Chemically-informed design principles for controlling spin and charge multipolar order

There has been significant recent interest in characterizing both ground-state and excited-state properties of matter in terms of the ordering of multipole moments in local atomic spin and charge densities. For example, altermagnetism may be distinguished from conventional antiferromagnetism by a non-vanishing "global" high-order spin multipole. In this work, we present chemical design principles for tuning the strength of high-order multipoles in commonly-encountered crystal field environments. Using a group-theoretic analysis, we identify structural and orbital parameters which maximize or minimize different multipole moments. Our results may inform the design and tuning of a variety of novel functional materials.