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The recently discovered twist-bend nematic phase, $\rm N_{tb}$, is anon-uniform equilibrium nematic phase that presents a spontaneous bend with aprecession of the nematic director, $\textbf{n}$, on a conical helix with atilt angle $\theta$ and helical pitch $P$. The stability of the $\rm N_{tb}$phase has been recently demonstrated from the elastic point of view byextending the Frank elastic energy density of the nematic phase to include thesymmetry element of helical axis, $\bf t$. In the present communication, weinvestigate the influence of an external bulk field (magnetic or electric) onthe pitch of the $\rm N_{tb}$ phase. For a material with positive magneticsusceptibility anisotropy, when the magnetic field $\bf{H}$ is parallel to thehelical axis, $\bf{t}$, the field modifies the coupling parameter between thedirector and the helical axis, thus shifting the interval of values for whichthis coupling results in the $\rm N_{tb}$ phase. If $\bf{H}$ is perpendicularto $\bf{t}$, it is shown that the pitch of the nematic director $\bf n$precession increases with $\bf{H}$, and at a critical value of $H_c$ it becomesinfinite as in a cholesteric liquid crystal, that is, one gets a uniformorientation of n. Our results include the behaviour of a cholesteric underfield as a limiting case.

Unwinding of the twist-bend nematic structure under an external field