Temperature dependence of the frequencies and effective damping parameters of ferrimagnetic resonance

Recent experiments on all-optical switching in GdFeCo and CoGd have raised the question about the importance of the angular momentum or the magnetization compensation point for ultrafast magnetization dynamics. We investigate the dynamics of ferrimagnets by means of computer simulations as well as analytically. The results from atomistic modeling are explained by a theory based on the two-sublattice Landau-Lifshitz-Bloch equation. Similarly to the experimental results and unlike predictions based on the macroscopic Landau-Lifshitz equation, we find an increase in the effective damping at temperatures approaching the Curie temperature. Further results for the temperature dependence of the frequencies and effective damping parameters of the normal modes represent an improvement of former approximated solutions, building a better basis for comparison to recent experiments.

Figure 1

Schematic of the two resonance modes in ferrimagnets. (a) For the ferromagnetic mode, the sublattices remain antiparallel; (b) for the exchange mode, the sublattices are tilted at a characteristic angle.

Figure 2

Temperature dependence of the equilibrium magnetization of the sublattices. At the magnetization compensation point, $T_{\mathrm{M}}$, the sublattice magnetizations cancel each other, while at the angular momentum compensation point, $T_{\mathrm{A}}$, the angular momenta of both sublattices are equal. Above the critical point $T_{\mathrm{C}}$ the system is paramagnetic.

Figure 3

Frequencies and effective damping parameters in the zero-anisotropy case. Temperature dependence of (a) frequencies and (b) effective damping parameters ${\alpha }_{\mathrm{eff}}$. Numerically obtained data points are compared with analytical solutions. The switching of the external magnetic field ${\mathbf{H}}^0$ leads to a gap in the solutions at the magnetization compensation point $T_{\mathrm{M}}$.

Figure 4

Frequencies and effective damping parameters in the finite-anisotropy case. Temperature dependence of (a) frequencies and (b) effective damping parameters ${\alpha }_{\mathrm{eff}}$. Numerically obtained data points are compared with analytical solutions.

Figure 5

Frequencies and effective damping parameters in the finite-anisotropy case. Temperature dependence of (a) the ferromagnetic mode frequency, (b) the exchange mode frequency, and (c) the effective damping parameter ${\alpha }_{\mathrm{eff}}$ of the FMM for different strengths of the magnetocrystalline anisotropy. Analytical results as explained in the text.