Experimental observation of the quantum Hall effect and Berry's phase in graphene

Abstract

Since the celebrated discovery of graphene 1,2 , the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors 3 , Ising superconductors 4-6 that can be tuned into a quantum metal 7 , possible Mott insulators with tunable charge-density waves 8 , and topological semi-metals with edge transport 9,10 . Despite this progress, there is still no 2D crystal with intrinsic magnetism 11-16 , which would be useful for many technologies such as sensing, information, and data storage 17 . Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem 18 . However, magnetic anisotropy removes this restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase transition, showcasing the hallmark thickness-dependent physical properties typical of van der Waals crystals 19-21 . Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect 22 , while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics 13,23 , and van der Waals engineering for novel interface phenomena 17 . Extended DataFigure 1 | Atomic force microscopy (AFM) and magneto-optic Kerr effect (MOKE) measurements of graphite-encapsulated few-layer CrI3. a, Optical microscope image of a bilayer CrI3 flake on 285 nm SiO2. b, AFM data for the CrI3 flake in a encapsulated in graphite, showing a line cut across the flake with a step height of 1.5 nm. c, Optical microscope image of a tri-layer CrI3 flake on 285 nm SiO2. d, AFM data for the CrI3 flake shown in c encapsulated in graphite. A line cut taken across the flake shows a step height of 2.2 nm. All scale bars are 2 µm in length. e and f show the MOKE signal as a function of applied magnetic field for the encapsulated bilayer in b and the encapsulated trilayer in d respectively. Extended Data Figure 2 | Magneto-optical Kerr effect experimental setup. Schematic of the optical setup used to measure Magneto-optical Kerr effect in CrI3 samples. 633 nm optical excitation is provided by a power-stabilized HeNe laser. A mechanical chopper and photoelastic modulator provide intensity and polarization modulation, respectively. The modulated beam is directed through a polarizing beam splitter to the sample, housed in a closed-cycle cryostat at 15 K. A magnetic field is applied at the sample using a 7 T solenoidal superconducting magnet in Farad...

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