Effects of interactions on the relaxation processes in magnetic nanostructures

Controlling the relaxation of magnetization in magnetic nanostructures is key to optimizing magnetic storage device performance. This relaxation is governed by both intrinsic and extrinsic relaxation mechanisms and with the latter strongly dependent on the interactions between the nanostructures. In the present work we investigate laser induced magnetization dynamics in a broadband optical resonance type experiment revealing the role of interactions between nanostructures on the relaxation processes of granular magnetic structures. The results are corroborated by constructing a temperature dependent numerical micromagnetic model of magnetization dynamics based on the Landau-Lifshitz-Bloch equation. The model predicts a strong dependence of damping on the key material properties of coupled granular nanostructures in good agreement with the experimental data. We show that the intergranular, magnetostatic and exchange interactions provide a large extrinsic contribution to the damping. Finally we show that the mechanism can be attributed to an increase in spin-wave degeneracy with the ferromagnetic resonance mode as revealed by semianalytical spin-wave calculations.

Figure 1

Hysteresis loops for the series of CoPt with variable exchange. Increasing exchange leads to increasingly square loops as expected.

Figure 2

Example of a time resolved magnetization trace determined experimentally. Also shown in the inset is an example of the fit to data that was used to extract the damping, where the raw data is shown as points and fitted function is shown as a line.

Figure 3

Dependence of the measured Gilbert damping constant on the exchange field. A nonmonotonic dependence of $\alpha$ on $H_{ex}$ is clear. (Inset) Variation of the cluster size with exchange field determined using the method given in Ref. [13] and described in the text.

Figure 4

Schematic of the setup of the simulations. The anisotropy is perpendicular to the plane with the applied field at an angle $\theta$ to the plane. The magnetization equilibrates to $\mathbf{M}$ before the laser pulse is applied. The laser pulse results in relaxation of the magnetization by precession to the new orientation, ${\mathbf{M}}^{{}^{\prime }}$.

Figure 5

Numerically calculated hysteresis curves for a range of intergranular exchange constants in good qualitative agreement with the experimental hysteresis loops (Fig. 1).

Figure 6

Example of the transverse magnetization dynamics after a heat pulse (points) with a fit to the dynamics (lines). (Inset) Example of the longitudinal magnetization dynamics after a pulse.

Figure 7

Damping as a function of saturation magnetization for a range of values of the intergranular exchange, $H_{\mathrm{exch}}^{\mathrm{sat}}$.

Figure 8

Damping as a function of intergranular exchange for a range of values of saturation magnetization. For low values of $M_s$ the value of the damping varies very little and remains around the value of the input damping parameter. As $M_s$ increases, the variation with intergranular exchange becomes much greater as the interplay between the demagnetizing fields and exchange becomes important.

Figure 9

Spin-wave degeneracy (shown schematically in the inset) as a function of exchange stiffness for a range of values of saturation magnetization. There is clearly a direct correlation between the degeneracy and the damping shown in Fig. 3 and a similar trend for fixed exchange stiffness and varying ${\mathrm{M}}_s$.