High-frequency magnon excitation due to femtosecond spin-transfer torques

Femtosecond laser pulses can induce ultrafast demagnetization as well as generate bursts of hot-electron spin currents. In trilayer spin valves consisting of two metallic ferromagnetic layers separated by a nonmagnetic one, hot-electron spin currents excited by an ultrashort laser pulse propagate from the first ferromagnetic layer through the spacer, reaching the second magnetic layer. When the magnetizations of the two magnetic layers are noncollinear, this spin current exerts a torque on magnetic moments in the second ferromagnet. Since this torque is acting only within the subpicosecond timescale, it excites coherent high-frequency magnons, as recently demonstrated in experiments. Here, we calculate the temporal shape of the hot-electron spin currents using the superdiffusive transport model and simulate the response of the magnetic system to the resulting ultrashort spin-transfer torque pulse by means of atomistic spin-dynamics simulations. Our results confirm that the acting spin-current pulse is short enough to excite magnons with frequencies beyond $1\mathrm{THz}$, a frequency range out of reach for current-induced spin-transfer torques. We demonstrate the formation of thickness-dependent standing spin waves during the first picoseconds after laser excitation. In addition, we vary the penetration depth of the spin-transfer torque to reveal its influence on the excited magnons. Our simulations clearly show a suppression effect of magnons with short wavelengths already for penetration depths in the range of $1\mathrm{nm}$, confirming experimental findings reporting penetration depths below $2\mathrm{nm}$.

Figure 1

Studied trilayer structure $\mathrm{FM}1\left|\mathrm{NM}\right|\mathrm{FM}2$ made of two ferromagnetic layers (FM1 and FM2) separated by a nonmagnetic one (NM). Magnetic moments are presented by the red arrows. Layer FM1, which is assumed to have perpendicular magnetic anisotropy, is excited by a femtosecond laser pulse from the back of the device. A spin current of hot electrons (green balls) generated in FM1 is transmitted through the NM layer into FM2, where it exerts a spin-transfer torque on the magnetic moments, causing spin-wave excitations.

Figure 2

Laser fluence of the laser pulse and calculated superdiffusive hot-electron spin current $j_s$ per atom entering the second FM as a function of time $t$. Note that the maximum of the laser pulse is at $t_0=150\mathrm{fs}$.

Figure 3

Calculated spatial profile of the transverse magnetization components at different times.

Figure 4

Frequency spectra of the excited magnetization dynamics. Top: Calculated averaged magnetization components $\langle m_y\rangle$ and $\langle m_z\rangle$ of the last layer in the system. Bottom: Amplitude of the magnons as a function of frequencies obtained by Fourier transformation of the magnetization data.

Figure 5

Frequency of magnons as a function of the wave vector for one-dimensional spin-wave propagation. The red points show data obtained by our numerical simulations, whereas the red and blue lines show the analytical model based on Eqs. (9) and (11). The dotted red line shows a fit to the data points.

Figure 6

Magnon frequency spectra for different thicknesses of FM2. The red lines show the spin-wave amplitude as a function of the frequency obtained by Fourier transformation in time of the magnetization of the last layer. The vertical black lines illustrate the predicted peak positions for standing waves with wave vectors given by Eq. (8).

Figure 7

Calculated magnon amplitudes as a function of the frequency for different penetration depths ${\lambda }_{\mathrm{s}}$.

Figure 8

Calculated spin-wave amplitudes as a function of wave vector $q_z$ obtained by space-domain Fourier transformation at different times. For better visualization of the occurring peaks in the Fourier spectrum, the data at different times are shifted upwards with increasing time.

Figure 9

Lifetime of magnons as a function of the frequency given by Eq. (16) and a damping constant of $\alpha =0.01$.

Figure 10

Exchange interactions for the six nearest neighbors calculated for a bcc Fe lattice as a function of the distance between the atoms. The distance is given in units of the Fe lattice constant $a$.

Figure 11

Magnon frequency spectra computed for the nearest-neighbor approximation to the exchange interactions. The red line shows the spin-wave amplitude as a function of the frequency obtained by a time-domain Fourier transformation of the magnetization of the last layer. The vertical black lines illustrate the predicted peak positions for standing waves with wave vectors given by Eq. (8).