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Single crystals of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl were investigated usinghigh-resolution capacitance dilatometry in magnetic fields up to 15 T.Pronounced magnetoelastic coupling is found upon evolution of long-rangeantiferromagnetic order at T$_{\mathrm{N}} = 26.4(3)$ K. Gr\"{u}neisen analysisreveals moderate effects of uniaxial pressure on T$_{\mathrm{N}}$, of $1.8(4)$K/GPa, $-0.62(15)$ K/GPa and $0.33(10)$ K/GPa for $p \parallel a$, $b$, and$c$, respectively. Below 22 K, Gr\"{u}neisen scaling fails which implies thepresence of competing interactions. The structural phase transition atT$_{\mathrm{S}} = 120.7(5)$ K is much more sensitive to uniaxial pressure thanT$_{\mathrm{N}}$, with strong effects of up to $27(3)$ K/GPa ($p \parallel c$).Magnetostriction and magnetization measurements reveal a linear magnetoelasticcoupling for $B\parallel c$ below T$_{\mathrm{N}}$, as well as a mixed phasebehavior above the tricritical point around 0.4 T. An analysis of the criticalbehavior in zero-field points to three-dimensional (3D) Ising-like magneticordering. In addition, the magnetic phase diagrams for fields along the maincrystalline axes are reported.

Linear magnetoelastic coupling and magnetic phase diagrams of the buckled-kagom\'{e} antiferromagnet Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl