Decomposition of Response Tensors for Materials Design

A common approach to designing materials with enhanced response is to exploit competing phases and their corresponding order parameters. Similarly, both linear and nonlinear response to external fields is commonly used to probe and identify order parameters and their symmetry properties. However, not every phase transition in solids has an obvious and unique signature in macroscopic response. For example, magnetic susceptibility can be used to study ferromagnetic phase transitions and their time-reversal odd axial order parameters, but there is no commonly used order parameter to probe ferroaxial phase transitions where the order parameter is a time-reversal even axial vector. Similarly, there is no macroscopic measurement proposed to separate the different time-reversal breaking "imaginary" charge density wave states proposed to be present in the AV3Sb5 Kagome metals. In this talk, we present a general group and representation theory guided first principles approach to study phase transitions and order parameters in crystalline solids, and their signatures in response tensors. Considering piezoresistivity, piezomagnetism, and magnetoelectricity as examples, we discuss test cases in ferroaxial, kagome charge density wave, and altermagnetic materials.