Rotational bands in open antiferromagnetic rings: A neutron spectroscopy study of ${\text{Cr}}_8\text{Zn}$

Low-lying excitations in closed antiferromagnetic rings can be described in terms of rotational bands, which reflect the peculiar internal spin structure of the corresponding eigenstates. Here we use inelastic neutron-scattering measurements on the ${\text{Cr}}_8\text{Zn}$ molecule to investigate the validity of the rotational band picture in magnetically open rings. We determine the parameters of the microscopic spin Hamiltonian describing each ${\text{Cr}}_8\text{Zn}$ molecule and we analyze how the spin dynamics changes with respect to the parent closed-ring compound ${\text{Cr}}_8$. Qualitative differences can be found not only in the energy-level diagrams but also in the internal structure of the spin eigenstates, probed through the wave-vector transfer dependence of the neutron cross section. The usual rotational bands picture fails because quantum fluctuations of the total-spin length of the two sublattices do not occur jointly due to the ring opening.

Figure 1

(Color online) The structure of a ${\text{Cr}}_8\text{Zn}$ molecule. Hydrogen atoms have been omitted for clarity.

Figure 2

(Color online) (a) Energy difference between two adjacent levels of the $L$ band for ${\text{Cr}}_8$ and ${\text{Cr}}_8\text{Zn}$. A deviation from the Landé rule can be seen for the open-ring ${\text{Cr}}_8\text{Zn}$. (b) Modulus of the scalar product between $L$-band states for the closed ${\text{Cr}}_8$ and the open ${\text{Cr}}_8\text{Zn}$ rings. (c) Weight of the Landé component (i.e., with $S_{\text{odd}}=S_{\text{even}}=6$) in the $L$-band states of ${\text{Cr}}_8$ and ${\text{Cr}}_8\text{Zn}$. (d) Weight of the component with $S_{\text{odd}}=S_{\text{even}}$ in the $L$-band states of ${\text{Cr}}_8$ and ${\text{Cr}}_8\text{Zn}$. This represents the probability of finding the same length for the total-spin of the two sublattices.

Figure 3

(Color online) Energy of the low-lying triplet eigenstates of $H_{\text{iso}}$ for ${\text{Cr}}_8$ and ${\text{Cr}}_8\text{Zn}$. For the latter, the labelling of states as $L$ or $E$ refers to the dominant component in the state.

Figure 4

(Color online) ${\text{Cr}}_8\text{Zn}$ INS spectra at low energy collected with $\lambda =7\text{Å}$ at $T=1.5\text{K}$ (squares) and $T=7\text{K}$ (circles) in panel (a) and with $\lambda =3.8\text{Å}$ at $T=1.5\text{K}$ (squares), $T=7\text{K}$ (circles), and $T=12\text{K}$ (triangles) in panel (b). Solid lines represent calculated spectra with INS cross section obtained in Ref. 7 and from eigenvalues and eigenvectors of Eq. (1) with the following set of parameters: $J=1.32\text{meV}$, $J_{\text{nnn}}=-0.01\text{meV}$, $d=-0.028\text{meV}$, $\left|e\right|=0.003\text{meV}$, where $J_{\text{nnn}}$ is the parameter of next-nearest-neighbors exchange interaction. The error bars in all the figures represent standard deviations in the measurement.

Figure 5

(Color online) INS spectra as a function of the scattering vector amplitude $Q$ obtained with incident wavelength $\lambda =7$ and $3.8\text{Å}$ and sample temperature $T=1.5\text{K}$. Calculations are represented by continuous lines. The upper curve and points in panel (a) have been shifted by an offset for clarity.