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We study the magnetoelectric and electrocaloric response ofstrain-engineered, multiferroic SrMnO$_3$, using a phenomenological Landautheory with all parameters obtained from \emph{first-principles}-basedcalculations. This allows to make realistic and materials-specific predictionsabout the magnitude of the corresponding effects. We find that in the vicinityof a tetracritical point, where magnetic and ferroelectric phase boundariesintersect, an electric field has a huge effect on the antiferromagnetic order,corresponding to a magnetoelectric response several orders of magnitude largerthan in conventional linear magnetoelectrics. Furthermore, the strongmagnetoelectric coupling leads to a magnetic, cross-caloric contribution to theelectrocaloric effect, which increases the overall caloric response by about60\%. This opens up new potential applications of antiferromagneticmultiferroics in the context of environmentally friendly solid state coolingtechnologies.

Prediction of a Giant Magnetoelectric Cross-Caloric Effect Around a Tetracritical Point in Multiferroic SrMnO$_3$