Standing Spin Waves as a Basis for the Control of Terahertz Spin Dynamics: Time Dependent Density Functional Theory Study

We report on the linear response density functional study of the magnetization dynamics in Co(100) film driven by a nonuniform magnetic field. At resonant frequencies in the terahertz range, the magnetic field excites standing spin waves of the system and the induced magnetization penetrates the whole volume of the film. The pattern of magnetization precession is strongly influenced by the spin-flip excitations of single electrons which lead to the Landau damping of the spin-wave modes. Our results pave the way for the precise control of terahertz magnetization dynamics in itinerant magnets.

Figure 1

The frequency dependence of the magnitude of the magnetization induced in the surface layer upon applying oscillating magnetic field in the same layer. The results are given in arbitrary units common for all figures in the paper. The inset shows the schematics of our theoretical experiment. $1\mathrm{THz}\approx 4.135\mathrm{meV}$.

Figure 2

The frequency dependence of the magnitude of the magnetization induced in different layers upon applying oscillating magnetic field in various layers. Two upper curves: the magnitude of magnetization induced in the 6th and 3rd layers upon application of the field in the 1st and the 3rd layers, respectively. The bottom curve presents the magnetization induced in the first layer by a field uniform in the whole film. The curves are shifted vertically for the sake of clarity.

Figure 3

Layer-resolved profile of induced magnetization upon applying oscillating magnetic field in the surface layer. Two resonant frequencies marked ${\omega }_{1,2}$ in Fig. 1 are considered together with their counterparts of opposite polarization ($-{\omega }_{1,2}$). The angles along the lines represent the relative phases of the moments in their precessional motion.

Figure 4

Spectral power of spin excitations. (a) Eigenvalues ${\chi }_{\lambda }^{+}(\omega )$ of the loss matrix, atomic units. Six Lorentzian peaks can be distinguished. The envelope denotes the sum over all the eigenvalues. (b) Corresponding eigenvectors. The arrows present layer-resolved transverse components of the magnetization at a certain moment in time. With time, all moments precess about the $z$ axis.