Selective Excitation of Terahertz Magnetic and Electric Dipoles in ${\mathrm{Er}}^{3+}$ Ions by Femtosecond Laser Pulses in ${\mathrm{ErFeO}}_3$

We show that femtosecond laser pulse excitation of the orthoferrite ${\mathrm{ErFeO}}_3$ triggers pico- and subpicosecond dynamics of magnetic and electric dipoles associated with the low energy electronic states of the ${\mathrm{Er}}^{3+}$ ions. These dynamics are readily revealed by using polarization sensitive terahertz emission spectroscopy. It is shown that by changing the polarization of the femtosecond laser pulse one can excite either electric dipole-active or magnetic dipole-active transitions between the Kramers doublets of the ${{}^{4}I}_{15/2}$ ground state of the ${\mathrm{Er}}^{3+}$ ($4f^{11}$) ions. These observations serve as a proof of principle of polarization-selective control of both electric and magnetic degrees of freedom at terahertz frequencies, opening up new vistas for optical manipulation of magnetoelectric materials.

Figure 1

Arrangement of magnetic moments of the ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Er}}^{3+}$ sublattices of ${\mathrm{ErFeO}}_3$ in the ${\mathrm{\Gamma }}_2$ (a) and ${\mathrm{\Gamma }}_4$ phases (b).

Figure 2

The energy level structure of the ground state ${{}^{4}I}_{15/2}$ of the ${\mathrm{Er}}^{3+}$ ion in ${\mathrm{ErFeO}}_3$ [18] and the possible transitions marked by arrows.

Figure 3

The geometry of the optical pump/THz emission experiment. The direction of the laser pulse propagation and of the THz emission; the measured polarization of the THz electric field are shown with respect to the crystallographic axes. (a) The $y$-cut sample emits electric field polarized in the ($xz$) plane. (b) The $x$-cut sample emits electric field polarized in the ($yz$) plane.

Figure 4

(a) The THz waveforms generated in the $y$-cut ${\mathrm{ErFeO}}_3$ at 20 K by circularly polarized light of opposite helicities. The half-difference of these waveforms is shown shifted along the vertical axis. (b) The spectrum of the helicity dependent contribution obtained by Fourier transformation of the waveform shown in (a) and fitted with three Lorentzian contours.

Figure 5

(a) The central frequencies of the spectral bands are shown vs temperature for the $x$-polarized emission from the $y$-cut ${\mathrm{ErFeO}}_3$ sample. (b) The same for the $z$-polarized emission from the $y$-cut sample. (c) The same for the $y$-polarized emission from the $x$-cut sample. In all panels, the filled symbols correspond to magnetic-dipole (squares) and electric-dipole (triangles) excited modes, which are not sensitive to the pump polarization. The open circles correspond to magnetic-dipole modes excited by the circularly polarized light. The gray area indicates the spin-reorientation temperature interval. The frequencies are assigned to the modes of ${\mathrm{Er}}^{3+}$ ions based on their symmetry.