Upper Limit of Carbon Concentration in Ferromagnetic L1₀-Ordered FePt-C for Tb/in² Data Storage Density Heat-Assisted Magnetic Recording Media

In high-density magnetic recording media, magnetically isolated grains are required to increase the signal-to-noise ratio (SNR). Carbon can be used to isolate FePt grains enabling their grain size smaller than 4.3 nm. Carbon atoms segregate to the boundaries during growth and provide an exchange-breaking layer, however, some other carbon atoms remain dissolved in the magnetic alloy. To identify the upper limit of carbon concentration in $L 1_{0}$ -ordered (Fe_0.5Pt_0.5)_100–xC_x, first-principles calculations are performed based on the density functional theory (DFT). The Brillouin function and Callen–Callen empirical relation determine the temperature-dependent magnetization and magneto-crystalline anisotropy energy enabling the determination of magnetic properties and Curie temperature required by 4 Tb/in² heat-assisted magnetic recording (HAMR) media and beyond. The calculated magnetization ( $M_{s}$ ) of $L 1_{0}$ -ordered (Fe_0.5Pt_0.5)_100–xC_x decreases to 770 emu/cm³ at $x =20$ from 1030 emu/cm³ at $x = 0$ at 300 K, and the magnetocrystalline anisotropy constant ( $K_{u}$ ) to 2.05 MJ/m³ at $x =20$ from 15.48 MJ/m³ at 300 K. It is striking to find that the Curie temperature ( $T_{C}$ ) increases to 728 K at $x =20$ from 719 K at $x =0$ . Regardless of carbon concentration, the magnetic anisotropy direction is the out-of-plane. Combining $M_{s}$ and $K_{u}$ at 300 K with $T_{C}$ , the $M_{s}$ – $K_{u}$ –C concentration relation is plotted to guide the design of $L 1_{0}$ -ordered Fe-Pt film for Tb/in² recording media. It is found that the upper limit of carbon concentration is determined to be about 12 at.% to retain $M_{s} \ge800$ emu/cm³, $T_{C} \ge430$ K, and $K_{u} \ge 5$ MJ/m³, which are necessary to achieve areal densities of 4 Tb/in² and beyond.