Critical Collapse of the Exchange Enhanced Spin Splitting in 2-D Systems

TL;DR

This study investigates the critical filling factor for spin splitting in 2D GaAs heterojunctions, revealing a universal relationship involving exchange energy and disorder potential, and clarifying previous measurement discrepancies.

Contribution

It introduces an empirical relationship linking critical filling factor, exchange energy, and disorder potential, and explains the origin of discrepancies in g-factor measurements.

Findings

Critical filling factor v_c relates to exchange energy and disorder potential.

Spin gap energy increases linearly with magnetic field.

Exchange and Zeeman energies sum to determine spin gap in tilted fields.

Abstract

The critical filling factor v_c where Shubnikov-de Haas oscillations become spin split is investigated for a set of GaAs-GaAlAs heterojunctions. Finite temperature magnetoresistance measurements are used to extract the value of v_c at zero temperature. The critically point is where the disorder potential has the same magnitude as the exchange energy, leading to the empirical relationship v_c = g* n t h / 2 m_0. This is valid for all the samples studied, where the density n and single particle lifetime t both vary by more than an order of magnitude and g* the exchange enhanced g-factor has a weak dependence on density. For each sample the spin gap energy shows a linear increase with magnetic field. Experiments in tilted magnetic field show the spin gap is the sum of the bare Zeeman energy and an exchange term. This explains why measurements of the enhanced g-factor from activation energy studies in perpendicular field and the coincidence method in tilted fields have previously disagreed.