Fractal perspective of RKKY exchange interactions in ${\mathrm{L}1}_0 \mathrm{FePt}$

This paper introduces an approach to approximating exchange interactions in FePt, characterizing their effect on the Curie temperature and magnetic anisotropy, properties crucial for heat-assisted magnetic recording. The proposed model employs the Ruderman-Kittel-Kasuya-Yosida (RKKY) function, offering a different perspective on magnetization processes within finite FePt grains. The RKKY function is derived as a specific instance of a fractal curve, such as the Jacobi elliptical function. The study showcases a holographic implementation of these exchange interactions, translatable into an atomistic spin dynamics model, yielding valid outcomes for finite-size scaling laws. The primary goal is to formulate an approximate spin Hamiltonian with fewer neighbors, enhancing the efficiency of simulations for the FePt which is a candidate for heat-assisted magnetic recording media. Additionally, the research delves into how the number of interactions per bond impacts magnetization evolution across different temperatures and system sizes. Our findings suggest that this model is more computationally efficient for Monte Carlo simulations than the comprehensive density-functional-theory-based spin Hamiltonian proposed by Mryasov et al.

Figure 1

Plot of Jacobi elliptic cn at different resolution scales: (a) and (b) show two-dimensional (2D) representations of $\frac{\text{cn}(u·k|s)}{u^3}$, where $k$ is set at 0.98, $s$ takes values from 0 to 1, and $u$ has different scale resolutions. (c) shows the exchange constant values at different distances calculated within DFT. The solid line represents the fit using Eq. (2) giving a value for $k_f$ around $0.98{\mathrm{nm}}^{-1}$. (d) illustrates a 3D plot of $\text{cn}(u,k)$ where $u$ varies between $-5\pi$ and $5\pi$.

Figure 2

The temperature magnetization dependence for different diameters of FePt cylinder and different cutoff ranges using the RKKY model of exchange interaction coupling.

Figure 3

The size distribution of Curie temperature for different ranges of cutoff. The solid lines stand for the fitting using Eq. (9). (a) shows the size distribution using the DFT-based Hamiltonian, and (b) corresponds to the RKKY model.

Figure 4

Plot of reduced free energy $\mathcal{F}$ for a FePt cylinder with a basal diameter of 5 nm and a height of 10 nm using a full DFT-Hamiltonian and RKKY function up to 5 u.c. range at different simulation temperatures.

Figure 5

Plot of scaling factor $n$ as a function of diameter of the $\text{L}{1}_0$ FePt cylinder using the RKKY function with a two-ion contribution. The shaded gray area shows the minimum to the maximum range that the scaling factor might vary.