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

TL;DR

The paper develops a general, analytic framework for field-induced IC transitions in easy-plane helical antiferromagnets by expanding in the small in-plane field $h$ and examining cases where ${\bf k}_0$ is near ${\bf g}/n$ with $n=2,3,4$. It derives closed-form expressions for the critical field $h_c$ and reveals distinct scaling behavior for incommensurate vs commensurate ordering vectors, including the emergence of higher-harmonic content in the spin texture. The theory is applied to the triangular-lattice compound ${\rm RbFe(MoO_4)_2}$, providing refined model parameters that better describe experimental data and predicting the field-driven evolution of the ordering vector and magnon spectra. Overall, the work clarifies the nature (often first-order) of IC transitions in these magnets and offers quantitative predictions for candidate materials beyond ${\rm RbFe(MoO_4)_2}$.

Abstract

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 $\rm RbFe(MoO_4)_2$.

Figures (2)

• Figure 1: Magnon spectra extracted from neutron scattering experiment (data are taken from Figs. 2(c) and 2(d) of Ref. rbfemoo5) and calculated in the linear spin-wave theory using Eq. \ref{['spec']}. Three branches in the theory correspond to $\epsilon_{\bf k}$, $\epsilon_{\bf k+k_0}$, and $\epsilon_{\bf k-k_0}$.
• Figure 2: a) Dependence of the critical field $h_c$ given by Eq. \ref{['hc']} on $J$ when all other model parameters are fixed to their values from Eq. \ref{['param']}. The vertical dashed line marks $J$ value from Eq. \ref{['param']}. b) Same as a) but for the dependence on $J_2$.