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Register a new userMathematical modeling of hysteresis loops in ferroelectric materials
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In published papers, the Gibbs free energy of ferroelectric materials has usually been quantified by the retention of 6th or 8th order polarization terms. In this paper, a newly analytical model of Gibbs free energy, thereout, a new model of polarization-electric field hysteresis loops in ferroelectric materials has been derived mathematically. As a model validation, four patterns of polarization-electric field hysteresis loops of ferroelectric materials have been depicted by using the model. The calculated results indicated that the self-similar model can characterize the various patterns of hysteresis loops in ferroelectric materials through adjusting the external excitation or the synthetically parameter (e.g., electric, temperature, and stress, etc.) employed in the model.
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Cumulative growth of successive minor hysteresis loops in Co/Pd multilayers with perpendicular anisotropy was studied in the context of time dependent magnetization reversal dynamics. We show that in disordered ferromagnets, where magnetization reversal involves nucleation, domains expansion and annihilation, differences between the time dependencies of these processes are responsible for accumulation of nuclei for rapid domain expansion, for the asymmetry of forward and backward magnetization reversals and for the respective cumulative growth of hysteresis loops. Loops stop changing and become macroscopically reproducible when populations of upward and downward nucleation domains balance each other and the respective upward and downward reversal times stabilize.
For the first time in a bulk proper uniaxial ferroelectrics, double antiferroelectric-like hysteresis loops have been observed in the case of Sn$_2$P$_2$S$_6$ crystal. The quantum anharmonic oscillator model was proposed for description of such polarization switching process. This phenomenon is related to three-well local potential of spontaneous polarization fluctuations at peculiar negative ratio of coupling constants which correspond to inter-site interaction in given sublattice and interaction between two sublattices of Sn$_2$P$_2$S$_6$ modeled crystal structure. Obtained data can be used for development of triple-level cell type memory technology.
A new mathematical model of hysteresis loop has been derived. Model consists in an extansion of tanh($cdot$) by extanding the base of exp function into an arbitrary positive number. The presented model is self-similar and invariant with respect to scaling. Scaling of magnetic hysteresis loop has been done using the notion of homogenous function in general sense.
Ferroelectric materials are characterized by degenerate ground states with multiple polarization directions. In a ferroelectric capacitor this should manifest as equally favourable up and down polarization states. However, this ideal behavior is rarely observed in ferroelectric thin films and superlattice devices, which generally exhibit a built-in bias which favors one polarization state over the other. Often this polarization asymmetry can be attributed to the electrodes. In this study we examine bias in PbTiO$_3$-based ferroelectric superlattices that is not due to the electrodes, but rather to the nature of the defects that form at the interfaces during growth. Using a combination of experiments and first-principles simulations, we are able to explain the sign of the observed built-in bias and its evolution with composition. Our insights allow us to design devices with zero built-in bias by controlling the composition and periodicity of the superlattices.
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