Quantum Magnetism

• A longstanding problem which has attracted much interest recently concerns the mechanism whereby spin-orbit interactions give rise to magnetic anisotropy in magnetic insulators. Until recently the discussions of the origins of anisotropy found in cuprates were confined to the orthorhombic structure (i.e. La₂CuO₄). However, more recently a family of copper oxide materials of similar structure, but which are actually tetragonal, have been studied and found to have roughly the same out-of-plane anisotropy as La₂CuO₄. The earlier studied did not predict any anisotropy in the tetragonal limit. Explaining this discrepancy was the main purpose of our work. We developed a theory which for the first time corrects, extends, and clarifies results concerning the spin Hamiltonian used to describe the ground manifold of Hubbard models for magnetic insulators in the presence of spin-orbit interactions. (See T. Yildirim et al, Phys. Rev. Lett. 73, 2919 (1994)). The biggest impact of this work is the demonstration that almost all previous work which invoked the orthorhombic distortion to explain the observed anisotropy in cuprates (causing the spins to lie in the Cu-O plane) are wrong. Our theory clearly shows that this anisotropy is due to spin-orbit and Coulomb exchange interactions and independent of distortion. I have been invited to many labs, including NEC and IBM, to give seminars on this work.

• Magnetic interactions in the tetragonal copper oxide systems (which exhibit high temperature superconductivity after doping) have been extensively studied with the hope that a step towards the understanding of the high-temperature superconductivity would be to understand the simpler undoped systems such as Sr₂CuO₂Cl₂ and R₂CuO₄ (R=Pr, Nd, etc). Despite the fact that all cuprates have a very similar structures, they exhibit very different three dimensional (3D) spin ordering. Hence the nature of magnetic interactions which determine the 3D magnetic spin structure was not known. We show that the spin Hamiltonian of the tetragonal lamellar antiferromagnets contains several novel anisotropies (See T. Yildirim et al, Phys. Rev. Lett. 72, 3710 (1994)). Using these anisotropic interactions, we developed a theory that successfully explains for the first time the spin structures of many cuprates. This work has been presented at many labs including NEC and IBM.