Néel-Vector Tunneling in Antiferromagnetic Molecular Clusters

From inelastic neutron scattering experiments, we demonstrate quantum tunneling of the Néel vector in the antiferromagnetic molecular ferric wheel ${\mathrm{CsFe}}_8$. Analysis of the linewidth of the tunneling transition evidences coherent tunneling.

Figure 1

(a) Crystal structure of ${\mathrm{CsFe}}_8$ [with Fe as dark gray spheres (red online) and H atoms omitted]. (b) Classical ground-state spin configuration for the two orientations of the Néel vector [long up and down arrows (dark green online)] with $\mathbf{n}=\pm z$. (c) Low-lying energy spectrum of $\widehat{H}$ in units of $J$ for an octanuclear $s=5/2$ wheel as function of $k_z/J$. At small anisotropies, the levels can be classified by the spin quantum numbers $S$ and $M$. For large anisotropies, $S$ loses its significance ($M$ remains an exact quantum number), and the region of Néel-vector tunneling is entered [transition from dark to light gray shading (from blue to green shading online)]. The arrows show transitions I, II, and $\alpha$, and the double arrows the energy gaps ${\Delta }_{01}$ and ${\Delta }_{12}$.

Figure 2

(a) Neutron energy-loss spectrum of ${\mathrm{CsFe}}_8$ at $T=2.4\mathrm{K}$ ($\lambda =5.0\AA$). Data were summed over all detector banks. As discussed in the text, transition I corresponds to NVT with tunneling gap $\Delta$. (b) Schematic drawing of the potential energy vs the direction of the Néel vector in ${\mathrm{CsFe}}_8$. The two states $|\uparrow ⟩$ and $|\downarrow ⟩$ at 2.07 meV, corresponding to the Néel vector localized in the $-z$ and $+z$ directions, respectively, are mixed due to tunneling through the barrier of height 2.40 meV, resulting in the eigenstates $|\uparrow ⟩+|\downarrow ⟩$ and $|\uparrow ⟩-|\downarrow ⟩$ and a tunneling gap of $\Delta =0.51\mathrm{meV}$.

Figure 3

Neutron energy-loss spectrum of ${\mathrm{CsFe}}_8$ at $T=2.2\mathrm{K}$ and 9.7 K ($\lambda =8.0\AA$), showing peak I with high resolution. The peak shape is independent of temperature with a FWHM as indicated.

Figure 4

(a) Dependence of the intensity of peak I on momentum transfer $Q$. The solid line represents the theoretical curve for a $\Delta q=\pi$ transition. The analytical result was scaled, and a constant background accounting for the incoherent scattering in nondeuterated samples was added. (b) Neutron spectrum of ${\mathrm{CsFe}}_8$ at $T=9.7\mathrm{K}$ ($\lambda =5.0\AA$).