Piezoaxial coupling for strain-selected ferroaxial domain control

We formulate a symmetry-based hierarchy of strain-derived conjugate fields for ferroaxial order, and demonstrate strain-selected ferroaxial domain control using first-principles calculations. Since ferroaxial order is even under both spatial inversion and time reversal, ordinary electric and magnetic fields cannot serve as universal linear conjugate fields. Homogeneous strain, however, can generate symmetry-allowed piezoaxial fields whose leading order is determined by the parent point group and by the chosen ferroaxial-axis component. For basal-plane strain, the leading field is linear in orthorhombic systems, quadratic in tetragonal systems, and cubic in trigonal and hexagonal systems. Cubic parent groups further split into two classes: cubic-I groups, $23$ and $m\bar{3}$, allow linear full-strain fields for selected axes, whereas cubic-II groups, $432$, $\bar{4}3m$, and $m\bar{3}m$, forbid linear fields and require quadratic or cubic strain combinations depending on the selected axis. In trigonal systems, the basal-plane deviatoric strain with signed amplitude $\varepsilon_{\rm u}$ and principal-axis angle $\theta$ gives the single-axis field $h\propto\varepsilon_{\rm u}^3\sin6\theta$. First-principles calculations for the trigonal ferroaxial compound Na$_2$BaMg(PO$_4$)$_2$ verify both the predicted angular dependence and cubic strain scaling of the ferroaxial domain splitting, and fixed-strain atomic relaxations show strain-selected evolution from the para-axial structure. These results establish static homogeneous strain as a symmetry-allowed conjugate field for ferroaxial order and suggest a route to ferroaxial domain control through strain-field cooling.