Jahn-Teller Effect for Controlling Quantum Correlations in Hexanuclear Fe$^{3+}$ Magnets

Abstract

We investigate the low-temperature magnetic and quantum properties of hexanuclear Fe$^ {3+}_6$ 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$^{3+}_6$ complex as a promising molecular platform for tunable quantum correlations, with potential applications in quantum information processing and molecular qubits.

Figures (4)

• Figure 1: The molecular structure of the Fe$^{3+}_6$ complex. We label the first triangular subunit as subsystem $\mathcal{A}$ and the second one as subsystem $\mathcal{B}$.
• Figure 2: (a) Ground-state phase diagram of the $\text{Fe}^{3+}$ complex described by the Hamiltonian (\ref{['Eq:Hamiltonian']}) in the ($J_2, J_3, B$) parameter space, assuming $J_1 = 42.2\, \text{cm}^{-1}$. The different ground states are represented by distinct symbols: black pentagons for $M/M_\text{s} = 1$, cyan triangles for $M/M_\text{s} = \frac{2}{3}$, yellow hexagons for $M/M_\text{s} = \frac{1}{3}$, and blue circles for $M/M_\text{s} = 0$. (b) Ground-state phase diagram in the $B-J_3$ plane for fixed values of $J_1 = 42.2\, \text{cm}^{-1}$ and $J_2 = 34.2\, \text{cm}^{-1}$. (c) Ground-state phase diagram in the $B-J_2$ plane, assuming $J_1 = 42.2\, \text{cm}^{-1}$ and $J_3 = 0.015\, \text{cm}^{-1}$. (d) Magnetization as a function of the magnetic field $B$ for various fixed temperatures $T$. Experimental data from Oyarzabal2015 are shown as black circles, while theoretical magnetization curves are represented by lines. The blue solid line corresponds to the best-fit magnetization curve, obtained using the parameter set $J_1 = 42.2\, \text{cm}^{-1}$, $J_2 = 34.2\, \text{cm}^{-1}$, and $J_3 = 0.015\, \text{cm}^{-1}$, as reported in Oyarzabal2015.
• Figure 3: (a) Magnetic-field dependence of the tripartite negativity $\mathcal{N}_{123}$ of the Fe$^{3+}$ complex under JT effect at different temperatures. The coupling constants $J_1 = 42.2\, \text{cm}^{-1}$, $J_2 = 34.2\,\text{cm}^{-1}$, $J_3 = 0.015\,\text{cm}^{-1}$, and the gyromagnetic factor $g = 2.0$ are taken from previous experimental analysis Oyarzabal2015. (b) The negativity $\mathcal{N}_{123}$ with equilateral triangle shape of subunits with $J_1 = J_2 = 42.2\, \text{cm}^{-1}$ and $J_3 = 0.015\,\text{cm}^{-1}$.
• Figure 4: (a) Magnetic-field dependence of the conditional entropy $\mathcal{S}_\mathcal{A|B}$ of the Fe$^{3+}$ complex under JT effect at different temperatures. The coupling constants are $J_1 = 42.2\, \text{cm}^{-1}$, $J_2 = 34.2\,\text{cm}^{-1}$, $J_3 = 0.015\,\text{cm}^{-1}$, and the gyromagnetic factor is $g = 2.0$Oyarzabal2015. (b) The conditional entropy $\mathcal{S}_\mathcal{A|B}$ of the equilateral triangle shape of the subsystems $\mathcal{A}$ and $\mathcal{B}$ with $J_1 = J_2 = 42.2\, \text{cm}^{-1}$ and $J_3 = 0.015\,\text{cm}^{-1}$. (c) Conditional von Neumann entropy $\mathcal{S}_\mathcal{A|B}$ in the ($B, J_3$) plane, assuming $J_1 = 42.2\, \text{cm}^{-1}$ and $J_2 = 34.2\,\text{cm}^{-1}$.