  We consider the quantum correlations (entanglement and quantum discord)
dynamics of two coupled spin qubits with Dzyaloshinsky-Moriya interaction
influenced by a locally external magnetic field along $z$-direction and coupled
to bath spin-1/2 particles as independent non-Markovian environment. We find
that with increasing $D_{z}$ and decreasing $J_{z}$, the value of entanglement
and quantum discord increase for both antiferromagnetic and ferromagnetic
materials. Not that, this growth is more for the ferromagnetic materials. In
addition, we perceive that entanglement and quantum discord decrease with
increased temperature and increased coupling constants between reduced system
and bath. But, strong quantum correlations within the spins of bath reduce
decoherence effects. We discuss about type of the constituent material of the
central spins that it can speedup the quantum information processing and as a
result, we perceive that one can improve and control the quantum information
processing with correct selection of the properties of the reduced system ($J$,
$J_{z}$, $D_{z}$).
