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The magneto-electrocaloric effect which can be defined as the couplingbetween magnetocaloric and electrocaloric effects attracts currentlyconsiderable attention due to the advantages provided by the caloric effect indesigning solid-state refrigeration technologies. The magneto-electrocaloriceffect of a multiferroic antiferromagnetic spin system with the DzyaloshinskiiMoriya (DM) interaction is investigated in this paper. The DM interaction isassimilated to a coupling between an external site-dependent electric field anda local electric polarization. The external magnetic is also considered as asite-dependent magnetic field. The spin-wave theory is used as adiagonalization method and through the canonical partition function, somethermodynamic properties such as the Boltzmann entropy and the specific heatcapacity are obtained. Then, the adiabatic magnetic, electric, andmagnetoelectric cooling rates are also derived. The graphs obtained for theadiabatic magnetic, electric, and magnetoelectric cooling rate show acharacteristic behavior of the caloric or multi-caloric effect which is in goodagreement with some experimental and theoretical works. Besides, the entropyresponse due to the variation of the external site-dependent magnetic fieldexhibits two anomalous entropy peaks indicating the existence of anintermediate phase tuneable by the magnetic and electric site-dependentparameters. Overall, it is demonstrated that the cumulative influence of thesite-dependent magnetic and electric fields allows us not only to revealquantum critical points hidden in a multiferroic quantum spin system but alsoto control the caloric or multi-caloric effect essential in the construction ofsolid-state refrigeration devices.

Magneto-electric cooling rate of a multiferroic antiferromagnetic  quantum spin system: the cumulative influence of the site-dependent magnetic  and electric fields