Understanding various aspects of ferroelectricity in hafnia‐based nanomaterials is of vital importance for the development of future nonvolatile memory and logic devices. Here, the unconventional and weak electromechanical response of epitaxial La0.67Sr0.33MnO3/Hf0.5Zr0.5O2/La0.67Sr0.33MnO3 ferroelectric capacitors is investigated, via the sensitivity offered by nanobeam X‐ray diffraction experiments during application of electrical bias. It is shown that the pristine rhombohedral phase exhibits a linear piezoelectric effect with piezoelectric coefficient (|d33|) ≈ 0.5–0.8 pmV−1. It is found that the piezoelectric response is suppressed above the coercive voltage. For higher voltages, and with the onset of DC conductivity throughout the capacitor, a second‐order effect is observed. The work sheds light into the electromechanical response of rhombohedral Hf0.5Zr0.5O2 and suggests its (un)correlation with ferroelectric switching.