  We propose a novel type of quantum heat engine based on the ultrafast
dynamical control of the magnetic properties of a nano-scale working body. The
working principle relies on nonlinear phononics, an example for dynamical
materials design. We describe the general recipe for identifying candidate
materials, and also propose Cr$_{2}$O$_{3}$ as a promising working body for a
quantum Otto cycle. Using a spin Hamiltonian as a model for Cr$_{2}$O$_{3}$, we
investigate the performance in terms of efficiency, output power, and quantum
friction. To assess the assumptions underlying our effective spin Hamiltonian
we also consider a working substance composed of several unit cells. We show
that even without an implementation of transitionless driving, the quantum
friction is very low compared to the total produced work and the energy cost of
counterdiabatic driving is negligible. This is an advantage of the working
substance, as experimentally hard-to-implement shortcuts to adiabaticity are
not needed. Moreover, we discuss some remarkable thermodynamic features due to
the quantumness of the proposed system such as a non-monotonic dependence of
the efficiency on the temperature of the hot-bath. Finally, we explore the
dependence of the performance on the system parameters for a generic model of
this type of quantum heat engine and identify properties of the energy spectrum
required for a well-performing quantum heat engine.
