Dynamic hysteretic features of Ising-type thin films

In order to elucidate the nature of hysteresis characteristics in a magnetic Ising-type thin film with a certain thickness, such as types of frequency dispersion curves, decay of hysteresis loop area, corresponding coercive field and remanent magnetization values, etc., we investigate the hysteretic response of each layer within effective-field theory. Throughout the analysis, the best appropriate parameter values are chosen since they would allow us to observe the reversed magnetic hysteresis after a certain value of external field frequency. This eccentric phenomenon has prompted us to associate it to the domain nucleation and growth mechanism in the dynamic process. Exotic shapes of the response for different layer indices in two different regimes of modified surface exchange are particularly emphasized.

Figure 1

The frequency dispersion of HLA for each layer of $L=7$ at a fixed temperature $k_{B}T/J_3=3.5$. The curves were plotted for the selected amplitude representatives as $h_0=1.0$ and $2.5$ in each group of triple columns. The sequence of dispersions is reversed in two different regimes of modified exchange interaction.

Figure 2

The frequency dispersion of a coercive field for the same selected system parameters of the film depicted in Fig. 1. The sequence of dispersions is reversed in two different regimes of modified exchange interaction.

Figure 3

The frequency dispersion of remanent magnetization for the same selected system parameters of the film depicted in Fig. 1. The sequence of dispersions is reversed in two different regimes of modified exchange interaction.

Figure 4

Well-selected hysteresis collection of each layer for the film with thickness $L=7$. Modified exchange interaction ${\Delta }_s$ ranges from 0.0053 (first column) to 0.3053 (second column) and 0.6053 (third column) with varying frequency as $\omega =0.07$, $0.3$, and $0.53$ for related amplitude representatives at $k_{B}T/J_3=3.5$. The reader can recognize the hierarchical evolution in the print gray-scale version by following the Supplemental Material given in in Ref. [19]. Here we note that the surface loop ($k=1$) is more saturated in any case for ${\Delta }_s<{\Delta }_s^{*}$ value and the sequence of hysteresis is reversed in two different regimes of modified exchange interaction.