Effects of a Magnetic Field on a Modulated Phase

The effects of a magnetic field on a modulated phase is studied. A modulated phase is found to have two critical fields $H_{1}$ and $H_{2}$. For a large enough magnetic field. $H_1$ can be approximated by a linear law. As a result, the minimum magnetic field needed to destroy a modulated phase is a constant. The minimum magnetic field also greatly depends on the order of a commensurate. A very high order commensurate phase and an incommensurate phase are impossible to survive a magnetic field. The behaviour of a magnetoelastic chain in a magnetic field is can be described by a harmless Devil's staircase. The inverse temperature is found to play a role similar to that of a special magnetic field. The deeper physics underlying these new phenomena is the breaking of the left-right symmetry of a phase diagram. As a result a controllable path to a modulated phase is found.