Dimensionally constrained D'yakonov–Perel' spin relaxation in n-InGaAs channels: transition from 2D to 1D

We investigate both the spin dynamics and the magnetotransport properties of two-dimensional (2D) n-InGaAs channels as a function of the channel width. We find that the electron spin scattering in the channels is limited by a dimensionally constrained D’yakonov–Perel’ mechanism, while the magnetotransport reveals purely 2D behaviour. For submicron channels the spin relaxation times increase for decreasing widths, while the magnetotransport data exhibit no band bending effects for the investigated samples. Temperature and photon energy dependent measurements rule out dissipative effects and further corroborate the experimental observation of a dimensionally constrained spin relaxation. Semiconductor spintronics seeks extra functionality compared with conventional electronics by exploiting the carrier spin degree of freedom [1]–[4]. For a potential information processing scheme which combines quantum mechanical and classical data, it is of particular interest to manipulate and to control carrier spin dynamics in non-magnetic materials by utilizing the spin–orbit interaction [5]–[8]. In threeand two-dimensional (3D and 2D) carrier systems, spin–orbit coupling creates a randomizing momentum-dependent effective magnetic field; the corresponding relaxation process is known as the D’yakonov–Perel’ (DP) mechanism [9]. In an ideal 1D system, a complete suppression of the DP spin relaxation has been predicted, 3 Author to whom any correspondence should be addressed. New Journal of Physics 9 (2007) 342 PII: S1367-2630(07)47415-8 1367-2630/07/010342+12$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 DEUTSCHE PHYSIKALISCHE GESELLSCHAFT if the lateral width of a 2D channel is reduced to be on the order of the electron mean free path [10]–[13]. The predictions are made for semiconductor heterostructures, such as InGaAs quantum wells, in which the spin–orbit interactions are dominated by structural inversion asymmetry (SIA) [14]–[19]. Such solid-state systems have been proposed as candidates for spintronic devices, including spin transistors [7], due to their potential scalability and compatibility with existing semiconductor technology [20]–[23]. For the regime approaching the 1D limit, we recently reported a progressive slowing of the spin relaxation in InGaAs channels, which is in agreement with a dimensionally constrained DP mechanism [24]. A similar dimensional crossover has been observed by means of a weak antilocalization analysis of magnetotransport studies on InAs channels [25]. The dimensional crossover can be understood in terms of an interplay between the channel width, the spin precession length over which the electrons remain spin polarized [26, 27], and the effect of spin scattering at the boundaries of the channels [28]. Here, we present additional magnetotransport measurements on the same 2D, n-doped InGaAs quantum well channels previously measured. The magnetotransport measurements reveal that the electron gases can be considered to be 2D for channel widths w larger than 500 nm, while the time-resolved Faraday rotation (TRFR) data on the spin dynamics can be understood in terms of a dimensionally constrained DP mechanism for w < 5μm. Temperature and photon energy dependent measurements demonstrate that energy dissipative effects play only a minor role to the spin dynamics in the channels. We further find that channels along the crystallographic directions [100] and [010] show longer spin relaxation times than channels along [110] and [−110]. We interpret the anisotropy such that the cubic spin-orbit coupling terms due to bulk inversion asymmetry (BIA) start to dominate the spin relaxation in the narrowest channels [27], [29]–[32]. For the narrowest channels, the spin relaxation process due to the Elliott–Yafet (EY) mechanism becomes important due to increased impurity scattering [33]. The spin splitting in a 2D quantum well due to SIA can be expressed in the form of an effective angular frequency vector as (k) = (1/lSP)[v(k)× ẑ], (1) with k the momentum vector and v(k) the velocity of an electron [3]. ẑ is the unit vector perpendicular to the quantum well, and lSP is the spin precession length, over which the electrons remain spin polarized. In the case of motional narrowing [34], the corresponding spin relaxation rate can be described as τ−1 SP = | (k)|2 τM/2, (2) with τM the momentum scattering time. Given a system with a fixed mean free path, a larger effective angular frequency induces faster spin rotations and, in turn, a shorter spin relaxation time. Figure 1(a) depicts the orientation of the spin eigenfunctions for two spin-split subbands E+ and E− of a zincblende quantum well in the presence of SIA (E+ and E− are defined as in [29]). For SIA, the spin eigenfunctions are always oriented perpendicular to k, and in turn, a constant value of | (k)| is expected that only depends on the magnitude of k. Figure 1(b) shows the orientation for the spin eigenfunctions in the case of BIA. Here, both the direction of the spin eigenfunctions and the absolute value of | (k)| depend significantly on the vector k [29]. The directions along [100] and [010] show similar behaviour, distinct from the directions [110] and [−110]. Therefore, we expect a k-vector anisotropy in spin systems where the DP spin relaxation due to BIA dominates the spin relaxation [35]. In particular, linear-in-k terms due to pure BIA New Journal of Physics 9 (2007) 342 (http://www.njp.org/) 3 DEUTSCHE PHYSIKALISCHE GESELLSCHAFT