Measurement of ferroaxial moments via piezoresistivity

There has been recent interest in electronic states with unusual combinations of spatial and time-reversal symmetry breakings. One such example are ferroaxial phases, which are described by dipolar electric toroidal moments whose condensation preserves inversion and time-reversal, breaking only mirror symmetries. Detection of ferroaxial order, however, has been difficult as the order parameter does not couple directly to electric or magnetic fields. Using representation theory, we determine all tensors that share an irreducible representation with the ferroaxial moment and hence can be used to directly detect it. Searching through materials databases, we identify a list of existing candidate materials that exhibit ferroaxial order as their primary order parameter across a phase transition. Focusing on the piezoresistivity, we use first-principles density functional theory to demonstrate that certain off-diagonal elements of the response tensor become non-zero only in the ferroaxial phase of the double perovskite fluorite CaSnF6.