
temperature. It is possible that the triclinic modification of these compounds
is a quantum spin liquid.
