We study the effect of the oxide layer on the current-induced spin-orbit torques (SOTs) in perpendicularly magnetized Hf|CoFeB|MgO (MgO-capped) or Hf|CoFeB|TaOx (TaOx-capped) structures. The effective fields corresponding to both the field-like and damping-like current-induced SOTs are characterized using electric transport measurements. Both torques are found to be significantly stronger in MgO-capped structures than those in TaOx-capped structures. The difference in field-like and damping-like SOTs in the different structures may be attributed to the different Rashba-like Hamiltonian, arising from the difference in the electric potential profiles across the oxide|ferromagnet interfaces in the two cases, as well as possible structural and oxidation differences in the underlying CoFeB and Hf layers. Our results show that the oxide layer in heavy-metal|ferromagnet|oxide trilayer structures has a very significant effect on the generated SOTs for manipulation of ferromagnetic layers. These findings could potentially be used to engineer SOT devices with enhanced current-induced switching efficiency. (C) 2015 AIP Publishing LLC.