Jahn-Teller effect for controlling quantum correlations in hexanuclear Fe$$^{3+}$$ magnets

We theoretically investigate the low-temperature magnetic and quantum properties of hexanuclear Fe[Formula: see text] complexes under an external magnetic field. We primarily study the impact of competing exchange interactions and their asymmetries induced by the Jahn-Teller distortion on the quantum properties of the complexes. The inequality in exchange interactions lifts the ground-state degeneracy that gives rise to complex quantum behavior. By constructing the ground-state phase diagram and analyzing magnetization, we identify key magnetic phases and critical phenomena. We further quantify quantum correlations using tripartite entanglement negativity and conditional von Neumann entropy to unveil how the Jahn-Teller effect enhances intra-triangle entanglement while modulating inter-triangle correlations. Our findings highlight the Fe[Formula: see text] complex as a promising molecular platform for tunable quantum correlations, with potential applications in quantum information processing and molecular qubits.