  The low-dimensional ferroelectrics, ferrielectrics and antiferroelectrics are
of urgent scientific interest due to their unusual polar, piezoelectric,
electrocaloric and pyroelectric properties. The strain engineering and strain
control of the ferroelectric properties of layered 2D Van der Waals materials,
such as CuInP$_2$(S,Se)$_6$ monolayers, thin films and nanoflakes, are of
fundamental interest and especially promising for their advanced applications
in nanoscale nonvolatile memories, energy conversion and storage, nano-coolers
and sensors. Here, we study the polar, piezoelectric, electrocaloric and
pyroelectric properties of thin strained films of a ferrielectric
CuInP$_2$S$_6$ covered by semiconducting electrodes and reveal an unusually
strong effect of a mismatch strain on these properties. In particular, the sign
of the mismatch strain and its magnitude determine the complicated behavior of
piezoelectric, electrocaloric and pyroelectric responses. The strain effect on
these properties is opposite, i.e., "anomalous", in comparison with many other
ferroelectric films, for which the out-of-plane remanent polarization,
piezoelectric, electrocaloric and pyroelectric responses increase strongly for
tensile strains and decrease or vanish for compressive strains.
