Influence of Interplane Interactions on Formation of Magnetization Plateaus in Generalized 3D Ising Models with Magnetically Coupled Shastry-Sutherland Layers

Abstract

The combination of the standard Metropolis algorithm and the parallel tempering method is used to examine the influence of interplane interactions on the formation of magnetization plateaus in two types of generalized Ising models with magnetically coupled Shastry-Sutherland layers. In the first model, we consider the first (J1) and second (J2) intraplane and first (I1) and second (I2) interplane nearest neighbour (NN) interactions, while in the second one, we consider all intraplane and interplane interactions between spins inside an sphere of radius r < 6, and the interaction between two spins at Ri and Rj lattice sites is modeled by a simple one-parametric formula with exponentially decaying amplitudes $J_{\text {ij}} \sim e^{-\alpha |\textbf {R}_{\textbf {i}}-\textbf {R}_{\textbf {j}}|}$ . It is shown that the NN interplane interaction I1 does not change qualitatively the magnetic phase diagram of the model found for J1 and J2 (I1 = 0), while the next NN interaction I2 influences strongly both the stability regions of magnetic phases found for J1 and J2 (I1 = 0, I2 = 0) as well as the formation of new phases. In particular, we have found that the ferromagnetic interaction I2 suppresses the stability regions of magnetic plateau phases found for nonzero J1 and J2, while the antiferromagnetic I2 interaction forms, in addition to the standard 1/3 and 1/2 plateaus, the following set of new macroscopic magnetization plateaus: m/ms = 1/6,1/4,2/3, and 3/4. Practically the same plateaus are formed by the second model in the limit of strongly decaying spin interactions ( $\alpha \sim 4$ ), while in the opposite limit (α 1/2 and m/ms < 1/3 disappear and the magnetization curves become continuous in these regions.