The discovery of superconductivity in the doped copper oxides  has stimulated the study of the magnetism in these materials, both because of its intrinsic interest and its connection to high temperature superconductivity. The undoped parent compounds are antiferromagnetic (AF) insulators. The long-range AF order is rapidly destroyed with doping, and upon further doping the system becomes superconducting, while short-range AF correlations still persist.
The copper oxide materials are strongly anisotropic, both with respect to their transport and magnetic properties. It is widely believed that the CuO  planes are responsible for the properties of those materials. Doping introduces holes which are the charge carriers in the AF square lattice of the CuO  planes. The simplest model that seems to contain the physics of the CuO  planes is the t-J model, which describes holes moving in a Heisenberg spin system. In this system the holes are strongly coupled to the spin array, the motion of holes generating spin fluctuations.
A striking feature of the copper oxides is the strong sensitivity of their magnetic properties to hole concentration. Our work has been concerned with the understanding of this aspect. We have studied the effects of doping on a set of magnetic properties, namely, spin excitations, susceptibility, and staggered magnetization, within the t-J model. Quantum many-particle techniques were used to calculate the renormalization of the magnetic properties induced by the hole-magnon interaction. We found that those properties strongly depend on doping due to the hole-magnon interaction generated by hole motion, our results showing good agreement with experimental data on the copper oxide high temperature superconductors. [2, 3] We are now studying the effects of doping on other magnetic properties, and also on transport properties, seeking to understand the interplay between spin and charge in those materials.
This work has been carried out in collaboration with R. Orbach ( University of California, Riveside, U.S.A. ).