Abstract
Electronic systems with multiple degenerate degrees of freedom can support a rich variety of broken symmetry states. In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin–valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can break this symmetry, manifesting as further Hall plateaus outside the normal integer sequence. Here we report the observation of a number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using tilted field magnetotransport. The large activation gaps confirm the Coulomb origin of all the broken symmetry states, but the order depends strongly on LL index. In the high-energy LLs the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets hosting skyrmionic excitations at half filling, whereas in the ‘relativistic’ zero LL lattice scale interactions drive the system to a spin unpolarized state.
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Acknowledgements
We acknowledge discussions with I. Aleiner, A. Macdonald, Y. Barlas, R. Cote, W. Luo and M. Kharitonov. The measurements were made at NHMFL, which is supported by National Science Foundation Cooperative Agreement DMR-0654118, the State of Florida and the US Department of Energy. We thank S. Hannahs, T. Murphy, J.-H. Park and S. Maier for experimental assistance at NHMFL. This work is supported by the US Defense Advanced Research Projects Agency Carbon Electronics for RF Applications, the Air Force Office of Scientific Research Multidisciplinary University Research Initiative, the Focus Center Research Program through the Center for Circuit and System Solutions and Functional Engineered Nano Architectonics, the Nanoscale Science and Engineering Center (CHE-0117752) and the New York Division of Science, Technology and Innovation. P.K. and A.F.Y. acknowledge support from the US Department of Energy (DE-FG02-05ER46215).
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A.F.Y., C.R.D. and P.K. conceived the experiment and analysed the data. A.F.Y., C.R.D., L.W. and H.R. fabricated the samples. A.F.Y., C.R.D., L.W., H.R. and P.C-Z. made the measurements. A.F.Y., C.R.D. and P.K. wrote the paper. T.T. and K.W. synthesized the hBN crystals. J.H., K.L.S. and P.K. advised on experiments.
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Young, A., Dean, C., Wang, L. et al. Spin and valley quantum Hall ferromagnetism in graphene. Nature Phys 8, 550–556 (2012). https://doi.org/10.1038/nphys2307
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DOI: https://doi.org/10.1038/nphys2307
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