Resonant optical control of the structural distortions that drive ultrafast demagnetization in ${\mathrm{Cr}}_2{\mathrm{O}}_3$

We study how the color and polarization of ultrashort pulses of visible light can be used to control the demagnetization processes of the antiferromagnetic insulator ${\mathrm{Cr}}_2{\mathrm{O}}_3$. We utilize time-resolved second harmonic generation (SHG) to probe how changes in the magnetic and structural state evolve in time. We show that varying the pump photon-energy to excite either localized transitions within the Cr or charge transfer states leads to markedly different dynamics. Through a full polarization analysis of the SHG signal, symmetry considerations, and density functional theory calculations, we show that, in the nonequilibrium state, SHG is sensitive to both lattice displacements and changes to the magnetic order, which allows us to conclude that different excited states couple to phonon modes of different symmetries. Furthermore, the spin-scattering rate depends on the induced distortion, enabling us to control the timescale for the demagnetization process. Our results suggest that selective photoexcitation of antiferromagnetic insulators allows fast and efficient manipulation of their magnetic state.

Figure 1

(a) The absorbance of ${\mathrm{Cr}}_2{\mathrm{O}}_3$. Black markers correspond to measured values of our $10\mu \mathrm{m}$ thick sample at 77 K. The blue line is a guide to the eye based on the measurements found in Ref [21]. The ${}^{4}T_1$ and ${}^{4}T_2$ states correspond to transitions within crystal field split states of the Cr $3d$ levels which preserve the spin of the electron. The ${}^{2}E$ state corresponds to a spin-forbidden transition. The colored arrows indicate the pump wavelengths used in the time resolved experiments and the black dashed arrow corresponds to the second harmonic of the probe. (b) Polarization and temperature dependence of the SHG signal from ${\mathrm{Cr}}_2{\mathrm{O}}_3$ measured with a fundamental photon energy of 1.08 eV. Solid lines are fits to the data using Eq. (1). (c) Temperature dependence of the antiferromagnetic order parameter $l\left(T\right)$ extracted from the fits from (b) giving $T_{\mathrm{N}}=314\pm 5$ K. (d) Raman spectrum for two different excitation wavelengths, demonstrating coupling to $E_g$ modes is stronger for longer wavelengths at room temperature.

Figure 2

(a) Visible-pump SHG-probe signal at the three different pump photon energies, 3.0 eV (blue circles), 2.5 eV (green triangles), and 1.8 eV (red squares). Dashed lines correspond to the fits to Eq. (2). Arrows indicate the times at which the polarization dependence shown in Fig. 3 were performed. The inset shows a schematic of the counterpropagating pump-probe setup (P, polarizer; WP, wave plate; IF, interference filters). (b) Fluence dependence of the SHG transient signal at 3 eV from 0.25 to 2 mJ ${\mathrm{cm}}^{-2}$ showing linear behavior. Dashed lines correspond to fits using Eq. (2). (c) Fit parameters of the data in (b) showing that both the amplitude of the peak and plateau signal vary linearly with fluence. The ${\tau }_{\mathrm{pm}}$ time constant is independent of fluence.

Figure 3

(a) Change in the polarization dependence of the SHG probe at 0 ps for two perpendicular pump polarizations $(x,y)$. Lighter points are not measured and reconstructed from the symmetry of the signal. Dashed lines in the 3.0 eV $\left(A_{1g}\right)$ and 1.8 eV $\left(E_g\right)$ plots are fits for the $c_i$ coefficients at constant magnetization. (b) Change in the probe polarization dependence at 2 ps and corresponding fit to the scattering pattern when the AFM order parameter $l$ is reduced by 0.75%.

Figure 4

(a) Sketch of the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ unit cell in the $xy$ plane showing the $A_{1g}$ and (b) $E_g$ displacements of the oxygen ions around a Cr ion (darker colors correspond to atoms at different $z$ positions). (c) DFT calculations for changes in the magnitude of the nonlinear susceptibility for $A_{1g}$ and $E_g$ displacements of 0.05 Å. The shaded area corresponds to the measured region. The dashed line shows the calculated equilibrium spectrum.

Figure 5

Part of the unit cell centered on the Cr ion and nearest oxygen neighbors. Bold arrows correspond to the spin state. Photoexcitation at 1.8 eV excites electrons from the $t_{2g}$ levels into the $e_g$ levels while preserving the spin state. The resulting charge redistribution is anisotropic (blue corresponds to more positively charged regions, red more negative) and couples strongly to the anisotropic $E_g$ phonon mode. The electrons are then scattered to a spin-flipped $t_{2g}$ state in 400 fs. Thus the distortion is relaxed and the system is demagnetized. Excitation at 3 eV causes charge transfer from O to Cr. This causes a symmetric charge redistribution mapping onto the $A_{1g}$ phonon mode and scattering occurring within 300 fs.