  Searching for new functionality in next generation electronic devices is a
principal driver of material physics research. Multiferroics simultaneously
exhibit electric and magnetic order parameters that may be coupled through
magnetoelectric (ME) effects. In single-phase materials the ME effect arises
from one of three known mechanisms: inverse Dzyaloshinskii-Moriya (IDM)
interaction, spin dependent ligand-metal (p-d) orbital hybridization, and
exchange striction. However, the coupling among these mechanisms remains
largely unexplored despite envisioned potential capabilities. Here, we present
cooperative tuning between both IDM interaction and p-d hybridization that
leads to discrete ME states in Ba0.5Sr2.5Co2Fe24O41. In-situ x-ray diffraction
exposes the microscopic interplay between these two mechanisms, marked by a
unique ME susceptibility upon electric and magnetic fields. The entangled
multi-ME coupling phenomenon observed in this room-temperature ME hexaferrite
offers a pathway to novel functional control for ME device applications.
