  We investigate the quench dynamics of a quantum dot strongly coupled to
spin-polarized ferromagnetic leads. The real-time evolution is calculated by
means of the time-dependent density-matrix numerical renormalization group
method implemented within the matrix product states framework. We examine the
system's response to a quench in the spin-dependent coupling strength to
ferromagnetic leads as well as in the position of the dot's orbital level. The
spin dynamics is analyzed by calculating the time-dependent expectation values
of the quantum dot's magnetization and occupation. Based on these, we determine
the time-dependence of a ferromagnetic-contact-induced exchange field and
predict its nonmonotonic build-up. In particular, two time scales are
identified, describing the development of the exchange field and the dot's
magnetization sign change. Finally, we study the effects of finite temperature
on the dynamical behavior of the system.
