Effects of spin-orbit coupling and s-d exchange interaction are probed by magnetoresistance measurements carried out down to 50 mK on ZnO and Zn_{1-x}Mn_{x}O with x = 3 and 7%. The films were obtained by laser ablation and doped with Al to electron concentration ~10^{20} cm^{-3}. A quantitative description of the data for ZnO:Al in terms of weak-localization theory makes it possible to determine the coupling constant lambda_{so} = (4.4 +- 0.4)*10^{-11} eVcm of the kp hamiltonian for the wurzite structure, H_{so} = lambda_{so}*c(s x k). A complex and large magnetoresistance of Zn_{1-x}Mn_{x}O:Al is interpreted in terms of the influence of the s-d spin-splitting and magnetic polaron formation on the disorder-modified electron-electron interactions. It is suggested that the proposed model explains the origin of magnetoresistance observed recently in many magnetic oxide systems.
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