Local Antiferromagnetic Correlations and $d_{x^2-y^2}$ Pairing
  The high $T_c$ cuprate superconductors doped near half-filling have short range antiferromagnetic correlations. Here we describe an intuitive local picture of why, if pairing occurs in the presence of short-range antiferromagnetic correlations, the orbital state will have $d_{x^2-y^2}$ symmetry. 
D.J. Scalapino, S.A. Trugman