# Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system

## TL;DR

This study demonstrates a gate-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system, revealing a density-dependent spin polarization change that enables potential Majorana mode applications.

## Contribution

It introduces a novel method to induce ferromagnetic transitions via gate control in a 2D hole system without in-plane magnetic fields, highlighting the role of carrier interactions.

## Key findings

- Ferromagnetic transition occurs at a critical density of ~2.4×10^10 cm^-2.
- Resistance peaks indicate formation of microscopic spin domains.
- The Zeeman to cyclotron gap ratio exceeds 1 below critical density.

## Abstract

Quantum Hall ferromagnetic transitions are typically achieved by increasing the Zeeman energy through in-situ sample rotation, while transitions in systems with pseudo-spin indices can be induced by gate control. We report here a gate-controlled quantum Hall ferromagnetic transition between two real spin states in a conventional two-dimensional system without any in-plane magnetic field. We show that the ratio of the Zeeman splitting to the cyclotron gap in a Ge two-dimensional hole system increases with decreasing density owing to inter-carrier interactions. Below a critical density of $\sim2.4\times 10^{10}$ cm$^{-2}$, this ratio grows greater than $1$, resulting in a ferromagnetic ground state at filling factor $\nu=2$. At the critical density, a resistance peak due to the formation of microscopic domains of opposite spin orientations is observed. Such gate-controlled spin-polarizations in the quantum Hall regime opens the door to realizing Majorana modes using two-dimensional systems in conventional, low-spin-orbit-coupling semiconductors.