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Motivated by the recent neutron scattering experiment on Rb2Cu3SnF12 [Nat.Phys. 6, 865 (2010)], we investigate the effect of Dzyaloshinskii-Moriyainteractions in a theoretical model for the magnetic structure of thismaterial. Considering the valence bond solid ground state, which has a 12-siteunit cell, we develop the bond operator mean-field theory. It is shown that theDzyaloshinskii-Moriya interactions significantly modify the triplon dispersionsaround the Gamma point and cause a shift of the spin gap (the minimum triplongap) position from the K to Gamma point in the first Brilloin zone. The spingap is also evaluated in exact diagonalization studies on a 24-site cluster. Wediscuss a magnetic transition induced by the Dzyaloshinskii-Moriya interactionsin the bond operator framework. Moreover, the magnetization process underexternal magnetic fields is studied within the exact diagonalization and strongcoupling expansion approaches. We find that the results of all above approachesare consistent with the experimental findings.

Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-1/2 deformed kagome lattice antiferromagnet