We describe the dynamics of quantum discord of two interacting spin-1/2 subjected to controllable time-dependent magnetic fields. The exact time evolution of discord is given for various input mixed states consisting of classical mixtures of two Bell states. The quantum discord manifests a complex oscillatory behaviour in time and is compared with that of quantum entanglement, measured by concurrence. The interplay of the action of the time-dependent magnetic fields and the spin-coupling mechanism in the occurrence and evolution of quantum correlations is examined in detail.
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