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

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