Multipartite Entanglement and Quantum Sensing in a Spin-5/2 Heisenberg Molecular Iron(III) Triangle

Abstract: This study provides insights into the static and dynamic quantum properties of the trinuclear high-spin iron(III) molecular complex $[\mathrm{Fe}_3\mathrm{Cl}_3(\mathrm{saltag^\mathrm{Br}})(\mathrm{py})_6]\mathrm{ClO}_4$ to be further abbreviated as Fe$_3$. Using exact diagonalization of a spin-5/2 Heisenberg triangle in a magnetic field, we model the corresponding quantum behavior of the molecular compound Fe$_3$. Our rigorous analysis employs various key metrics to explore a rich quantum behavior of this molecular compound. At sufficiently low temperatures, the bipartite negativity reveals that the pairwise entanglement between any pair of iron(III) magnetic ions of the molecular complex Fe$_3$ can be significantly enhanced by a small magnetic field. This enhancement is followed by unconventional step-like changes characterized by a sequence of plateaus and sudden downturns as the magnetic field further increases. A qualitatively similar behavior is also observed in the genuine tripartite entanglement among all three iron(III) magnetic ions in the trinuclear complex Fe$_3$. Notably, the bipartite and tripartite entanglement persist in the molecular complex Fe$_3$ up to moderate temperatures of approximately 30~K and 70~K, respectively. Additionally, we demonstrate the achievement of quantum-enhanced sensitivity by initializing the molecular complex Fe$_3$ in Dicke states. Finally, we investigated a quantum-sensing protocol by applying a local magnetic field specifically to one iron(III) magnetic ion of the molecular compound Fe$_3$ and performing readout sequentially on one of two remaining iron(III) magnetic ions.