Theoretical Investigations of Hysteresis Loops of Ferroelectric or Ferrielectric Nanotubes with Core/Shell Morphology

In this paper, the hysteresis behavior of the nanotubes, consisting of a ferroelectric core of spin-1/2 surrounded by a ferroelectric shell of spin-1/2 with ferro- or anti-ferroelectric interfacial coupling is studied by using the transverse Ising model (TIM). Based on a probability distribution method, the effective field theory has been used to examine the effects of the interfacial coupling constant, the transverse field, and the temperature on the hysteresis loops of the nanotubes. A number of characteristic behaviors have been found, such as the existence of triple hysteresis loops for appropriate values of the system parameters. The remanent polarization and the coercive field, as functions of the temperature, are examined.