In condensed matter physics, spin-orbit-entangled materials host a variety of exotic quantum states. Among the most fascinating of these are "hidden multipolar orders." Unlike conventional magnetic states, where electron spins align in straightforward ways, multipolar orders involve highly complex, higher-order electronic alignments (such as quadrupoles or octupoles). Because these intricate patterns are notoriously difficult to detect using standard experimental probes, they are considered "hidden." Understanding and ultimately controlling these elusive states is a major frontier in the design of next-generation quantum materials.
Addressing this challenge, in this work we investigated how doping-induced small polarons impact the low-temperature multipolar orders of the 5d2 double perovskite Ba_2CaOsO_6. By computing intersite exchange interactions between 5d1 localized hole polarons and 5d2 magnetic ions from first principles, we demonstrated a striking reversal of the dominant octupolar exchange from ferromagnetic to antiferromagnetic.
Then, by solving the corresponding effective Hamiltonian, we found that this reversal accounts for the progressive suppression of the ferro-octupolar order and the reduction of the ordering temperature upon sodium (Na) doping. These findings clarify previously ambiguous experimental observations and demonstrate that charge doping in the form of small polarons offers a viable route to tuning intersite exchange interactions in spin-orbit-entangled materials—ultimately enabling the emergence of novel quantum orders.
