Umklapp scattering from spin fluctuations in Copper-Oxides

The $\mathbf k$-dependent electronic momentum relaxation rate due to Umklapp scattering from antiferromagnetic spin fluctuations is studied within a renormalized mean-field approach to an extended $t-J$ model appropriate to YBa$_2$Cu$_3$O$_{7-x}$ and other cuprates. Transport coefficients are calculated in a relaxation time approximation. We compare these results with those obtained with the phenomenological assumption that all scattering processes dissipate momentum. We show that the latter, which violates momentum conservation, leads to quite different magnitudes and temperature dependences of resistivities and Hall coefficients.