Calculated Magnetic Exchange Interactions in High-Temeprature Superconductors

Using a first principles linear response approach, we study the magnetic exchange interactions J for a series of superconducting cuprates. We reproduce the observed spin-wave dispersions together with other experimental trends, and show that different cuprates have similar J’s regardless their T${}_c$. The nearest neighbor J is not sensitive to the hole-doping, which agrees with recent experiments. For the undoped cuprates, the second nearest neighbor J is ferromagnetic, but changes its sign with hole-doping. We also find that, in contrast to the hopping integral, the exchange interaction is not sensitive to the position of apical oxygen. To see the effect of the long–range nature of the exchange on the superconducting T${}_c$, we study the dynamical spin susceptibility $\chi (q,\omega )$ within the t–J model using a dynamical cluster approximation.