Towards multiscale modeling of magnetic materials: Simulations of FePt

The established methods for the numerical evaluation of magnetic material properties exist only in certain limits, including first-principles methods, spin models, and micromagnetics. In the present paper, we introduce a multiscale modeling approach, bridging the gaps between the three approaches above. The goal is to describe thermodynamic equilibrium and nonequilibrium properties of magnetic materials on length scales up to micrometers, starting from first principles. In the first step, we model, as an example, bulk FePt in the ordered $\text{L}{1}_0$ phase by using an effective, classical spin Hamiltonian that was constructed earlier on the basis of first-principles methods. The next step is to simulate this spin model by using the stochastic Landau–Lifshitz–Gilbert equation. The temperature dependent micromagnetic parameters, which are evaluated with these atomistic simulations, are consequently used to develop a many macrospin micromagnetic approach, based on the Landau–Lifshitz–Bloch equation. As an example, we calculate the magnetization dynamics following a picosecond heat pulse resembling pump-probe experiments.

Figure 1

(Color online) Spontaneous equilibrium magnetization vs temperature for the atomistic FePt model. The solid line is a fit to the data extrapolating to $T_C$ as for an infinite system.

Figure 2

(Color online) Equilibrium parallel and transverse susceptibility vs temperature for our atomistic FePt model. The solid lines are fits extrapolating the critical behavior.

Figure 3

(Color online) Exchange stiffness vs temperature for the atomistic FePt model. The solid line is a fit extrapolating the critical behavior.

Figure 4

(Color online) Relaxation of the $z$ component of the magnetization for different temperatures. The data are from an atomistic simulation; the solid lines from a macrospin LLB model $\left(\lambda =0.1\right)$.

Figure 5

(Color online) Relaxation of one of the transverse components of the magnetization for different temperatures. The data are from an atomistic simulation; the solid lines from a macrospin LLB model $\left(\lambda =0.1\right)$.

Figure 6

(Color online) $z$ component of the magnetization vs time for two different pulse heights (750 and 550 K) with different pulse durations (1 and 3 ps) for atomistic (symbols) and single macrospin simulations (lines). In one case, the pulse height is below $T_C$ (circles) and in the other one (squares), well above $T_C$ $\left(\lambda =0.1\right)$.

Figure 7

(Color online) $z$ component of the magnetization vs time for different values of $\lambda$ for a $16\times 16\times 24$ macrospin model with $\Delta =3\text{nm}$. The pulse width is in all cases 1 ps and the height is varied from 550 K up to 850 K $\left(\lambda =0.1\right)$.