Influence of Dzyaloshinskii-Moriya interactions on magnetic structure of a spin-12 deformed kagome lattice antiferromagnet

Motivated by the recent neutron-scattering experiment on Rb ₂Cu₃SnF₁₂, 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 Γ point and cause a shift of the spin-gap (the minimum triplon gap) position from the K to Γ point in the first Brillouin 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 approach. We find that the results of both approaches are consistent with the experimental findings.