We thoroughly study the zero temperature properties of a monoaxial chiral spin system under the tilted magnetic field. The magnetic phase diagram includes two kinds of continuous phase transition and one discontinuous phase transition. We clarify the properties of the phase transition in terms of the helical wave picture and the particle (soliton) picture, and also in terms of the interaction between solitons. The interacting-soliton picture well describes most of the discontinuous phase transition. In addition, we investigate several instabilities of the modulated structures such as an isolated soliton and the surface modulation, since their instabilities should be important to the observable changes of the magnetic properties. For this purpose, we perform the energy landscape analyses as well as the excitation spectral analyses; The former approach gives an intuitive interpretation. We clarify the mechanisms of the instabilities through these analyses, and draw the stability lines of solitons in the magnetic phase diagram.
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