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Bloch ferromagnetism of composite fermions


In 1929, Felix Bloch suggested that the paramagnetic Fermi sea of electrons should make a spontaneous transition to a fully magnetized state at very low densities, because the exchange energy gained by aligning the spins exceeds the enhancement in the kinetic energy1. However, experimental realizations of this effect have been hard to implement. Here, we report the observation of an abrupt, interaction-driven transition to full magnetization, highly reminiscent of Bloch ferromagnetism. Our platform utilizes the two-dimensional Fermi sea of composite fermions near half-filling of the lowest Landau level. We measure the Fermi wavevector—which directly provides the spin polarization—and observe a sudden transition from a partially spin-polarized to a fully spin-polarized ground state as we lower the density of the composite fermions. Our theoretical calculations that take Landau level mixing into account provide a semi-quantitative account of this phenomenon.

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Fig. 1: Evolution of the spin polarization of CFs as a function of electron density.
Fig. 2: Geometric resonance features of CFs near ν = 1/2.
Fig. 3: Tilt evolution of the CF geometric resonance features near ν = 1/2.
Fig. 4: The critical Zeeman energy \({E}_{\rm{Z}}^{{\rm{crit}}}\) as a function of rs or n for fixed filling factor ν = 1/2.

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.


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We acknowledge support through the the National Science Foundation (grant DMR 1709076) for measurements and the US Department of Energy Basic Energy Science (grant DEFG02-00-ER45841), the National Science Foundation (grants ECCS 1906253 and MRSEC DMR 1420541) and the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant GBMF9615) for sample fabrication and characterization. The theoretical work at Penn State (T.Z., S.P. and J.K.J.) was supported in part by the US Department of Energy, Office of Basic Energy Sciences, under grant no. DE-SC0005042. J.K.J. thanks the the Indian Institute Science, Bangalore, where part of this work was performed, for their hospitality, and the Infosys Foundation for making the visit possible. M.S. acknowledges a QuantEmX travel grant from the Institute for Complex Adaptive Matter (ICAM) and the Gordon and Betty Moore Foundation through grant no. GBMF5305. We also thank R. Warburton and R. Winkler for illuminating discussions.

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Authors and Affiliations



M.S.H. fabricated the devices, performed the measurements and analysed the data. M.S.H., M.A.M., J.K.J. and M.S. discussed the data. T.Z., S.P. and J.K.J. performed the theoretical calculations. Y.J.C., L.N.P., K.W.W. and K.W.B. grew the quantum well samples via molecular beam epitaxy. M.K.M. and K.A.V.R. helped with the measurements. M.S.H., T.Z., S.P., J.K.J. and M.S. co-wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Md Shafayat Hossain, J. K. Jain or M. Shayegan.

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The authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Comparison between the patterned and unpatterned sections of the Hall bar.

Comparison between the patterned and unpatterned sections of the Hall bar. a-c, Magneto-resistance traces for four densities, taken in the patterned (a = 190 nm) and unpatterned sections, are shown. Traces are vertically offset for clarity. While we observe clear geometric resonance minima flanking ν = 1/2 in the traces taken from the section patterned with an a = 190 superlattice, the unpatterned section traces do not exhibit any such features, as expected. The cartoons in the upper panels show the spin configurations for different densities.

Source data

Supplementary information

Supplementary Information

Supplementary Discussion (Sections I–VI), Figs. 1–7 and Table 1.

Source data

Source Data Fig. 1

Numerical data used to generate graphs in the figures.

Source Data Fig. 2

Numerical data used to generate graphs in the figures.

Source Data Fig. 3

Numerical data used to generate graphs in the figures.

Source Data Fig. 4

Numerical data used to generate graphs in the figures.

Source Data Extended Data Fig. 1

Numerical data used to generate graphs in the figures.

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Hossain, M.S., Zhao, T., Pu, S. et al. Bloch ferromagnetism of composite fermions. Nat. Phys. 17, 48–52 (2021).

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