Real-time electrical detection of coherent spin oscillations

We demonstrate that the bandwidth of pulsed electrically detected magnetic resonance can be increased to at least 80 MHz using a radio-frequency-reflectometry detection scheme. Using this technique, we measure coherent spin oscillations in real time during a resonant microwave pulse. We find that the observed signal is in quantitative agreement with simulations based on rate equations modeling the recombination dynamics of the spin system under study. The increased bandwidth opens the way to electrically study faster spin-dependent recombination processes, e.g., in direct semiconductors which so far have almost exclusively been studied by optically detected magnetic resonance.

Figure 1

(a) Basic concept of a pulsed EDMR measurement. The symmetry of the spin pair determines the recombination rate with parallel spin pairs recombining much slower than antiparallel spin pairs due to the Pauli principle. While conventional pulsed EDMR can only assess the state of the spin pair at the end of the mw pulse by measuring the photocurrent transient, rf-EDMR can directly monitor the coherent spin oscillations during the mw pulse shown on a logarithmic time scale. (b) Schematic of the rf-EDMR $LCR$ tank circuit and homodyne detection setup.

Figure 2

(a) Absolute value of the reflection coefficient $|S_{11}|$ as a function of the rf $f_{\mathrm{rf}}$. (b) Amplitude of the high-field ${}^{31}$P hyperfine peak measured by cw rf-EDMR as a function of $f_{\mathrm{rf}}$.

Figure 3

(a) Relative change of the sample resistance for different magnetic fields chosen such that the mw pulse resonantly excites the ${}^{31}$P spins (blue), the P${}_{\mathrm{b}0}$ spins (red), or none of the spins (black). To improve the signal-to-noise ratio, a lock-in detection scheme [23] is implemented employing square-wave frequency modulation with a frequency of 500 Hz. (b) Pulsed rf-EDMR spectrum recorded by boxcar integration of the $\Delta R/R$ transient after a 9.739 GHz mw pulse as a function of the magnetic field $B_0$. The spectral positions of the mw pulses used in (a) are indicated by the color-coded arrows. (c) Frequency of the oscillations $f_{\mathrm{Rabi}}$ depicted in (d) as a function of the square root of the mw power $P_{\mathrm{in}}$ showing a linear dependence (red line). (d) First two microseconds of the transients from (a) after subtraction of a second order polynomial background revealing oscillations on the two resonant traces. (e) Coherent spin oscillations measured by reconstructing the spin state after mw pulses of varying length $T_{\mathrm{p}}$ [13]. To this end, the preamplifier-detected current transient after each pulse is integrated resulting in a charge $Q$ proportional to the number of antiparallel spin pairs at the end of the pulse.

Figure 4

(a) Definition of the time constants of the ${}^{31}$P-P${}_{\mathrm{b}}0$ recombination process. (b) Simulation of the relative resistance change during and after a $2\text{−}\mu$s-long mw pulse. (c) First $2\mu$s of the data shown in panel (a) after subtraction of a second order polynomial background.