Sum-frequency excitation of coherent magnons

Coherent excitation of magnons is conventionally achieved through Raman scattering processes, in which the difference-frequency components of the driving field are resonant with the magnon energy. Here, we describe mechanisms by which the sum-frequency components of the driving field can be used to coherently excite magnons through two-particle absorption processes. We use the Landau-Lifshitz-Gilbert formalism to compare the spin-precession amplitudes that different types of impulsive stimulated and ionic Raman scattering processes and their sum-frequency counterparts induce in an antiferromagnetic model system. We show that sum-frequency mechanisms enabled by linearly polarized driving fields yield excitation efficiencies comparable or larger than established Raman techniques, while elliptical polarizations produce only weak and circular polarizations no sum-frequency components at all. The mechanisms presented here complete the map for dynamical spin control by means of Raman-type processes.

Figure 1

Fundamental one-magnon scattering processes of photons and coherent infrared-active phonons. (a) Impulsive stimulated Raman scattering, (b) ionic Raman scattering, (c) two-photon absorption, (d) two-phonon absorption. (e) Schematic frequency spectrum of a magnon and optomagnetic drives in the visible and terahertz range. Shown are the frequency of the magnon, ${\mathrm{\Omega }}_{\mathrm{m}}$ (green), the center frequencies of the visible and terahertz pulses, ${\omega }_{\mathrm{VIS}}$ (blue) and ${\omega }_{\mathrm{THz}}$ (red), as well as the difference- and sum-frequency components of the respective driving forces, ${\omega }_1-{\omega }_2$ and ${\omega }_1+{\omega }_2$. In this example, the difference-frequency components of the visible-light pulse and the sum-frequency components of the terahertz pulse overlap with the magnon mode and are therefore able to excite it.

Figure 2

Schematic of the pump-probe geometry. The spins of the antiferromagnetic model are aligned along the $z$ direction. The in-plane magnon mode excited by the pump pulse in this geometry (either directly, or through coherently excited phonons) distorts the spins antiferromagnetically along the $y$ direction, $l_y\left(t\right)$, as well as ferromagnetically along the $x$ direction, $m_x\left(t\right)$. The probe pulse then undergoes a Faraday rotation $\theta \left(t\right)$, which follows the oscillation of $m_x\left(t\right)$.

Figure 3

Spin dynamics induced by the inverse Faraday and inverse Cotton-Mouton effects. In (a)–(d), we compare the effective magnetic fields, $B_s^{\mathrm{IFE}}$ and $B_1^{\mathrm{ICME}}$, produced by the different optical drives in the near-infrared (${\omega }_0\equiv 1$ eV, $\tau =90$ fs) and terahertz (${\omega }_0=2.5\mathrm{THz}, \tau =1$ ps and ${\omega }_0\equiv 0.5\mathrm{THz}, \tau =5$ ps) spectral ranges in the 5 THz and 1 THz magnon systems. With these parameters, all three pulses have the same total energy. In (e)–(h) we compare the Faraday rotations $\theta$ around the $x$ direction arising from the spin dynamics induced by the effective magnetic fields. The Faraday rotations are directly proportional to the induced spin-precession amplitudes, $\theta \left(t\right)\propto \mathbf{m}\left(t\right)$, see Eq. (28). Both the effective magnetic fields and the rotations are normalized to those generated by the respective high-frequency drives, $B_0$ and ${\theta }_0$.

Figure 4

Spin dynamics induced by the phonon inverse Faraday and phonon inverse Cotton-Mouton effects. In (a)–(d), we compare the effective magnetic fields, $B_s^{\mathrm{PIFE}}$ and $B_1^{\mathrm{PICME}}$, produced by the different phonons (15, 2.5, and 0.5 THz) in the 5 THz and 1 THz magnon systems. In (e)–(h) we compare the Faraday rotations $\theta$ around the $x$ direction arising from the spin dynamics induced by the effective phonomagnetic fields. The Faraday rotations are directly proportional to the induced spin-precession amplitudes, $\theta \left(t\right)\propto \mathbf{m}\left(t\right)$, see Eq. (28). Both the effective magnetic fields and the rotations are normalized to those generated by the respective high-frequency drives, $B_0$ and ${\theta }_0$.

Figure 5

Time evolution of the phonon amplitudes $Q_z$ in response to the excitations by resonant terahertz pulses. (a) 15 and 2.5 THz phonons in the 5 THz magnon system, and (b) 15 and 0.5 THz phonons in the 1 THz magnon system. We chose the pulse energies such that the maxima of $Q_z$ are equal for the high- and low-frequency phonons, respectively. In the case of circular excitation, $Q_y$ (not shown) is shifted in phase by $\pi /4$ with respect to $Q_z$ and in the case of linear excitation it is in phase with $Q_z$.