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Soliton Wall Superlattice Charge-Density-Wave Phase in Quasi-One-Dimensional Conductor (Per)$_2$Pt(mnt)$_2$

We demonstrate that the Pauli spin-splitting effects in a magnetic field improve nesting properties of a realistic quasi-one-dimensional electron spectrum. As a result, a high resistance Peierls charge-density-wave (CDW) phase is stabilized in high enough magnetic fields in (Per)$_2$Pt(mnt)$_2$ conductor. We show that, in low and very high magnetic fields, the Pauli spin-splitting effects lead to a stabilization of a soliton wall superlattice (SWS) CDW phase, which is characterized by periodically arranged soliton and anti-soliton walls. We suggest experimental studies of the predicted first order phase transitions between the Peierls and SWS phases to discover a unique SWS phase. It is important that, in the absence of a magnetic field and in a limit of very high magnetic fields, the suggested model is equivalent to the exactly solvable model of Brazovskii, Dzyaloshinskii, and Kirova.