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.