Field-induced transitions from incommensurate to commensurate phases in helical antiferromagnets

Heisenberg antiferromagnet with an easy-plane anisotropy is discussed in which a magnetic spiral is induced by Dzyaloshinskii-Moriya interaction and/or frustration of the exchange coupling. The distortion of the spiral by small in-plane magnetic field is described analytically. It is found that the field can gradually change the vector of the magnetic structure ${\bf k}_0$ and can produce transitions between phases with incommensurate and commensurate magnetic orderings when ${\bf k}_0$ is close to ${\bf g}/n$, where ${\bf g}$ is a reciprocal lattice vector and $n$ is integer. Analytical expressions for critical fields are derived for $n=2$, 3, and 4. Application of the theory to the triangular-lattice compound $\rm RbFe(MoO_4)_2$ is discussed alongside its potential applicability to other materials. As a by-product of the main consideration, model parameters are found which describe more accurately the full set of available experimental data suggested before for $\rm RbFe(MoO_4)_2$.