Radiofrequency driving of coherent electron spin dynamics inn-GaAs detected by Faraday rotation

Abstract

We suggest a new pump-probe method for studying semiconductor spin dynamics based on pumping of carrier spins by a pulse of oscillating radiofrequency (rf) magnetic field and probing by measuring the Faraday rotation of a short laser pulse. We demonstrate this technique on n-GaAs and observe the onset and decay of coherent spin precession during and after the course of rf pulse excitation. We show that the rf field resonantly addresses the electron spins with Larmor frequencies close to that of the rf field. This opens the opportunity to determine the homogeneous spin coherence time T2, that is inaccessible directly in standard all-optical pump-probe experiments.Introduction. When a magnetic field B is applied to an ensemble of electron spins, they all precess with the Larmor frequency ω L = gµ B B/ , where g is the electron g factor, µ B is the Bohr magneton, and is the Planck constant. This ensemble precession is hardly detectable since the relative phases of the spins are random so that macroscopic spin polarization averages to zero. However, we can induce a common phase by applying a weak radiofrequency (rf) magnetic field oscillating with a frequency ω close to ω L . In analogy with a driven harmonic oscillator, the electron spins after some time will resume the frequency and phase of the rf field. As a result the in-phase spin precession motions form a macroscopic spin polarization that can be detected optically by measuring the Faraday/Kerr rotation of the linear polarization of a laser pulse which arrival time is synchronized with the rf field oscillation. By applying an rf field of finite duration and scanning the relative delay of the optical probe it is possible to measure the coherent electron spin dynamics.

Optical detection of electron spin dynamics driven by fast variations of a magnetic field: a simple method to measure $$T_1$$, $$T_2$$, and $$T_2^*$$ in semiconductors

“…The magnetic field amplitude generated by the coil is estimated from the current driven through the coil, its diameter and number of windings. The estimation is confirmed by measurements of the Rabi frequency 25 . The rf field pulse created by the coil acts as pump pulse in the spin dynamics experiment.…”

“…the onset of a transverse oscillating component of . Note that in an electron spin ensemble with inhomogeneous g -factor distribution, the rf field affects only the spins with for and the pulse duration longer than 25 unlike in the previous experiment, where all spins become involved. Thus, after the rf field is switched off, only these spins contribute to the spin polarization decay with a decay time close to rather than .…”

“…1 . The experiment is performed on a Si-doped GaAs sample with the electron concentration of (350-μm-thick bulk wafer) near the metal-to-insulator transition 20 , 25 . The sample is placed in a variable temperature He-bath cryostat ( T = 1.6–300 K) with a permanent magnet (NdFeB cube with 3.5 cm edge length) placed outside in a controllable distance (5-30 cm).…”

“…The delay between the pump rf pulses and the probe laser pulses is varied electronically using a function generator, see also Ref. 25 . The probe laser pulses are linearly polarized and their polarization after transmission through the sample is rotated by 45° with respect to the horizontal plane using a wave plate.…”

“…This method can be used also in the time-resolved mode (pulsed EPR) 22 – 24 . Recently, a combination of the pump-probe and EPR techniques was proposed, where the electron spin ensemble is driven by the rf pump pulse and the spin precession is probed optically by a laser pulse, for which the Faraday rotation is measured 25 . This radio-optical pump-probe technique is easy in implementation.…”