Spin dynamics of magnetic nanoparticles: Beyond Brown’s theory

An investigation of thermally induced spin dynamics of magnetic nanoparticles is presented. We use an atomistic model for the magnetic interactions within an effective, classical spin Hamiltonian constructed on the basis of first-principles calculations for $L{1}_0$ FePt. Using Langevin dynamics we investigate how the internal degrees of freedom affect the switching behavior at elevated temperatures. We find significant deviations from a single-spin model, arising from the temperature dependence of the intrinsic properties, from longitudinal magnetization fluctuations, and from both thermal and athermal finite-size effects. These findings underline the importance of atomistic simulations for the understanding of fast magnetization dynamics.

Figure 1

(Color online) Top: Absolute value of reduced magnetization versus temperature for different particle sizes. Equilibrium values are compared with values during switching. Bottom: Corresponding anisotropy energy constant per spin.

Figure 2

(Color online) Switching times vs inverse temperature for different particle sizes. Top: Comparison of our numerical data with the escape time following Brown’s formula. Bottom: Comparison of the same numerical data with a Brown-type formula where the temperature dependence of $K_1\left(T\right)$ and $M\left(T\right)$ is taken into account.

Figure 3

(Color online) Dynamic coercivity vs temperature for different particle sizes. The solid lines are Eq. (3) where the temperature dependence of $K_1\left(T\right)$ and $M\left(T\right)$ is taken into account.