Magnetic structure and high-field magnetization of the distorted kagome lattice antiferromagnet Cs$_2$Cu$_3$SnF$_{12}$.

High-resolution time-of-flight powder neutron diffraction and high-field magnetization were measured to investigate the magnetic structure and existence of a field-induced magnetic phase transition in the distorted kagome antiferromagnet Cs$_2$Cu$_3$SnF$_{12}$. Upon cooling from room temperature, the compound undergoes the structural phase transition at $T_\textrm{t}=185$ K from rhombohedral space group $R\bar{3}m$ with the perfect kagome spin network to monoclinic space group $P2_1/n$ with the distorted kagome planes. The distortion results in three inequivalent exchange interactions among $S=1/2$ Cu$^{2+}$ spins that magnetically order below $T_\textrm{N}=20.2$ K. Magnetization measured with a magnetic field applied within the kagome plane reveals small in-plane ferromagnetism resulted from spin canting. On the other hand, the out-of-plane magnetization does not show a clear hysteresis loop of the ferromagnetic component nor a prominent anomaly up to 170 T, suggestive of the robustness of the magnetic structure against the external magnetic field, with the exception of the subtle knee-like bend around 90 T, which could indicate the 1/3 magnetization plateau. The combined analysis using irreducible representation of magnetic space groups and magnetic structure refinement on the neutron powder diffraction data reveals that the magnetic moments order in magnetic space group $P2_1'/n'$ with the all-in-all-out spin structure, which by symmetry allows for the in-plane canting, consistent with the in-plane ferromagnetism observed in the magnetization.