$J_{\mathrm{eff}}=1/2$ Hyperoctagon Lattice in Cobalt Oxalate Metal-Organic Framework

We report the magnetic properties of a cobalt oxalate metal-organic framework featuring the hyperoctagon lattice. Our thermodynamic measurements reveal the $J_{\mathrm{eff}}=1/2$ state of the high-spin ${\mathrm{Co}}^{2+}$ ($3d^7$) ion and the two successive magnetic transitions at zero field with two-stage entropy release. ${}^{13}\mathrm{C}$-NMR measurements reveal the absence of an internal magnetic field in the intermediate temperature phase. Multiple field-induced phases are observed before full saturation at around 40 T. We argue the unique cobalt oxalate network gives rise to the Kitaev interaction and/or a bond frustration effect, providing an unconventional platform for frustrated magnetism on the hyperoctagon lattice.

Figure 1

(a) Hyperoctagon lattice of Co in ${\mathrm{Co}}_2{(\mathrm{ox})}_3$ network. All Co ions are crystallographically equivalent. (b) Local structure of ${\mathrm{Co}}_2{(\mathrm{ox})}_3$ network seen from the trigonal axis of Co at the center. The numbers indicate the position in the unit cell as shown in (d). (c) Tilting of the planes perpendicular to the trigonal axis (pink triangles and green lines). The red line is shared by the neighboring planes. (d) ${\mathrm{Co}}_2{(\mathrm{ox})}_3$ network in the unit cell. ${\mathrm{CoO}}_6$ octahedra labeled by different numbers have different trigonal axis directions. Figures are depicted by VESTA software [27].

Figure 2

(a) Temperature dependence of inverse susceptibility of the powder sample at 1 T with a Curie-Weiss fit (solid line). (b) Temperature dependence of magnetic susceptibility (left axis) and the temperature derivative (right axis) at 1, 3, and 6 T. The data at 3 and 6 T is shifted for clarity. (c) Temperature dependence of specific heat divided by temperature (red, left axis) measured on the powder pellet at zero field. The black dashed line shows the estimated lattice contribution. Temperature dependence of magnetic specific heat (green, left axis) and magnetic entropy (blue, right axis) are also plotted. (d) Temperature dependence of specific heat divided by temperature at various magnetic fields.

Figure 3

(a) Magnetization curve measured on the powder sample in the pulsed magnetic field at 1.4 K (red) and by the SQUID at 1.8 K (blue). The field derivative of the pulsed field data is plotted in the right axis. The dashed line shows a linear fit above 40 T. (b) Magnetization curves at different temperatures (left) and their magnetic field derivatives (right): data are shown with offset. (c) Field dependence of the magnetic torque divided by the magnetic field (red) and its magnetic field derivative (blue) measured on one single crystal.

Figure 4

(a) $H–T$ phase diagram determined by the anomalies observed in $\chi$ (squares), $C_{\text{p}}/T$ (triangles), and $M$ (circles). Phases are labeled by I, I’, II, and III. Para and P indicate the paramagnetic and fully polarized states, respectively. (b) ${}^{13}\mathrm{C}$-NMR spectra measured on the powder sample at 2.619 T at selected temperatures below 30 K. The dashed line indicates the frequency for the NMR shift $K=0$. (c) Temperature dependence of the full width at half maximum of the spectra (black squares, left axis) and the isotropic part of the NMR shift (red circles, right axis).