Stability conditions of a twist-bend nematic phase according to Barbero's theory

The stability conditions of twist-bend nematics given by Barbero et al. [Phys. Rev. E 92, 030501(R) (2015)] lead to doubtful conclusions when the influence of the magnetic field on the NTB structure is analyzed. For this reason, the stability criteria have been redetermined in the present paper. The calculations have revealed that some of the conditions presented by Barbero and his co-workers are incorrect. It has been shown that the parameters boK33 and & eta; must be positive to induce the formation of a stable twist-bend nematic phase. Furthermore, some additional criteria concerning the value of & eta; have been derived. The phenomenon of the shift of the stability interval in the magnetic field has been analyzed in detail.