Magnetic field study of poly (p-phenylenevinylene) derivatives

The Mielke-Tasaki type of ferromagnetism in poly(p-phenylenevinylene) (PPV) and its derivatives by the action of the external B magnetic field in the highly p-doped ground state is demonstrated. The system contains no magnetic atoms and the action of the B on the spins is not considered. Exact dispersion equation and bare band structures of PPV derivatives in the presence of an external homogenous magnetic field are presented. Conditions for totally flat band structure are given. On the other hand, the lack of the completely flat band structure for the most important PPV derivatives is also demonstrated. Calculations on the lowest and on other bands and on the periodicity of the bare band structure in dependence of magnitude of B are computed in an approximate manner. The magnetic field role of the vinylene chain is presented. The ground state wave function is deduced for the half-filled lowest band concentrating case by the Method of the Positive Semidefinite Operators. It is pointed out that solutions exist solely in discrete values of B. The saturated ferromagnetic property of the ground state is shown. Our results are generalizable to the case of longer chain containig polymers in which the neighbouring carbon rings are connected with each other with more double bonds.