Terahertz Radiation from Magnetic Excitations in Diluted Magnetic Semiconductors

We probed, in the time domain, the THz electromagnetic radiation originating from spins in CdMnTe diluted magnetic semiconductor quantum wells containing high-mobility electron gas. Taking advantage of the efficient Raman generation process, the spin precession was induced by low power near-infrared pulses. We provide a full theoretical first-principles description of spin-wave generation, spin precession, and of emission of THz radiation. Our results open new perspectives for improved control of the direct coupling between spin and an electromagnetic field, e.g., by using semiconductor technology to insert the THz sources in cavities or pillars.

Figure 1

(a) Time-dependent radiated fields for various magnetic fields ($B$). A vertical offset is added for clarity. Fitted sinusoids are superposed. (b) (squares) Amplitude of the transient oscillation extracted from (a), as a function of the magnetic field. (line) Radiated amplitude calculated for one quantum well (see text). (Inset) Sketch of the experiment: a near-infrared (NIR) pulse (100 fs) with circular polarization is focused, with normal incidence, on the QW structure. The sample is immersed in a bath of superfluid helium inside a split-coil magnet with a static field $B$ up to 8 T applied along the quantum well plane (parallel to the $z$ direction). The THz transient electric field is collected along the $z$ direction [18].

Figure 2

(a) Transient electric field amplitude as a function of central wavelength of the pulse. The pulse energy was $136\mathrm{nJ}/{\mathrm{cm}}^2$. (b) Variation of the detected radiated amplitude (squares) with the pulse energy and comparison with the calculations carried to first order with Eqs. (3, 4) and to all orders [18]. (c) Fourier transforms of the electric field transients shown in Fig. 1a. Two peaks, labeled ${\nu }_1$ and ${\nu }_2$, are identified. The bottom curve is the result of linearly polarized excitation at $B=8\mathrm{T}$. All the curves above, from $B=0\mathrm{T}$ to $B=8\mathrm{T}$, are obtained with a circular pulse.

Figure 3

(a) ${\nu }_1$ (orange squares) and ${\nu }_2$ (red squares) are the frequencies present in the transient radiated field. Raman (blue dots) is the optical spin mode frequency determined by Raman measurements. The Raman determination is fitted with Eq. (1) for $x=1.75\%$, $T=2.34\mathrm{K}$, and $g_{\mathrm{e}}=-1.64$ (blue curve). Rabi are the frequencies given by Eq. (5) (dashed and dotted purple curves). ${\omega }_{\mathrm{Mn}}$ are the Mn precession frequencies from theory (dashed green curve) and simulations (solid green curve). ${\nu }_1$ num., ${\nu }_2$ num., and ${\nu }_1$ filtered are frequencies deduced from the simulated $S_x(t)$ before (red and orange curves) and after (light orange curve) filtering. (b) Normalized $S_x(t)$, $S_y(t)$, and $S_z(t)$ as calculated from Eq. (6) for $B=8\mathrm{T}$. The dashed $S_x(t)$ curve is obtained after numerical high-pass filtering. (c) $\mathbf{S}(t)$ (red) and $\mathbf{M}(t)$ (green) are the spin trajectories. The external magnetic field $B\mathbf{z}$ is vertical downward. After the pulse, electrons spins have been tilted in the $y$ direction with normalized $S_{y0}=0.4$, while the Mn spins are parallel to the $y$ axis. The latter precess slowly in the ($xy$) plane as indicated by the green arrow. Electron spins try to precess around the Mn spin axis as indicated by the orange arrow. After the relaxation of their transverse components (respective to the rotating Mn precession axis), the electron spins follow the slow Mn precession.