Abstract 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.

中文翻译：

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聚（对亚苯基亚乙烯基）衍生物的磁场研究

摘要 证明了在高 p 掺杂基态的外部 B 磁场的作用下，聚对苯撑乙烯撑 (PPV) 及其衍生物中的 Mielke-Tasaki 型铁磁性。该系统不包含磁性原子，并且不考虑 B 对自旋的作用。给出了在外部均匀磁场存在下 PPV 衍生物的精确色散方程和裸带结构。给出了完全平带结构的条件。另一方面，也证明了最重要的 PPV 衍生物缺乏完全平坦的带结构。以近似方式计算对最低和其他带以及裸带结构依赖于 B 大小的周期性的计算。介绍了亚乙烯基链的磁场作用。用半正定算符方法推导出半满最低带集中情况的基态波函数。指出解仅存在于离散的 B 值中。显示了基态的饱和铁磁特性。我们的结果可推广到含有更长链的聚合物的情况，其中相邻的碳环通过更多的双键相互连接。