Here we report the evolution of structural, magnetic and transport properties in MnBi$_{2-x}$Sb$_x$Te$_4$ (0$leq x leq$2) single crystals. MnSb$_2$Te$_4$, isostructural to MnBi$_2$Te$_4$, has the lattice parameters of textit{a}=4.2445(3)$AA$ and textit{c}=40.869(5)$AA$, respectively. With increasing Sb content in MnBi$_{2-x}$Sb$_x$Te$_4$, the textit{a}-lattice decreases linearly following the Vegards law while the textit{c}-lattice shows little compositional dependence. The textit{a}-lattice contraction occurs by reducing Mn-Te-Mn bond angle while Mn-Te bond length remains nearly constant. The anisotropic magnetic properties suggest an antiferromagnetic order below T$_N$=19,K for MnSb$_2$Te$_4$ with the magnetic moments aligned along the crystallographic textit{c}-axis. The antiferromagnetic ordering temperature slightly decreases from 24,K for MnBi$_2$Te$_4$ to 19,K for MnSb$_2$Te$_4$. More dramatic change was observed for the critical magnetic fields required for the spin-flop transition and moment saturation. With increasing Sb content, both critical fields decrease and in MnSb$_2$Te$_4$ a small field of 3,kOe is enough to saturate the moment. In high magnetic fields, the saturation moment shows significant suppression from 3.56$mu_B$/Mn for MnBi$_2$Te$_4$ to 1.57$mu_B$/Mn for MnSb$_2$Te$_4$. Data analyses suggest that both the interlayer magnetic interaction and single ion anisotropy decrease with increasing Sb content. The partial substitution of Bi by Sb also dramatically affects the transport properties. A crossover from n-type to p-type conducting behavior is observed around x=0.63. Our results show close correlation between structural, magnetic and transport properties in MnBi$_{2-x}$Sb$_x$Te$_4$ and that partial substitution of Bi by Sb is an effective approach to fine tuning both the magnetism and transport properties of MnBi$_{2-x}$Sb$_x$Te$_4$.
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