  We present a generalization of Extended Lagrangian Born-Oppenheimer molecular
dynamics [Phys. Rev. Lett. vol. 100, 123004 (2008); Eur. Phys. J. B vol. 94,
164 (2021)] that also includes the electronic spin-degrees of freedom as
extended dynamical variables. To integrate the combined spin and charge degrees
of freedom, we use a preconditioned low-rank Krylov subspace approximation. Our
approach is demonstrated for quantum-mechanical molecular dynamics simulations
of iron, using spin-polarized self-consistent charge density functional
tight-binding theory. We also show how the low-rank Krylov subspace
approximation can be used to accelerate the self-consistent field convergence.
