Laser Excitation of Lattice-Driven Anharmonic Magnetization Dynamics in Dielectric ${\mathrm{FeBO}}_3$

Femtosecond laser pulses trigger in dielectric ${\mathrm{FeBO}}_3$ coherent oscillations of the magnetic anisotropy followed by spins. The oscillations are driven by optically excited lattice vibrations strongly coupled to the magnetic system. Unlike the spin resonances, this mode is characterized by a very small damping ratio and can be easily pushed into an anharmonic regime.

Figure 1

(a) Experimental geometry of the optical pump-probe setup. (b) Static Faraday rotation in ${\mathrm{FeBO}}_3$ as a function of in-plane external magnetic field. (c) Femtosecond laser excitation of short-living high frequency FMR mode at $f_{\mathrm{F}\mathrm{M}\mathrm{R}}=6.9\mathrm{GHz}$. (d) Femtosecond laser excitation of the long-living lattice-driven magnetic mode at $f=0.5\mathrm{GHz}$. The external magnetic field is 40 Oe and the pump fluence is $38\mathrm{m}\mathrm{J}/{\mathrm{c}\mathrm{m}}^2$. The sample thickness is $9\mu \mathrm{m}$. (e) Schematic representation of light-induced FMR. Instantaneously induced magnetic anisotropy $\delta {\mathbf{H}}_{\mathbf{a}}$ causes the magnetization $\mathbf{M}$ deviation from equilibrium followed by the precession around the effective magnetic fields ${\mathbf{H}}_{\mathbf{eff}}={\mathbf{H}}_{\mathbf{ext}}+{\mathbf{H}}_{\mathbf{a}}$. (f) Schematic representation of light-induced lattice-mediated oscillations of magnetic anisotropy. Ultrafast excitation of lattice induces periodic tensile and compression of the primitive cell, which generates a periodically modulated magnetic anisotropy $\delta {\mathbf{H}}_{\mathbf{a}}$ and leads to a change of the equilibrium ${\mathbf{H}}_{\mathbf{eff}}^{\prime }={\mathbf{H}}_{\mathbf{ext}}+{\mathbf{H}}_{\mathbf{a}}+\delta {\mathbf{H}}_{\mathbf{a}}$. In the present picture $f\ll f_{\mathrm{F}\mathrm{M}\mathrm{R}}$. For simplicity a bcc primitive cell with a magnetic atom (red) inside is chosen.

Figure 2

(a) Probe polarization rotation as a function of time delay between linearly polarized pump and probe pulses for different values of the applied magnetic field. (b) Field dependence of frequencies of two harmonics. (c) Experimental data (points) and theoretical fit based on the theory (solid lines) of the amplitudes of the 1st and the 2nd harmonics of spin oscillations as a function of magnetic field. Fit parameters are ${\mathrm{G}}_4=4.3\times {10}^7\mathrm{erg}/{\mathrm{cm}}^3$ and ${\mathrm{G}}_6=5.7\times {10}^4\mathrm{erg}/{\mathrm{cm}}^3$, and the laser-induced strain amplitude is $s_{zz}^0=3.3\times {10}^{-4}$. Sample thickness is $9\mu \mathrm{m}$. Pump fluence is $38\mathrm{m}\mathrm{J}/{\mathrm{c}\mathrm{m}}^2$.

Figure 3

(a) Magnetization deviation as a function of time for samples with various thicknesses. (b) Lowest frequency in the spectrum vs sample thickness: dots are experimental data, thick line is a hyperbolic fit $f=V_S/2d$. (c) Differential transmission signal for the sample with the thickness of $4\mu \mathrm{m}$. (e) Normalized FFT spectra of the Faraday rotation (black) and the differential transmission (red) for a $4\mu \mathrm{m}$ thick sample. Solid lines are Lorentzian fits. The external field is 25 Oe. Pump fluence is $38\mathrm{m}\mathrm{J}/{\mathrm{c}\mathrm{m}}^2$. The origin of the splitting of the $f$ line in the FFT spectrum for the Faraday rotation could be due to a nonlinearity of the magnetoacoustic interation and an inhomogeneity of the sample thickness over the probed area.

Figure 4

(a) Probe polarization rotation as a function of time delay between the linearly polarized pump and probe pulses for different values of pump fluence. (b) FFT spectrum for different pump fluences. (c) Pump fluence dependence of the observed harmonics. The dashed lines are guides to the eye. External magnetic field is 100 Oe. Sample thickness is $9\mu \mathrm{m}$.