Magnetic-field-induced instability of the cooperative paramagnetic state in Zn${}_x$Co${}_{4-x}$(OD)${}_6$Cl${}_2$

Using elastic and inelastic neutron scattering techniques with and without application of an external magnetic field $H$, the magnetic ground states of Zn${}_x$Co${}_{4-x}$(OD)${}_6$Cl${}_2$ ($x=0,1$) were studied. Our results show that for $x=0$, the ground state is a magnetic long-range ordered (LRO) state where each tetrahedron forms an “umbrella”-type structure. On the other hand, for $x=1$, no static ordering was observed down to 1.5 K, which resembles the behavior found in the isostructural quantum system Zn${}_x$Cu${}_{4-x}$(OD)${}_6$Cl${}_2$. When $H$ field is applied, however, the $x=1$ system develops the same LRO state as $x=0$. This indicates that the $x=1$ disordered state is in the vicinity of the $x=0$ ordered state.

Figure 1

Neutron powder diffraction data of (a) Co${}_4$(OD)${}_6$Cl${}_2$ and (b) ZnCo${}_3$(OD)${}_6$Cl${}_2$ measured at 1.5 K below transition temperature $T$ $=$ 10.5 K. Circles are the data and the black line represents the calculated intensity obtained from the refinement by fullprof. Green bars represent nuclear and magnetic Bragg peak positions and blue lines indicate difference between data and calculation. Impurity peaks are excluded in (b). The inset of (a) shows temperature dependence of integrated intensities of (1,0,1) and (0,0,3) peaks. (c) shows the schematic diagram of magnetic structure obtained from the refinement of Co${}_4$(OD)${}_6$Cl${}_2$. Error bars in all figures represent 1 standard deviation from counting statistics.

Figure 2

Inelastic neutron scattering data of Co${}_4$(OD)${}_6$Cl${}_2$ [(a)–(f)] and ZnCo${}_3$(OD)${}_6$Cl${}_2$ [(g)–(l)] measured at the DCS at NIST using three different wave lengths of incident neutron, $\lambda$ $=$ 1.8 Å, 2.5 Å, and 4.8 Å. (a) and (b): Contour maps of neutron scattering intensity $I(Q,\omega )$ as a function of energy transfer $\hslash \omega$ and momentum transfer $Q$ obtained at 1.5 K below $T_N$ $=$ 10.5 K with $\lambda$ $=$ 1.8 Å and $\lambda$ $=$ 2.5 Å, respectively. (c): Neutron scattering intensities as a function of energy transfer measured at 1.5 K, 15 K, 50 K, and 150 K obtained from the integration of $I(Q,\omega )$ over 0.5 Å${}^{-1}$ $<$ $Q$ $<$ 4 Å${}^{-1}$. Solid lines are obtained from fitting by Lorentzian functions. (d)–(f): Integrated intensity, peak position, and FWHM of excitation modes as a function of temperature, respectively. (g)–(l) are plotted for ZnCo${}_3$(OD)${}_6$Cl${}_2$ in the same manner as Co${}_4$(OD)${}_6$Cl${}_2$.

Figure 3

Linear spin wave calculation results. Contour map of powder-averaged neutron scattering cross section as a function of $Q$ and $\hslash \omega$. (a) $D_i<J_1$, (b) $D_i\gg J_1$ for Co2 kagome spins. See the text for explanation.

Figure 4

Elastic neutron scattering patterns of (a) Co${}_4$(OD)${}_6$Cl${}_2$ and (b) ZnCo${}_3$(OD)${}_6$Cl${}_2$ as a function of $Q$ up to 2.0 Å${}^{-1}$, obtained on V2 at $T$ $=$ 1.5 K under external magnetic fields of 0 (black circle) and 13.5 T (red triangle). (c) Integrated intensity of (1,0,1) Bragg peak as a function of external magnetic field from 0 to 13.5 T for ZnCo${}_3$(OD)${}_6$Cl${}_2$.