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