Spin-orbit scattering and pair breaking in a structurally disordered copper oxide layer

To leading order in displacement size, the scattering of electrons in a Cu-O plane from O displacements perpendicular to that plane is due to spin-orbit coupling. This scattering is investigated with the following results: (1) As a consequence of time-reversal symmetry, spin fluctuations, which can strongly enhance scattering from a spin impurity, do not enhance spin-orbit scattering; and (2) for a superconductor with a ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ gap function, pair breaking from spin-orbit scattering can be strong, particularly in a structurally disordered phase where locally ${\mathrm{CuO}}_6$ octahedra tilt as in the orthorhombic phase of ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, but globally the average structure is tetragonal. These results are discussed in the context of the (La,Nd)-(Sr,Ba)-Cu-O system where certain structural transitions are observed to suppress superconductivity.