We present a comprehensive experimental and theoretical study of the structural, electronic, magnetic, and thermodynamic properties of a ${\mathrm{Pb}}_6{\mathrm{Co}}_9{\left({\mathrm{TeO}}_6\right)}_5$ single crystal. The ${\mathrm{Pb}}_6{\mathrm{Co}}_9{\left({\mathrm{TeO}}_6\right)}_5$ crystal has shown a unique type of magnetic spin-lattice coupling, in which the lattice structure consists of four different Co ions sites with distorted octahedral coordinations. The x-ray photoelectron spectroscopy (XPS) results confirmed the oxidation states of Pb, Co, Te, and O elements in the sample. Moreover, XPS spectra revealed the adsorbed oxygen in the defect/vacancy sites of the lattice structure. The dc magnetization measurements exhibited a complex magnetic behavior with ferrimagnetic (FIM) transition with Curie temperature $T_C$ at $\sim 21$ K. At lower magnetic fields $H$, the zero-field-cooled and field-cooled curves showed a broad hump at $\sim 10.8$ K and a shoulder peak at $\sim 6.2$ K, which are suppressed at higher magnetic fields. The ac susceptibility data indicated spin-glass-like features. The heat capacity $C_P$ measurements confirmed the FIM transition at $T_C$ at $\sim 21$ K, but without any trace of additional peaks at lower temperatures. The estimated Curie-Weiss constant ${\theta }_{\mathrm{CW}}$ showed a peculiar field-dependent behavior along the $H\parallel c$ direction of the single crystal, where ${\theta }_{\mathrm{CW}}$ is less field dependent for the $H\perp c$ direction. A large coercivity (13 kOe) is observed at 2 K for $H\parallel c$, whereas the magnetization curve of the single crystal is dominated by an antiferromagnetic feature for $H\perp c$. The behaviors indicate the anisotropy nature of the exchange interactions in the compound. The local spin density approximation $+ U$ total energy calculations were performed for various collinear spin configurations of a classical Heisenberg model in order to obtain the magnetic exchange interactions $J_i$ at different distances for different neighbors.

• Received 28 January 2021
• Revised 2 September 2021
• Accepted 15 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.174442