The 1999 demonstration by Ohno, Young, Beschoten, Matsukura, Ohno and Awschalom of electrical spin injection from the ferromagnetic semiconductor (Ga,Mn)As into a non-magnetic (In,Ga)As quantum well established hysteretic, magnetization-tracking circular polarization of the electroluminescence, but left the magnitude and parameter dependences of that polarization without a quantitative explanation. This problem asks for a mechanism-resolved quantitative account of the electroluminescence polarization emitted by these spin-light-emitting diodes: predicting its degree from the band structure, transport, and optical properties of (Ga,Mn)As and the device, identifying the mechanisms behind its dependence on GaAs spacer thickness, injection current density, and light-collection geometry, and fixing the roles of hole spin relaxation during transport through the GaAs spacer and across interfaces and of heavy-hole/light-hole (valence-band) mixing in the quantum well. A direct experimental follow-up by the same collaboration in 2002 sharpened the phenomenology (a monotonic spacer-thickness dependence for vertical collection, a fourteen-fold anisotropy between collection directions, and a sign reversal beyond roughly 220 nm) while stating that the underlying mechanism remained unclear. The constituent threads of the problem have been characterized and constrained but not jointly resolved, so the problem remains open.

Background

Spintronics seeks to exploit the spin angular momentum of carriers, in addition to their charge, for information processing and storage. A central requirement is electrical spin injection: creating a population of spin-polarized carriers in a non-magnetic semiconductor by driving current through a spin-polarizing contact. Early attempts with ferromagnetic metal contacts on semiconductors were hindered by the conductivity-mismatch problem (the large conductivity difference between a metal and a diffusive semiconductor which suppresses spin polarization of the injected current) and by the injection of high-energy carriers that depolarize rapidly. A route proposed to avoid both obstacles was to use a ferromagnetic semiconductor as the injector, since it is lattice-matched to III-V heterostructures and supplies spin-polarized carriers in quasi-equilibrium. The canonical such material is (Ga,Mn)As, a diluted magnetic semiconductor (a III-V host in which a fraction of Ga sites is replaced by magnetic Mn ions, producing hole-mediated ferromagnetism below a Curie temperature of order 50–200 K in early samples).

The natural testbed is the spin light-emitting diode (spin-LED): a p-i-n (p-type/intrinsic/n-type) heterostructure in which spin-polarized holes from a ferromagnetic p-type layer traverse an undoped GaAs spacer of thickness d and recombine in a strained (In,Ga)As quantum well (QW) with unpolarized electrons injected from the n-side. Because interband optical selection rules link the carrier spin to the photon helicity, the circular polarization of the electroluminescence (EL), P=(σ+−σ−)/(σ++σ−)P=(\sigma^+-\sigma^-)/(\sigma^++\sigma^-) with σ±\sigma^\pm the right- and left-circularly polarized spectral intensities, serves as an optical spin detector for the injected holes. In the idealized selection-rule picture the QW ground state is a pure heavy-hole (HH) exciton, whose angular momentum is pinned along the growth axis, and the circular polarization is directly proportional to the hole spin polarization along the observation direction. In reality, heavy and light holes (LH) mix in strained or confined structures; Uenoyama and Sham (1990) and Maialle (1998) showed theoretically that hole spin relaxation and valence-band mixing in quantum wells strongly modify the polarization of the emitted light, so the conversion between carrier spin polarization and measured optical polarization is itself a nontrivial part of the problem.

Ohno et al. (Nature 402, 790 (1999)) realized this program: in (Ga,Mn)As/GaAs/(In,Ga)As devices they observed EL polarization that is hysteretic in in-plane magnetic field below the Curie temperature, whose remanent value follows the independently measured (Ga,Mn)As magnetization, and which disappears in control devices (a non-magnetic GaAs:Be layer, and optical excitation of a contactless magnetic sample, the latter excluding reabsorption artifacts from the strong magnetic circular dichroism of (Ga,Mn)As, i.e. its magnetization-dependent differential absorption of the two circular polarizations). Hysteretic polarization persisted for spacers from 20 to 220 nm, while the polarization amplitude showed no systematic dependence on spacer thickness or injection current density, and the signal depended on the collection geometry (the light was collected from a cleaved facet, in the plane of the layers). The authors noted that a detailed theoretical understanding of the band structure, transport, and optical properties of (Ga,Mn)As was lacking, so the expected degree of EL polarization could not be quantitatively predicted, and that hole spin relaxation during transport through the GaAs spacer and across interfaces, and valence-band mixing in the QW, required further investigation.

The physics that makes this hard is now partially mapped. Holes in GaAs experience strong spin-orbit coupling: femtosecond measurements (Hilton and Tang, 2002) show spin-polarized holes in bulk GaAs relaxing on roughly hundred-femtosecond timescales, and later spin-LED work treats hole spin diffusion lengths of order tens of nanometers as the limiting design constraint for hole-injection devices — in evident tension with polarization surviving 20–220 nm of spacer transport. Quantum confinement and strain pin the HH angular momentum along the growth direction and the LH angular momentum in the layer plane, so polarization measured along different collection axes probes different hole spin components with different efficiencies; experiments on other spin-LED material systems (Fiederling et al., 2003; Kioseoglou et al., 2005) confirmed that emission geometry and heavy-/light-hole degeneracy drastically change what the measured circular polarization means. On the injector side, the mean-field and multiband theories of (Ga,Mn)As (Dietl et al., 2000; König, Jungwirth and MacDonald, 2001; Jungwirth et al., 2006; Dietl and Ohno, 2014) developed a quantitative picture of its valence band, hole spin polarization, and magnetotransport, and general frameworks for spin-polarized bipolar transport and optical orientation exist (Žutić, Fabian and Das Sarma, 2004; Fabian and Žutić, 2008). What has not been produced is the combination of these ingredients into a quantitative, experimentally validated account of the EL polarization actually emitted by the (Ga,Mn)As-based devices.

Problem Statement

Provide a quantitative, mechanism-resolved account of the circular polarization of the electroluminescence emitted by (Ga,Mn)As/GaAs/(In,Ga)As spin-light-emitting diodes under forward bias, of the type first reported by Ohno et al. (1999). Concretely: (1) starting from the band structure, transport, and optical properties of (Ga,Mn)As and of the GaAs/(In,Ga)As quantum well, predict the expected degree of EL polarization of these structures, including how it scales with the (Ga,Mn)As magnetization; (2) identify the physical mechanisms that determine the dependence of the polarization on the GaAs spacer thickness and on the injection current density — including whether and why the polarization is insensitive to current density, why in-plane (facet) collection gives a weak signal roughly independent of spacer thickness, and, in the light of the same group's 2002 measurements, why vertical collection yields a monotonically larger polarization at smaller spacer thickness with a sign reversal beyond roughly 220 nm; (3) determine how spin-polarized holes injected from (Ga,Mn)As relax and survive during transport through the undoped GaAs spacer and across the (Ga,Mn)As/GaAs and GaAs/QW interfaces, given the ultrafast hole spin relaxation measured in GaAs; and (4) determine the role of heavy-hole/light-hole (valence-band) mixing in the quantum well in setting the efficiency with which the injected hole spin polarization is converted into measured circular polarization along each collection direction. The objective is one coherent account that reproduces the observed polarization magnitudes and their parameter dependences from injector, spacer, and detector physics, is derived from the band structure, transport, and optical properties of (Ga,Mn)As and the quantum well with any parameters those inputs do not fix taken from independent measurement rather than adjusted to the reported polarization, and thereby identifies which mechanism dominates the observed collection-angle anisotropy and spacer-thickness behavior.

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