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In this work, we propose a class of ferroelectrics (which we denote"double-path" ferroelectrics), characterized by two competing polarizationswitching paths for which the change in polarization is different and in factof opposite sign. Depending on which path is favorable under given conditions,this leads to different identification of up- and down-polarized states. Sincethe sign of piezoelectric response depends on the assignment of up- ordown-polarized state for a specific structure, this means that the material canexhibit different signs of the piezoelectric response under differentconditions. We focus on HfO$_2$ as a key example. Our first-principlescalculations show that there are two competing paths in HfO$_2$, resulting fromdifferent displacements of the atoms from the initial to the final structures,and the change in polarization along these two paths is of opposite sign. Theseresults provide a natural explanation for the recently observed discrepancy inthe signs of piezoelectric responses in HfO$_2$ between theoreticalfirst-principles calculations and experimental observation. Further, thisallows predictions of how to favor one path over another by changes inconditions and compositional tuning. This family of materials also includesother candidates, such as CuInP$_2$S$_6$ and theoretically proposedLaVO$_3$-SrVO$_3$ superlattice. We finally note that double-path ferroelectricspossess novel electromechanical properties since the signs of theirpiezoelectric responses can be switched.

"Double-path" ferroelectrics and the sign of the piezoelectric response