  Quantum thermal machines make use of non-classical thermodynamic resources,
one of which is interactions between elements of the quantum working medium. In
this paper, we examine the performance of a quasi-static quantum Otto engine
based on two spins of arbitrary magnitudes subject to an external magnetic
field and coupled via an isotropic Heisenberg exchange interaction. It has been
earlier shown that the said interaction provides an enhancement of cycle
efficiency for two spin-1/2 particles, with an upper bound which is tighter
than the Carnot efficiency. However, the necessary conditions governing engine
performance and the relevant upper bound for efficiency are unknown for the
general case of arbitrary spin magnitudes. Analyzing extreme-case scenarios, we
formulate heuristics to infer the necessary conditions for an engine with
uncoupled as well as coupled spins model. These conditions lead us to a
connection between performance of quantum heat engines and the notion of
majorization. Further, the study of complete Otto cycles inherent in the
average cycle also yields interesting insights into the average performance.
