We study the performance of Kitaev-Heisenberg (KH) clusters as working media realizing a quantum Otto engine (QOE). An external Zeeman field with linear time dependency is used as the driving mechanism. The efficiency strongly depends on Kitaev $\left(\kappa \right)$ and Heisenberg $\left(J\right)$ exchange interaction. Interestingly, the efficiency is comparable when the relative magnitude of $\kappa$ and $J$ is the same but of opposite signs. The above results are explained due to a subtle interplay of frustration, quantum fluctuation, and duality of eigenspectra for the KH system when both the signs of $\kappa$ and $J$ are reversed. The maximum efficiency is shown to be dynamically related to eigenspectra forming discrete narrow bands, where total spin angular momentum becomes a good quantum number. We relate this optimum efficiency to the realization of weakly interacting magnons, where the system reduces to an approximate eigensystem of the external drive. Further, we show that consideration of negative bath temperature can increase the efficiency. Finally, we examine the generic spin-$S$ Kitaev model, which shows that efficiency decreases as $S$ is increased. We relate this dependency to a measure of quantum fluctuation which also decreases as $S$ is increased, establishing a possible advantage in efficiency for $S=1/2$ due to stronger quantum fluctuations. The results could be of practical interest for materials with KH interactions as a platform for QOE.

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• Frustrated magnetism
• Magnetism
• Quantum heat engines & refrigerators
• Exact diagonalization
• Kitaev-Heisenberg model