Nonlinear Decay of Quantum Confined Magnons in Itinerant Ferromagnets

Quantum confinement leads to the emergence of several magnon modes in ultrathin layered magnetic structures. We probe the lifetime of these quantum confined modes in a model system composed of three atomic layers of Co grown on different surfaces. We demonstrate that the quantum confined magnons exhibit nonlinear decay rates, which strongly depend on the mode number, in sharp contrast to what is assumed in the classical dynamics. Combining the experimental results with those of linear-response density-functional calculations we provide a quantitative explanation for this nonlinear damping effect. The results provide new insights into the decay mechanism of spin excitations in ultrathin films and multilayers and pave the way for tuning the dynamical properties of such structures.

Figure 1

(a) SPEELS spectra recorded on 3 ML $\mathrm{Co}/\mathrm{Ir}(001)$ at $(q_x,q_y)=(0.3,0.3){\AA }^{-1}$. $I_{\downarrow }$ ($I_{\uparrow }$) represents the spectrum when the spin polarization of the incoming electron beam is parallel (antiparallel) to the magnetization. The difference spectrum $I_{\downarrow }-I_{\uparrow }$ is shown in the lower panel. (b) The difference spectrum and the fits used to extract the dispersion relation and the lifetime of different quantum confined magnons indicated by $n=0–2$. (c) The dispersion relation of all confined magnon modes. The experimental data are shown by symbols and the calculated magnon Bloch spectral function using our adiabatic approach is presented as the color map. The dotted line shows the place in the surface Brillouin zone, where the spectra shown in (a) and (b) are recorded. (d) $\mathrm{Im}\chi (\omega ,\mathbf{q})$ at $(q_x,q_y)=(0.3,0.3){\AA }^{-1}$ calculated by LRTDDFT and convoluted with the experimental broadening.

Figure 2

The magnon linewidth versus energy for all quantum confined magnon modes in 3 ML Co on (a) Ir(001) and (b) Cu(001). The experimental results are shown by diamonds and the results of LRTDDFT calculations are shown by circles. The filled (open) symbols represent the data along the $\overline{\mathrm{\Gamma }}–\overline{\mathrm{M}}$ ($\overline{\mathrm{\Gamma }}–\overline{\mathrm{X}}$) direction. The black diamonds in (a) represent the results of the $n=0$ magnon mode of 3 ML $\mathrm{Co}/\mathrm{Ir}(111)$.

Figure 3

(a) The magnon Bloch spectral function of 3 ML Co on Ir(001) based on adiabatic calculations. The color scale represents the amplitude of the spectral function. The magnonic bands of a 4 ML film are also shown by the light-gray curves. The multimagnon scattering processes of the $n=1$ magnon mode within the 3 ML terraces are shown by the solid arrows. The decay processes within the terraces of different thicknesses (3 and 4 ML) are shown by the dashed arrows. (b) The magnonic density of states for a 3 and 4 ML film calculated based on the adiabatic approach. The direct decay of the $n=1$ magnon mode of the 3 ML film to the $n=0$ and $n=1$ of a 4 ML film is illustrated with the dashed arrows. The horizontal dotted light-blue line denotes the energy of the bottom of the $n=1$ mode of the 3 ML system (at $q_{\parallel }=0$), where this mode can scatter to the other modes. The indirect decay of the $n=2$ magnon mode of the 3 ML film to the $n=2$ and $n=1$ modes of the 4 ML film is schematically shown by the dotted black arrows.