Magnetic spin order in the honeycomb structured Pb6Co9(TeO6)5 compound

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We present a comprehensive experimental and theoretical study of the structural, electronic, magnetic, and thermodynamic properties of a ${\mathrm{Pb}}_{6}{\mathrm{Co}}_{9}{({\mathrm{TeO}}_{6})}_{5}$ single crystal. The ${\mathrm{Pb}}_{6}{\mathrm{Co}}_{9}{({\mathrm{TeO}}_{6})}_{5}$ 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 $\ensuremath{\sim}21$ K. At lower magnetic fields $H$, the zero-field-cooled and field-cooled curves showed a broad hump at $\ensuremath{\sim}10.8$ K and a shoulder peak at $\ensuremath{\sim}6.2$ 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 $\ensuremath{\sim}21$ K, but without any trace of additional peaks at lower temperatures. The estimated Curie-Weiss constant ${\ensuremath{\theta}}_{\mathrm{CW}}$ showed a peculiar field-dependent behavior along the $H\ensuremath{\parallel}c$ direction of the single crystal, where ${\ensuremath{\theta}}_{\mathrm{CW}}$ is less field dependent for the $H\ensuremath{\perp}c$ direction. A large coercivity (13 kOe) is observed at 2 K for $H\ensuremath{\parallel}c$, whereas the magnetization curve of the single crystal is dominated by an antiferromagnetic feature for $H\ensuremath{\perp}c$. 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.