Manipulation of ferromagnetism with a light-driven nonlinear Edelstein-Zeeman field

Abstract

Optical control of magnetization is often symmetry-forbidden because electric fields and magnetization transform differently under inversion and time-reversal. However, through even-order nonlinear response, optical excitation can generate a nonequilibrium magnetic density (the nonlinear Edelstein effect) that acts as an internal Edelstein-Zeeman field coupling to slower magnetic degrees of freedom. Here we demonstrate non-thermal, ultrafast optical control of ferromagnetism in the centrosymmetric van der Waals semiconductor Cr$_2$Ge$_2$Te$_6$ via a resonant nonlinear Edelstein effect. Using time-domain THz emission spectroscopy under near-infrared excitation, we directly observe magnetic dipole radiation arising from optically driven magnetization dynamics. The polarization, fluence, and temperature dependences of the THz emission are quantitatively captured by a mean-field description of a weakly anisotropic Heisenberg ferromagnet subject to an Edelstein-Zeeman field. Our results establish a general nonequilibrium route to optical control of magnetism in centrosymmetric materials.

Figures (4)

• Figure 1: Illustration of ferromagnetic control through the Edelstein-Zeeman field. In the presence of intense above-gap infrared electric field, $\bm{E}_{\rm{IR}}(t)$, a. the nonlinear Edelstein effect is produced in a globally centrosymmetric semiconducting sample, leading to a nonequilibrium inter-band coherence that rectifies with $\bm{E}_{\rm{IR}}(t)$ at second-order. Spin-orbit coupling at locally non-centrosymmetric sites in the unit cell will produce a hidden spin texture in the bands indicated by the purple and orange arrows which form Kramers' pairs at each momentum. The nonequilibrium electric dipole currents and electric quadrupole transitions dynamically split the Kramers' degeneracy, contributing to the b. total external field $\bm{H}_\mathrm{eff}(t)$ capable of driving the slower dynamics of the ferromagnetic moment, $\bm{M}(t)$. Consequently, low-frequency THz radiation is emitted through the magnetic dipole channel.
• Figure 2: THz emission from Cr$_2$Ge$_2$Te$_6$.a. Crystal structure of bulk Cr$_2$Ge$_2$Te$_6$. b. Schematic of the THz emission experiment. Near-infrared pump pulses (1.2 eV) are incident normal to the crystallographic ab-plane. The pump polarization angle $\varphi$, defined with respect to the crystal a-axis, is controlled using a half-wave plate, and the emitted THz field component parallel to the a-axis is detected. c. Time-domain THz emission waveform $E{\mathrm{THz}}$ as a function of pump-delay time $t{\mathrm{delay}}$. d. Pump polarization dependence of the THz emission amplitude at 7 K for low and high pump fluence. e. Pump polarization dependence of the THz emission measured at 7 K (ferromagnetic phase), 80 K (just above $T_c$), and 200 K (paramagnetic phase), with the fluence fixed at 100 $\mu$J/cm$^2$. f. Temperature dependence of the THz emission amplitude at a fluence of 100 $\mu$J/cm$^2$. The ferromagnetic phase is shaded in blue, and $T_c$ denotes the Curie temperature. Inset: dashed line indicates the pump polarization angle used for the temperature-dependent measurements.
• Figure 3: THz emission from Cr$_2$Ge$_2$Te$_6$ at 45$^\circ$ incidence.a. Schematic of the THz emission geometry at 45$^\circ$ pump incidence, with the emitted $p$-polarized THz field detected. b. Time-domain THz waveforms measured at 7 K with the pump polarization aligned parallel to the crystal a-axis. Traces at low and high pump fluence are shown in yellow and red, respectively. c. Pump polarization dependence of the THz emission amplitude at low and high pump fluence. d. Time-domain THz emission signal $E_{\mathrm{THz}}$ as a function of pump fluence, with the corresponding frequency spectra shown on the right.
• Figure 4: a. Deformation of the uniaxial Heisenberg ferromagnetic free energy by the in-plane Edelstein-Zeeman field $H^\mathrm{EZ}_y$ above the Curie temperature $T_c$ and in the presence of the planar Edelstein-Zeeman field $H^\mathrm{EZ}_y$. The magnetization vectors in the $(M_y, M_z)$-plane that minimize the free energy is shown below the schematic free energy surfaces. The color scale on the surfaces and contour plots correspond to the value of free energy. b. Simulated light-induced in-plane magnetization as a function of pump-fluence. c. Spectral weight of THz emission as a function of fluence at normal incidence. d. Simulated light-induced magnetization at $45^\circ$ incidence as a function of pump-fluence. e. Spectral weight of THz emission as a function of fluence at $45^\circ$ incidence.