Crystal growth, magnetic properties, and critical behavior of the itinerant ferromagnet <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">K</mml:mi> <mml:mrow> <mml:mn>0.79</mml:mn> </mml:mro

In this paper, we successfully grow layered single-crystal ${\mathrm{K}}_{0.79}{\mathrm{Co}}_{2}{\mathrm{S}}_{2}$ and systematically investigate its crystal structure, magnetic properties, electrical transport, specific heat, and even magnetic critical behavior. Single-crystal x-ray diffraction measurements indicate that ${\mathrm{K}}_{0.79}{\mathrm{Co}}_{2}{\mathrm{S}}_{2}$ crystallizes into a tetragonal structure with space group I4/mmm (No. 139) and lattice parameters of $a=b=3.711(4)\phantom{\rule{0.28em}{0ex}}\AA{}$ and $c=13.140(2)\phantom{\rule{0.28em}{0ex}}\AA{}$. Physical properties measurements demonstrate that ${\mathrm{K}}_{0.79}{\mathrm{Co}}_{2}{\mathrm{S}}_{2}$ displays a metallic behavior with a ferromagnetic phase transition at ${T}_{C}\ensuremath{\approx}113\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, which was confirmed by the anomaly in the vicinity of ${T}_{C}$ that occurs in electrical transport and specific heat curves. The calculated Rhodes-Wolfarth ratio $(\ensuremath{\approx}1.56)$ reveals the itinerant ferromagnetic characteristic of ${\mathrm{K}}_{0.79}{\mathrm{Co}}_{2}{\mathrm{S}}_{2}$. A set of critical exponents was generated to be $\ensuremath{\beta}=0.3006(4)$ with ${T}_{C}\ensuremath{\approx}113.3(6)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and $\ensuremath{\gamma}=1.1802(4)$ with ${T}_{C}\ensuremath{\approx}113.2(5)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ based on the modified Arrott plot and $\ensuremath{\delta}=5.18(7)$ is yielded using a critical isotherm analysis at ${T}_{C}$, revealing a three-dimensional critical behavior. The magnetic interaction is determined to be a three-dimensional long-range coupling with the magnetic exchange distance decaying as $J(r)\ensuremath{\sim}{r}^{\ensuremath{-}4.91}$. Furthermore, a maximum of the magnetic entropy change $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{M}^{max}$ for the applied field parallel to the $ab$ plane is estimated to be $\ensuremath{\approx}2.51$ $\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{kg}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ around ${T}_{C}$.