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High-resolution time-of-flight powder neutron diffraction and high-fieldmagnetization were measured to investigate the magnetic structure and existenceof a field-induced magnetic phase transition in the distorted kagomeantiferromagnet Cs$_2$Cu$_3$SnF$_{12}$. Upon cooling from room temperature, thecompound undergoes a structural phase transition at $T_\textrm{t}=185$ K fromthe rhombohedral space group $R\bar{3}m$ with the perfect kagome spin networkto the monoclinic space group $P2_1/n$ with the distorted kagome planes. Thedistortion results in three inequivalent exchange interactions among the$S=1/2$ Cu$^{2+}$ spins that magnetically order below $T_\textrm{N}=20.2$ K.Magnetization measured with a magnetic field applied within the kagome planereveals small in-plane ferromagnetism resulting from spin canting. On the otherhand, the out-of-plane magnetization does not show a clear hysteresis loop ofthe ferromagnetic component nor a prominent anomaly up to 170 T, with theexception of the subtle knee-like bend around 90 T, which could indicate the1/3 magnetization plateau. The combined analysis using the irreduciblerepresentations of the magnetic space groups and magnetic structure refinementon the neutron powder diffraction data suggests that the magnetic moments orderin the 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-planeferromagnetism observed in the magnetization.

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