On the non-Heisenberg contribution to the spin–spin interaction of an antiferromagnet with S=3/2

It is shown that the spin Hamiltonian of the spin–spin interactions, written with the use of effective spinons defined on the two lowest doublets of magnetic ions with a partially frozen orbital moment, has a non-Heisenberg form. The Heisenberg contribution is represented by spin–spin terms containing three powers of ion spin projections and is anisotropic and comparable to the bilinear spin–spin interaction.